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ASReml User Guide - VSN International

1. 05 101 Interactions 2 101 Expansions 2 ase s 44 4 Yee 44 oe eb bo eee Sa ge core es 101 Conditional factors 2 2 102 Associated Factors 0000002 pe eee 102 6 6 Alphabetic list of model functions 0 4 103 OF WeIGNES 2 2 5 0 wank aoe ee 2 od SA Shae wee K Be ene 108 6 8 Generalized Linear Mixed Models 00 108 Generalized Linear Mixed Models 040 112 Contents x 6 9 Missing values 000000 0 eee ee 112 Missing values in the response 2000 112 Missing values in the explanatory variables 113 6 10 Some technical details about model fitting in ASReml 114 Sparse versus dense o oo a a a 114 Ordering of terms in ASReml aoaaa aa a 114 Aliassing and singularities ooa a a 114 Examples of aliassing o oo a 2000022 tee 115 6 11 Wald F Statistics 2 2 e eo opa Goe acer ata i o a S 116 7 Command file Specifying the variance structures 117 T L lintroduction i425 62 idor 84 5584285 So eR G4 a 118 Non singular variance matrices 2 a 00 118 7 2 Variance model specification in ASReml 119 7 3 A sequence of structures forthe NIN data 119 7 4 Variance structures ooa ee 126 General syntax lt sor a do opa i e h Ra oa eka k pa 127 Variance header line 2 a ee 128 R structure definition 0 02 2 0000000 129 G structure header and defini
2. 243 15 1 Some information messages and comments 263 15 2 List of warning messages and likely meaning s 264 List of Tables XX 16 10 16 11 16 12 16 13 16 14 16 15 Alphabetical list of error messages and probable cause s remedies 268 A split plot field trial of oat varieties and nitrogen application 279 Rat data AOV decomposition a oa a aa a a 284 REML log likelihood ratio for the variance components in the volt ape data 24 6 donsa ui ee eR we a a E e oie iaei gia 290 Summary of variance models fitted to the plant data 292 Summary of Wald F statistics for fixed effects for variance models fitted to the plant data 2 0 0004 298 Field layout of Slate Hall Farm experiment 300 Summary of models for the Slate Hall data 2 22 305 Estimated variance components from univariate analyses of blood worm data a Model with homogeneous variance for all terms and b Model with heterogeneous variance for interactions involving tmt 315 Equivalence of random effects in bivariate and univariate analyses 317 Estimated variance parameters from bivariate analysis of bloodworm datas 2 4 444 be doh bh eck PA EAA ee he ne oe Cen 319 Orange data AOV decomposition o oaoa a 327 Sequence of models fitted to the Orange data 328 Response frequencies in a cheese tasting experiment 338 REML estim
3. 89 Summary of reserved words operators and functions 96 Alphabetic list of model functions and descriptions 103 Link qualifiers and functions 04 108 GLM distribution qualifiers The default link is listed first followed by permitted alternatives 00200000202 ae 109 Examples of aliassing in ASReml 115 Sequence of variance structures for the NIN field trial data 125 xviii List of Tables xix 7 2 Schematic outline of variance model specification in ASReml 127 7 3 Details of the variance models available in ASReml 132 7 4 List of R and G structure qualifiers 0 146 7 5 Examples of constraining variance parameters in ASReml 150 9 1 List of pedigree file qualifiers 2 168 10 1 List of prediction qualifiers 0 00 183 10 2 List of predict plot options 0 2 0 00 4 186 10 3 Trials classified by region and location 188 10 4 Trial means oaa 2 2 ee 188 10 5 LoGation Mans 2 he kop a p eae ee e e ee ee A 189 11 1 Command line options 0 0020 0004 198 11 2 The use of arguments in ASReml 4 204 11 3 High level qualifiers 0 020000 205 12 1 List of MERGE qualifiers 02 4 212 14 1 Summary of ASReml output files 2 221 14 2 ASReml output objects and where to find them
4. 16 Examples 292 Table 16 4 Summary of variance models fitted to the plant data number of REML model parameters log likelihood BIC Uniform 2 196 88 401 95 Power 2 182 98 374 15 Heterogeneous Power 6 171 50 367 57 Antedependence order 1 9 160 37 357 51 Unstructured 15 158 04 377 50 The two forms for X are given by x ofJ 341 units 3 5 16 3 x otl oip J TI CORU It follows that 2 2 2 og oi a ae 16 4 g2402 1 2 Portions of the two outputs are given below The REML log likelihoods for the two models are the same and it is easy to verify that the REML estimates of the variance parameters satisfy 16 4 viz 02 286 310 159 858 126 528 286 386 159 858 286 386 0 558191 id r units LogL 204 593 S2 224 61 60 df 0 1000 1 000 LogL 201 233 S2 186 52 60 df 0 2339 1 000 LogL 198 453 S2 155 09 60 df 0 4870 1 000 LogL 197 041 S52 133 85 60 df 0 9339 1 000 LogL 196 881 S2 127 56 60 df 1 204 1 000 LogL 196 877 S2 126 53 60 df 1 261 1 000 Final parameter values 1 2634 1 0000 Source Model terms Gamma Component Comp SE C units 14 14 1 26342 159 858 Zeal OP Variance 70 60 1 00000 126 528 4 90 0 P Ga CORU LogL 196 975 S2 264 10 60 df 1 000 0 5000 16 Examples 293 LogL 196 924 S2 270 14 60 df 1 000 0 5178 LogL 196 886 S2 278 58 60 df 1 000 0 5400 LogL 196 877 S2 286 23 60 df 1 000 0 5580 LogL 196 877 S2 286 31 60 df 1 000 0 5582 Final parameter values 1 0000 0
5. Job control command line options C F O R C CONTINUE indicates that the job is to continue iterating from the values in the rsv file This is equivalent to setting CONTINUE on the datafile line see Table 5 4 page 68 for details F FINAL indicates that the job is to continue for one more iteration from the values in the rsv file This is useful when using predict see Chapter 10 O ONERUN is used with the R option to make ASReml perform a single analysis when the R option would otherwise attempt multiple analyses The R option then builds some arguments into the output file name while other arguments are not For example ASRem1l nor2 mabphen 2 TWT out 621 out 929 results in one run with output files mabphen2_TWT R r RENAME r is used in conjunction with at least r argument s and does two things it modifies the output filename to include the first r arguments so the output is identified by these arguments and if there are more than r arguments the job is rerun moving the extra arguments up to position r unless ONERUN 0 is also set If r is not specified it is taken as 1 For example ASReml r2 job wwt gfw fd fat is equivalent to running three jobs ASReml r2 job wwt gfw jobwwt_gfw asr ASReml r2 job wwt fd jobwwt_fd asr ASReml r2 job wwt fat jobwwt_fat asr 11 Command file Running the job 202 ASReml2 Yy YVAR y overrides the value of response the variate to be anal
6. 298 16 7 Unreplicated early generation variety trial Wheat 305 16 8 Paired Case Control study Rice ooa 311 Standard analysis 2 a a a 312 A multivariate approach ooa aa a 317 Interpretation of results o oa a a a a a 321 16 9 Balanced longitudinal data Random coefficients and cubic smoothing splines Oranges ooa 323 16 10Generalized Linear Mixed Models aaa aaa 331 Binomial analysis of Footrot score oaoa a aa 331 Bivariate analysis of Foot score 20000 336 Multinomial Ordinal GLM analysis of Cheese taste 338 Contents xvii Multinomial Ordinal GLMM analysis of Footrot score 340 16 11Multivariate animal genetics data Sheep 341 Half sib analysis a a 2 342 Animal model 2 2 351 Bibliography 355 Index 362 List of Tables 2 1 3 1 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 7 1 Combination of models for G and R structures 16 Trial layout and allocation of varieties to plots in the NIN field trial 29 List of transformation qualifiers and their actions with examples 55 Qualifiers relating to data input and output 2 64 List of commonly used job control qualifiers 68 List of occasionally used job control qualifiers 72 List of rarely used job control qualifiers 79 List of very rarely used job control qualifiers
7. Examples Examples are as follows yield mu variety r repl predict variety is used to predict variety means in the NIN field trial analysis Random rep1 is ignored in the prediction yield mu x variety r repl predict variety predicts variety means at the average of x ignoring random repl yield mu x variety repl predict variety x 2 forms the hyper table based on variety and rep1 at the covariate value of 2 and then averages across repl to produce variety predictions GFW Fdiam Trait Trait Year r Trait Team predict Trait Team forms the hyper table for each trait based on Year and Team with each linear combination in each cell of the hyper table for each trait using Team and Year effects Team predictions are produced by averaging over years yield variety r site variety predict variety will ignore the site variety term in forming the predictions while predict variety AVERAGE site forms the hyper table based on site and variety with each linear combination in each cell using variety and site variety effects and then forms averages across sites to produce variety predictions yield site variety r site variety at site block predict variety puts variety in the classify set site in the averaging set and block in the ignore set Consequently it forms the sitexvariety hyper table from model terms site variety and site variety but ignoring all terms in at site block and then forms averages across
8. b gq _ 1g 2 13 as ar y 2 13 and the BLUP is a so called shrinkage estimate As ra becomes large relative to o the BLUP tends to the fixed effect solution while for small rog relative to a the BLUP tends towards zero the assumed initial mean Thus 2 13 represents a weighted mean which involves the prior assumption that the u have zero mean Note also that the BLUPs in this simple case are constrained to sum to zero This is essentially because the unit vector defining X can be found by summing the columns of the Z matrix This linear dependence of the matrices translates to dependence of the BLUPs and hence constraints This aspect occurs whenever the column space of X is contained in the column space of Z The dependence is slightly more complex with correlated random effects 2 Some theory 16 2 4 Combining variance models The combination of variance models within G structures and R structures and between G structures and R structures is a difficult and important concept The underlying principle is that each R and G variance model can only have a single scaling variance parameter associated with it If there is more than one scaling variance parameter for any R or G then the variance model is overspecified or nonidentifiable Some variance models are presented in Table 2 1 to illustrate this principle While all 9 forms of model in Table 2 1 can be specified within ASReml only models of forms 1 and 2 are reco
9. NORMAL ASReml2 REPLACE ASReml2 RESCALE ASReml2 SEED ASReml2 ISET SETN ASReml2 SETU ASReml2 SUB vlist vlist replaces the variate with normal ran dom variables having variance v replaces data values o with n in the cur rent variable I e IF DataValue EQ o DataValue n rescales the column s in the current variable G group of variables using Y Y 0 s sets the seed for the random number generator for vlist a list of n values the data values 1 n are replaced by the cor responding element from vlist data values that are lt 1 or gt n are re placed by zero vlist may run over several lines provided each incomplete line ends with a comma i e a comma is used as a continuation symbol see Other examples below SETN v n replaces data values 1 n with normal random variables having variance v Data values outside the range 1 n are set to 0 replaces data values 1 n with uniform random variables having range 0 v Data values outside the range 1 n are set to 0 replaces data values v with their in dex i where vlist is a vector of n values Data values not found in vlist are set to 0 vlist may run over several lines if necessary provided each incomplete line ends with a comma ASReml allows for a small rounding error when match ing It may not distinguish properly if values in vlist only differ in the sixth decimal place see Other examples be lo
10. SARGOLZAEI ISELF s ISKIP n SORT XLINK indicates the identifiers are numeric integer with less than 16 digits The de fault is integer values with less than 9 digits The alternative is alphanmeric identifiers with up to 255 character indicated by ALPHA tells ASReml to make the A inverse rather than trying to retrieve it from the ainverse bin file The default method for forming AW is based on the algorithm of Meuwissen and Luo 1992 indicates that the third identity is the sire of the dam rather than the dam The original routine for calculating A in ASReml was based on Quaas 1976 tells ASReml to ignore repeat occurrences of lines in the pedigree file Warning Use of this option will avoid the check that animals occur in chronological order but chronological order is still required an alternative procedure for computing A was developed by Sargolzaei et al 2005 allows partial selfing when third field is unknown It indicates that progeny from a cross where the second parent male_parent is unknown is assumed to be from selfing with probability s and from outcrossing with probability 1 s This is appropriate in some forestry tree breeding studies where seed collected from a tree may have been pollinated by the mother tree or pollinated by some other tree Dutkowski and Gilmour 2001 Do not use the SELF qualifier with the INBRED or MGS qualifiers allows you to skip n header lines a
11. terminates a DO transformation block takes antilog base e no argument re quired Jddm converts a number representing a date in the form ddmmccyy ddmmyy or ddmm into days Jmmd converts a date in the form ccyymmdd yymmdd or mmdd into days Jyyd converts a date in the form ccyyddd or yyddd into days These calculate the number of days since December 31 1900 and are valid for dates from January 1 1900 to December 31 2099 note that if cc is omitted it is taken as 19 if yy gt 32 and 20 if yy lt 33 the date must be entirely numeric characters such as may not be present but see DATE Mv converts data values of v to miss ing if M is used after A or I v should refer to the encoded factor level rather than the value in the data file see also Section 4 2 the maximum minimum and modulus of the field values and the value v assigns Haldane map positions s to marker variables and imputes missing values to the markers see below replaces any missing values in the vari ate with the value v If v is another field its value is copied See below ChrAadd G 10 MM ChrAdom DOM ChrAadd See below Rate EXP yield M 9 yield M lt 0 M gt 100 yield MAX 9 ChrAadd G 10 MM 1 Rate NA O WT Wt2 INA Wt1 5 Command file Reading the data 58 Table 5 1 List of transformation qualifiers and their actions with examples qualifier argument action examples
12. 20 Kenward and Roger Adjustments 24 Approximate stratum variances 2 0004 25 3 A guided tour 26 3 1 Introduction s soro aea 0 000000 a E a e ae a E A 27 3 2 Nebraska Intrastate Nursery NIN field experiment 27 Contents vii 3 3 The ASReml datafile 0 20020020058 28 3 4 The ASReml command file oaa 31 The title line 2 2 2 2 2020020000000 20200002008 31 Reading the data 0 20000020 ee ee 32 The data file line sis ei oe opaco dee p ta i eE o a 32 Tabulation sotoetan 2 O44 a a a dee a a aie eup ae Ge 32 Specifying the terms in the mixed model 33 Prediction 3 2 ec a dock 2 Be Re ee Goths al dink a ae 33 Variance structures ooo 33 3 5 Running the job 2 0 0 000022 eee 34 Forming a job template 0 20 00 04 35 3 6 Description of output files o aa a 0 00008 36 Whe sasr file s oora de dosye a a a iaa a a ie a a e i ee 36 Whe is Idle 2er es p ay ae a i a ap a eg wk a et a 38 The yht file 2 2 0 0 000000 a 38 3 7 Tabulation predicted values and functions of the variance components 39 4 Data file preparation 42 4 1 Introduction 0 0000 000000000 ee 43 4 2 The data file lt lt 24 462 Des Sate ee a a 43 Free format data files 00 2 0 00000 0004 43 Contents viii Fixed format data files o a 45 Preparing data files in Excel o oo aa 45 Binary format data files
13. Direct product structures To undertake variance modelling in ASReml you need to understand the formation of variance structures via direct products The direct product of two matrices A gt P and B is au B pB B gt a B m1 mp a Direct products in R structures Consider a vector of common errors associated with an experiment The usual least squares assumption and the default in ASReml is that these are indepen dently and identically distributed IID However if e was from a field experiment 2 Some theory 8 See Chapter 8 for further de tails laid out in a rectangular array of r rows by c columns we could arrange the resid uals as a matrix and might consider that they were autocorrelated within rows and columns Writing the residuals as a vector in field order that is by sort ing the residuals rows within columns plots within blocks the variance of the residuals might then be 2 Zelpe D Ur Pr where amp p and pr are correlation matrices for the row model order r auto correlation parameter pp and column model order c autocorrelation parameter Pc respectively More specifically a two dimensional separable autoregressive spatial structure AR1 AR1 is sometimes assumed for the common errors in a field trial analysis see Gogel 1997 and Cullis et al 1998 for examples In this case 1 1 Pr 1 Pe 1 See Pr 1 and Se Pe Pe 1 pr pe pe 1 pe pe ps 1 Alternat
14. which will cause the term to be defined but not fitted For example Trait male Trait female and Trait female 6 Command file Specifying the terms in the mixed model Table 6 1 Summary of reserved words operators and functions model term brief description common usage fixed random reserved terms operators commonly used functions mu mv Trait units Or at f n at f fac v fac v y lin f spl v k the constant term or intercept a term to estimate missing values multivariate counterpart to mu forms a factor with a level for each experimental unit placed between labels to specify an interaction forms nested expansion Section 6 5 forms factorial expansion Section 6 5 placed before model terms to ex clude them from the model placed at the end of a line to in dicate that the model specification continues on the next line treated as a space placed around some model terms when it is important the terms not be reordered Section 6 4 condition on level n of factor f n may be a list of values forms conditioning covariables for all levels of factor f forms a factor from v with a level for each unique value in v forms a factor with a level for each combination of values in v and y forms a variable from the factor f with values equal to 1 n cor responding to level 1 level n of the factor forms the design matrix for the ran dom compon
15. 11 Command file Running the job 207 High level qualifiers qualifier action PATH pathlist The PATH or PART control statement may list multiple path numbers so that the following lines are honoured if any one of the listed path numbers is active The PATH qualifier must appear at the beginning of its own line after the DOPATH qualifier A sequence of path numbers can be written using a b notation For example mydata asd DOPATH 4 PATH 2 4 6 10 One situation where this might be useful is where it is neces sary to run simpler models to get reasonable starting values for more complex variance models The more complex mod els are specified in later parts and the CONTINUE command is used to pick up the previous estimates Example The following code will run through 1000 models fitting 1000 different marker variables to some data For processing efficiently the 1000 marker variables are held in 1000 separate files in subfolder MLIB and indexed by Genotype Marker screen Genotype yield PhenData txt ICYCLE 1 1000 IMBF mbf Genotype MLIB Marker I csv rename Marker I yld mu r Marker I Having completed the run the Unix command sequence grep LogL screen asr sort gt screen srt sorts a summary of the results to identify the best fit The best fit can then be added to the model and the process repeated Assuming Marker35 was best the revised job could be Marker screen Genotype yield 11 Comma
16. Bibliography 357 Cullis B R Gogel B J Verbyla A P and Thompson R 1998 Spatial analysis of multi environment early generation trials Biometrics 54 1 18 Cullis B R Smith A B and Coombes N E 2006 On the design of early generation variety trials with correlated data Journal of Agricultural Bio logical and Environmental Statistics 11 381 393 Cullis B R Smith A B and Thompson R 2004 Perspectives of anova reml and a general linear mixed model in N M Adams M J Crowder D J Hand and D A Stephens eds Methods and Models in Statistics in honour of Professor John Nelder FRS pp 53 94 Dempster A P Selwyn M R Patel C M and Roth A J 1984 Statisti cal and computational aspects of mixed model analysis Applied Statistics 33 203 214 Diggle P J Ribeiro P J J and Christensen O F 2003 An introduction to model based geostatistics in J Moller ed Spatial Statistics and Compu tational Methods Springer Verlag pp 43 86 Draper N R and Smith H 1998 Applied Regression Analysis John Wiley and Sons New York 3rd Edition Dutkowski G and Gilmour A R 2001 Modification of the additive rela tionship matrix for open pollinated trials Developing the Eucalypt of the Future 10 15 September Valdivia Chile p 71 Engel B 1998 A simple illustration of the failure of PQL IRREML and APHL as approximate ml methods for mixed models for
17. NIN Alliance Trial 1989 variety 56 4 id pid raw repl 4 nloc yield lat long row 22 column 11 nine asd slip 1 1 amp 2 IPART 1 yield mu variety 6 Ir repl oo x Repl 1 2 0 IDV 0 1 Ipart 2 yield mu variety 9 12 11 row AR1 part predict voriety 8 s1 7 22 oll ARI 1 Following is the output from running this job ASReml 3 01d 01 Apr 2008 Build f 11 Apr 2008 11 Apr 2008 16 19 29 031 32 bit 32 Mbyte Windows Licensed to NSW Primary Industries nin alliance trial permanent ninerri FE A A RA I A a a Kk a ak 2k 2k 2k a ok Contact support asreml co uk for licensing and support arthur gilmour dpi nsw gov au FOO BBB ARG Folder C data ex manex Warning FIELD DEFINITION lines should be INDENTED There is no file called nine asd Invalid label for data field nine asd contains a reserved character or may get confused with a previous label or reserved word NB File names must not be indented Fault Error parsing nine asd SLIP 1 Last line read was nine asd SLIP 1 Currently defined structures COLS and LEVELS 1 variety 1 56 15 Error messages 250 2 id 1 vil 0 0 0 0 3 pid 1 i 0 0 0 0 4 raw 1 i 0 0 0 0 5 repl 1 4 0 0 0 0 6 nloc 1 i 0 0 0 0 7 yield al 1 0 0 0 0 8 lat 1 1 0 0 0 0 9 long t 1 0 0 0 0 10 row 1 22 0 0 0 0 11 column I 14 0 0 0 0 filename 12 nine asd 0 0 0 0 0 0 ninerri C data ex manex 12 factors defined max 500
18. where Cheese txt contains the data laid out as in Table 16 13 i e 4 rows and The model term Trait fits the thresholds and interpreting the model as a threshold model implies it should not be interacted with other terms Nevertheless sometimes an interaction is fitted Note that ASReml does not have a procedure for multinomial data which is not ordered except as fitted with a log linear model and fitting a bivariate analysis involving a multinomial trait is 10 columns not possible The output is Univariate analysis of Rating Summary of 4 records retained of 4 read Model term 1 Cheese Rating Rating Rating Rating Rating Rating Rating Rating Rating Total Trait WNHNNNNNNNN iS Forming 12 equations Initial updates will be shrunk by factor Size miss zero 4 Variate Variate Variate Variate Variate Variate Variate Variate Variate 8 0 oo of OO OO fD 6 ONFOOOOFRNN 12 dense MinNonO al 000 000 000 000 000 000 000 000 000 52 00 eee Owrerrere 0 010 Mean 2 5000 1 750 2 500 4 750 6 750 10 25 7 000 9 750 6 250 3 000 52 00 MaxNon0 StndDevn 4 6 000 9 000 12 00 11 00 23 00 8 000 19 00 16 00 11 00 52 00 Distribution and link Cum Multinomial Logit P 1 1 exp XB LogL value is unsuitable for comparing GLM models detected in design matrix Warning The Notice 1 LogL 26 2 LogL 26 3 LogL 26 4 LogL 26 5 LogL 26 1 sin
19. 1 components constrained 1 components constrained omponent 13769 0 30443 6 54715 2 0 837503 0 375382 Wald F statistics DenDF NumDF 1 1 1 13 6 469 0 18 5 F_ine 4241 53 86 39 4 84 Comp SE 7 08 STT 5 15 18 67 3 26 a 6 6 oo Gy ey hg eg e E Prob lt 001 lt 001 0 040 The increase in REML log likelihood is significant The predicted means for the varieties can be produced and printed in the pvs file as Warning mv_estimates Warning units is ignored for prediction is ignored for prediction variety 1 0000 2 0000 3 0000 4 0000 522 0000 523 0000 evaluated at 5 500 0 is evaluated at average value Predicted values of yield Predicted_Value Standard_Error 2 2 2 2 2 2 917 1782 957 7405 872 7615 986 4725 784 7683 904 9421 179 17S 176 178 179 T7 2881 7688 9880 7424 1541 5383 Ecode Pom m ti 16 Examples 311 524 0000 2740 0330 178 8465 E 525 0000 2669 9565 179 2444 E 526 0000 2385 9806 44 2159 E 527 0000 2697 0670 133 4406 E 528 0000 2727 0324 112 2650 E 529 0000 2699 8243 103 9062 E 530 0000 3010 3907 112 3080 E 531 0000 3020 0720 112 2553 E 532 0000 3067 4479 112 6645 E SED Overall Standard Error of Difference 245 8 Note that the replicated check lines have lower SE than the unreplicated test lines There will also be large diffeneces in SEDs Rather than obtaining the large table of all SEDs
20. 16 16 Rice bloodworm data Plot of square root of root weight for treated Versus CONtOl 4 ea oe woe ey A a ee ee Ea es ee Sa 312 BLUPs for treated for each variety plotted against BLUPs for control 320 Estimated deviations from regression of treated on control for each variety plotted against estimate for control 321 Estimated difference between control and treated for each variety plotted against estimate for control 0 4 322 Trellis plot of trunk circumference for each tree 2 324 Fitted cubic smoothing spline fortreel 326 Plot of fitted cubic smoothing spline for model 1 329 Trellis plot of trunk circumference for each tree at sample dates adjusted for season effects with fitted profiles across time and confidence intervals 0 000000 epee 330 Plot of the residuals from the nonlinear model of Pinheiro and Bates 331 Introduction What ASReml can do Installation User Interface How to use the guide Help and discussion list Typographic conventions 1 Introduction 2 1 1 What ASReml can do 1 2 ASReml pronounced A Rem el is used to fit linear mixed models to quite large data sets with complex variance models It extends the range of variance models available for the analysis of experimental data ASReml has application in the analysis of e un balanced longitudinal data e repeated measures data multivariate analysis of varia
21. 31 32 33 34 35 36 37 38 39 x48 x59 x60 x61 x62 x64 x65 x66 x70 xT 3273 x75 x91 ererrrere ererre erer i 59 49 59 64 Gi 55 57 58 59 64 59 59 63 Notice The DenDF values are calculated ignoring fixed boundary singular woo an CaN Oo o ooe 2 18 31 48 4 72 1 13 Leet 0 08 1379 0 04 1 44 variance parameters using empirical derivatives 129 mv_estimates 9 effects 9 idsize 92 effects 115 expt idsize 828 effects 127 at expt 6 type idsize meth 9 effects 128 at expt 7 type idsize meth 10 effects LINE REGRESSION RESIDUAL ADJUSTED FACTORS INCLUDED NO DF SUMSQUARES DF MEANSQU R SQUARED R SQUARED 39 38 37 36 35 34 1 3 0 1113D 02 452 0 2460 0 09098 0 08495 11 1000 FORK RK 2 3 0 1180D 02 452 0 2445 0 09648 0 09049 101100 FORK RK 3 3 0 1843D 01 452 0 2666 0 01507 0 00853 0 11 10 0 4 3 0 1095D 02 452 0 2464 0 08957 0 08353 1 1 0 1 0 0 5 3 0 1271D 02 452 0 2425 0 10390 0 09795 1004110 2K 2K 6 3 0 9291D 01 452 0 2501 0 07594 0 06981 0 10 1 1 0 7 3 0 9362D 01 452 0 2499 0 07652 0 07039 0 01110 8 3 0 1357D 02 452 0 2406 0 11091 0 10501 1 O 1 0 1 0 2K 2K 9 3 0 9404D 01 452 0 2498 0 07687 0 07074 0 11010 10 3 0 1266D 02 452 0 2426 0 10350 0 09755 1 100410 11 3 0 1261D 02 452 0 2427 0 10313 0 09717 100011 12 3 0 9672D 01 452 0 2492 0 07906 0 07295 0 1 0 0O 1 1 13 3 0 9579D 01 452 0 2494 0 07830 0 07218 0 O 1 0 1 1 14 3 0 9540D 01 452 0 2495 0 07797 0 07185 000111 15 3 0 1089D
22. 97 103 fac v y 96 104 fac v 96 104 e f n 104 giv f n 97 104 h 104 iCf 104 ide f 97 104 inv v 7 97 104 1 f 104 leg v n 97 104 lin f 96 104 log v r 97 105 mai f 97 105 mai 97 105 mbf v 7 98 mu 96 105 mv 96 105 out 105 p v n 106 pol v n 98 106 pow z p o 106 qt1 106 s v k 106 sin v 7r 98 106 spl v k 96 106 sqrt v r 98 106 uni f k 107 uni f n 98 uni f 98 Index 371 units 96 107 vect v 98 xfa f k 98 107 reserved words AEXP 135 AGAU 135 AINV 136 ANTE 1 135 AR2 132 AR3 132 ARMA 133 AR 1 132 CHOL 1 136 CIR 135 CORB 133 CORGB 134 CORGH 134 CORU 133 DIAG 135 EXP 134 FACV 1 136 FA 1 136 GAU 134 GIV 136 IDH 135 ID 132 IEUC 134 IEXP 134 IGAU 134 LVR 134 MA2 133 MAT 135 MA 1 133 OWN 135 SAR2 133 SAR 133 SPH 135 US 135 XFA 1 136 residual error T likelihood 12 response 94 running the job 34 scale parameter 7 score 13 Score test 71 section 9 Segmentation fault 232 separability 10 separable 123 singularities 114 slow processes 208 sparse 114 sparse fixed 94 spatial analysis 298 data 2 model 122 specifying the data 48 split plot design 279 tabulation 32 qualifiers 176 syntax 176 tests of hypotheses 20 Timing processes 209 title line 31 48 trait 43 158 transformation 52 syntax 54 Tutorial audio 4 typograph
23. A mixed model procedure for analysing ordered categorical data Biometrics 40 393 408 Haskard K A 2006 Anisotropic Mat rn correlation and other issues in model based geostatistics PhD thesis BiometricsSA University of Adelaide Hill W G and Thompson R 1978 Probabilities of non positive definite between group or genetic covariance matrices Biometrics 34 429 439 Kammann E E and Wand M P 2003 Geoadditive models Applied Statistics 52 1 1 18 Keen A 1994 Procedure IRREML GLW DLO Procedure Library Manual Agricultural Mathematics Group Wageningen The Netherlands pp Re port LWA 94 16 Kenward M G and Roger J H 1997 The precision of fixed effects estimates from restricted maximum likelihood Biometrics 53 983 997 Kenward M G and Roger J H 2009 An improved approximation to the precision of fixed effects from restricted maximum likelihood Computational Statistics and Data Analysis 53 2583 2595 Lane P W and Nelder J A 1982 Analysis of covariance and standardisation as instances of predicton Biometrics 38 613 621 McCullagh P and Nelder J A 1994 Generalized Linear Models 2 edn Chapman and Hall London McCulloch C and Searle S R 2001 Generalized Linear and Mixed Models Wiley Meuwissen T and Lou 1992 Forming iniverse nrm Genetics Selection and Evolution 24 305 313 Millar R and Willis T 1999 Estimating the relative densit
24. ASReml2 1YSS r ASReml2 qualifier ICINV n FACPOINTS n prints the portion of the inverse of the coefficient matrix per taining to the n term in the linear model Because the model has not been defined when ASReml reads this line it is up to the user to count the terms in the model to iden tify the portion of the inverse of the coefficient matrix to be printed The option is ignored if the portion is not wholly in the SPARSE stored equations The portion of the inverse is printed to a file with extension cii The sparse form of the matrix only is printed in the form i j C that is elements of C that were not needed in the estimation process are not included in the file affects the number of distinct points recognised by the fac model function Table 6 1 The default value of n is 1000 so that points closer than 0 1 of the range are regarded as the same point 5 Command file Reading the data 90 Table 5 6 List of very rarely used job control qualifiers qualifier action KNOTS n NOCHECK NOREORDER NOSCRATCH POLPOINTS n PPOINTS n REPORT ISCALE 1 changes the default knot points used when fitting a spline to data with more than n different values of the spline variable When there are more than n default 50 points ASReml will default to using n equally spaced knot points forces ASReml to use any explicitly set spline knot points see SPLINE even if they do
25. Logl not converged Warning Only one iteration performed Parameters unchanged after one iteration See discussion of ABORTASR NOW the change in REML log likelihood was small and convergence was assumed but the param eters are in fact still changing the maximum number of iterations was reached before the REML log likelihood con verged The user must decide whether to ac cept the results anyway to restart with the CONTINUE command line option see Section 11 3 on job control or to change the model and or initial values before proceding The se quence of estimates is reported in the res file It may be necessary to simplify the model and estimate the dominant components before es timating other terms if the LogL is oscilating Parameter values are not at the REML solu tion Parameters appear to be at the REML solu tion in that the parameter values are stable Messages beginning with the word Notice are not generally listed here They provide information the user should be aware of as it may affect the interpretation of results They are not in themselves errors in that the syntax is valid but they may reflect errors in the sense that the user may have intended something 15 Error messages 264 different Messages beginning with the word Warning highlight information that the user should check Again it may reflect an error if the user has intended something different Messages beginning with
26. O variance parameters maxi500 2 special structures last line read Last line read was nine asd SLIP 1 fault message Finished 11 Apr 2008 16 19 29 093 Error parsing nine asd SLIP 1 ASReml happily reads down to the nine asd line This line is not indented so nine asd is expected to be a file name but there is no such file in the folder C data ex manex 15 3 Things to check in the asr file The information that ASReml dumps in the asr file when an error is encountered is intended to give you some idea of the particular error e if there is no data summary ASReml has failed before or while reading the model line if ASReml has completed one iteration the problem is probably associated with starting values of the variance parameters or the logic of the model rather than the syntax per se Part of the file nin89 asr presented in Chapter 14 is displayed below to indicate the lines of the asr file that should be checked You should check that e sufficient workspace has been obtained e the records read lines read records used are correct e mean min max information is correct for each variable 15 Error messages 251 workspace working direc tory records read data summary check convergence e the Loglikelihood has converged and the variance parameters are stable e the fixed effects have the expected degrees of freedom ASReml 3 01d 01 Apr 2008 NIN alliance trial 1989 Build f 11 Apr 2008 32 bit
27. S2 Final parameter values 43 45 47 48 48 48 48 301 066 745 466 649 696 708 168 168 168 168 168 168 168 df df df df df df df 1 0 000 Results from analysis of yield Source Variance Residual Residual Model terms 242 AR AutoR AR AutoR Source of Variation 12 mu 1 variety 168 11 22 ni 0 4 0 6 Gamma 00000 37483 55505 Com 4 Q 0 Wald F statistics NumDF 1 55 DenDF 25 0 110 3 1 1 1 t 1 1 ii 000 0 4876 0 5388 000 0 4698 0 5895 000 0 4489 0 6395 000 0 4409 0 6514 000 0 4384 0 6544 000 0 4377 0 6552 000 0 4375 0 6554 0 43748 0 65550 ponent Comp SE C 8 7085 6 81 0 P 437483 5 43 OU 655505 11 63 OU F_inc Prob 331 85 lt 0 2 22 lt 0G1 Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using algebraic derivatives 13 mv_estimates 6 possible outliers in section Finished 11 Apr 2008 15 58 45 843 18 effects fitted 1 see res file LogL Converged 15 Error messages 253 15 4 An example See 2a in Sec This is the command file for a simple RCB tion 7 3 analysis of the NIN variety trial data in the first part However this file contains eight common mistakes in coding ASReml We also show two common mistakes associated with spatial analyses in the second part The errors are highlighted and the numbers indicate the order in which they are de
28. TOTAL n v p Qn The inverse is the default link function n is defined with the d 2n d1n 24 ITOTAL qualifier and would be degrees of freedom in the typical u application to mean squares The default value of is 1 H NEGBIN LOGARITHM IDENTITY INVERSE PHI v ptp o fits the Negative Binomial distribution Natural logarithms are d 2 4 y in 443 the default link function The default value of is 1 yin 4 General qualifiers AOD requests an Analysis of Deviance table be generated This is ASReml2 formed by fitting a series of sub models for terms in the DENSE Caution part building up to the full model and comparing the deviances An example if its use is LS BIN TOT COUNT AOD mu SEX GROUP AOD may not be used in association with PREDICT IDISP A includes an overdispersion scaling parameter h in the weights If DISP is specified with no argument ASReml estimates it as the residual variance of the working variable Traditionally it is estimated from the deviance residuals reported by ASReml as Variance heterogeneity An example if its use is count POIS DISP mu group 6 Command file Specifying the terms in the mixed model 111 Table 6 4 GLM distribution qualifiers qualifier action OFFSET o is used especially with binomial data to include an offset in the model where o is the number or name of a variable in the data The offset is only inclu
29. at Tr 1 lt 2 Litter effects IPATH 1 4 0 DIAG Diagonal structure 3 74 0 97 0 019 0 941 PATH 2 4 0 FAi GP Factor Analytic 1 S28 OL sil 4 95 4 63 0 037 0 941 PATH 3 40 US Unstructured 5 073 3 545 3 914 0 1274 0 08909 0 02865 0 07277 0 05090 0 001829 1 019 PATH Ait Table 16 16 Variance models fitted for each part of the ASReml job in the analysis of the genetic example term matrix PATH 1 PATH 2 PATH 3 sire DIAG FA1 US dam Dag CORGH CORGH US litter X DIAG FA1 US error Xi US US US In PATH 1 the error variance model is taken to be unstructured but the starting values are set to zero This instructs ASReml to obtain starting values from the sample covariance matrix of the data For incomplete data the matrix so obtained may not in general be positive definite Care should be taken when using this option for incomplete multivariate data The command to run PATH 1 is asreml nrw64 mt 1 The Loglikelihood from this run is 20000 1444 93 When the job runs the message 16 Examples 347 Non positive definite G matrix 0 singularities 1 negative pivots order 3 appears to the screen This refers to the 3 x 3 dam matrix which is estimated as Covariance Variance Correlation Matrix CORRelation 2 573 1 025 0 6568 3 024 3 382 0 7830 0 1526 0 2086 0 2098E 01 Note the correlation between wwt and ywt is estimated at 1 025 The results from this analysis can be automatically used
30. o aaa 0000 45 5 Command file Reading the data 46 5 1 Introduction ooa aaa 0000 ee 47 5 2 Important rules 2542 4 84 4 8484 295 oh 4 2845 54 G4 47 5 3 Titlene ya a Beige shoe ee ee EA Se a a Bone a ee E 48 5 4 Specifying and reading the data 04 48 Data field definition syntax ooo aa 49 Storage of alphabetic factor labels 0 51 Reordering the factor levels o oo a a a 51 Skipping input fields o o a 52 5 5 Transforming the data ooa aaa a 52 Transformation syntax ooo a a 54 QTL marker transformations ooa a a 59 Other rules and examples ao o 2 ee ee 61 Special note on covariates 0 00 00000048 62 5 6 Datafileline 2 2 2 ee 63 Data line syntax gess som a aoa i ma a a E aE e R ai p i 63 5 7 Data file qualifiers oaa 0000 eee 64 Contents ix Combining rows from separate files 67 5 8 Job control qualifiers 2 0 020000 a 68 6 Command file Specifying the terms in the mixed model 93 6 1 Introduction ss sors aes a a 00 000 0c ee 94 6 2 Specifying model formulae in ASReml 94 General niles 2 24 444 6 4 4 P44 OA bb baad oe wes 94 Examples lt 2 poeman at mee Gee Be ole ee eee 2 ee 99 6 3 Fixed terms in the model naoa aaa 202000 99 Primary fixed terms 2 2 2 99 Sparse fixed terms ooa a 100 6 4 Random terms inthe model 000 100 6 5 Interactions and conditional factors
31. panelcharsize n vertxlab abbrdlab n abbrxlab n abbrslab n specifies the relative size of the data points labels default 0 4 specifies the relative size of the labels used for the panels de fault 1 0 specifies that vertical annotation be used on the x axis default is horizontal specifies that the labels used for the data be abbreviated to n characters specifies that the labels used for the x axis annotation be appre viated to n characters specifies that the labels used for superimposed factors be abbre viated to n characters 10 Tabulation of the data and prediction from the model 188 ASReml3 Associated factors ASSOCIATE factors facilitates prediction when the levels of one factor group or classify the levels of another especially when there are many levels factors is an list of factors in the model which have this hierarchical relationship Typical examples are individually named lines grouped into families usually with unequal numbers of lines per family or trials conducted at locations within regions Declaring factors as associated allows ASReml to combine the levels of the factors appropriately For example in the preceding example when predicting a trial mean to add the effect of the location and region where the trial was conducted When identifying which levels are associated ASReml checks that the association is strictly hierarchal tree like That is each trial is
32. row 22 column 11 nin89aug asd skip 1 yield mu variety f mv 120 11 column ARi 0 3 22 row AR1 0 3 7 Command file Specifying the variance structures 124 See Section 7 4 3c Two dimensional separable autoregressive spatial model with mea surement error This model extends 3b by adding a random units term Thus V g ITa Xepe Ur pr The re served word units tells ASReml to construct an additional random term with one level for each experimental unit so that a second in dependent error term can be fitted A units term is fitted in the model in cases like this where a variance structure is applied to the errors Because a G structure is not explic itly specified here for units the default IDV NIN Alliance Trial 1989 variety A id row 22 column i1 nin89aug asd skip 1 yield mu variety r units If mv 120 11 column AR1 0 3 22 row AR1 0 3 structure is assumed The units term is often fitted in spatial models for field trial data to allow for a nugget effect 4 Two dimensional separable autoregressive spatial model with random replicate effects This is essentially a combination of 2b and 3c to demonstrate specifying an R structure and a G structure in the same model The variance header line 1 2 1 indicates that there is one R structure 1 that involves two variance mod els 2 and is therefore the direct product of two matrices and there is one G structure 1
33. row row AR1 0 1 This is a template in that it needs editing it has nominated an inappropriate response variable but it displays the first few lines of the data and infers whether fields are factors or variates as follows Missing fields and those with decimal points in the data value are taken as covariates integer fields are taken as simple factors and alphanumeric fields are taken as A factors 3 A guided tour 36 3 6 Description of output files job heading version Data summary A series of output files are produced with each ASReml run Nearly all files all that contain user information are ASCII files and can be viewed in any ASCII editor including ASReml W ConText and NotePad The primary output from the nin89 as job is written to nin89 asr This file contains a summary of the data the iteration sequence estimates of the variance parameters and an a table of Wald F statistics for testing fixed effects The estimates of all the fixed and random effects are written to nin89 sln The residuals predicted values of the observations and the diagonal elements of the hat matrix see Chapter 2 are returned in nin89 yht see Section 14 3 Other files produced by this job include the aov pvs res tab vvp and veo files see Section 14 4 The asr file Below is nin89 asr with pointers to the main sections The first line gives the version of ASReml used in square brackets and the title of the job The second lin
34. where gt 0 is a range parameter v gt 0 is a smoothness parameter T is the gamma function K is the modified Bessel function of the third kind of order v Abramowitz and Stegun 1965 section 9 6 and d is the distance defined in terms of X and Y axes hy zi j hy yi Yj Se cos a hy sin a hy Sy sin a hy cos a hy d 4 s2 sy For a given vy the range parameter affects the rate of decay of p with increas ing d The parameter v gt 0 controls the analytic smoothness of the underlying process us the process being v 1 times mean square differentiable where v is the smallest integer greater than or equal to v Stein 1999 page 31 Larger v correspond to smoother processes ASRemluses numerical derivatives for v when its current value is outside the interval 0 2 5 When v m with ma non negative integer pm is the product of exp d and a polynomial of degree m in d Thus v 5 yields the exponential correla tion function pm d 5 exp d and v 1 yields Whittle s elementary correlation function pm d 1 d Ki d Webster and Oliver 2001 7 Command file Specifying the variance structures 140 When v 1 5 then pm d 1 5 exp d 1 d which is the correlation function of a random field which is continuous and once differentiable This has been used recently by Kammann and Wand 2003 As v co then pm tends
35. 0 repl i repl O IDV 0 1 3 A guided tour 34 able variance structures models is presented in Table 7 3 Since IDV is the default variance structure for random effects the same analysis would be performed if these lines were omitted 3 5 Running the job Revised 08 See Chapter 11 Give command files the extension as Assuming you have located the nin89 asd file under Windows it will typically be located in ASRemlPath Examples and created the ASCII command file nin89 as described in the previous section in the same folder you can run the job AS RemlPath is typically C Program Files ASRem13 under Windows Installation details vary with the implementation and are distributed with the program You could use ASReml W or ConText to create nin89 as These programs can then run ASReml directly after they have been configured for ASReml An ASReml job is also run from a command line or by clicking the as file in Windows Explorer The basic command to run an ASReml job is ASRemiPath bin ASReml basename as where basename as is the name of the command file Typically a system PATH is defined which includes ASRemlPath bin so that just the program name ASRem1 is required at the command prompt For example the command to run nin89 as from the command prompt when attached to the appropriate folder is ASReml nin89 as However if the path to ASReml is not specified in your system s PATH envi ronment varia
36. 1 2 iw moving average Cans 6 1 6 Chi 0 j gt i 2 lal lt 1 MA2 2 order C 1 2 3 24w moving average C a 6 1 6 14 6 6 Cirat 0 1 F 0 03 Ci 0 7 gt 1 2 0 0 lt 1 0 lt 1 lt 1 ARMA autoregressive C 1 2 3 2 w moving average C1 0 0 14 0 20 Ca 0C _4 j7 gt t 1 0 lt 1 lt 1 CORU uniform C 1 C 145 1 2 1lt w correlation CORB banded C 1 w 1 w 2w 1 correlation Caja 1 lt j lt w 1 dj lt 1 ASReml2 7 Command file Specifying the variance structures 134 Table 7 3 Details of the variance models available in ASReml base description algebraic number of parameters identifier form corr homo s hetero s variance variance CORG general Ci 1 wld ww 44 ww correlation Co pp Ej w CORGH US Idig lt 1 One dimensional unequally spaced EXP exponential C 1 1 2 1l w C ginal t j a are coordinates 0 lt lt 1 GAU gaussian C 1 1 2 1l w Ce ae xi are coordinates 0 lt lt 1 Two dimensional irregularly spaced x and y vectors of coordinates bij min di d1 1 dij is euclidean distance IEXP isotropic C 1 1 2 1l w exponential Ci lTi Tiltu i xj 0 lt lt 1l IGAU isotropic C 1 1 2 1l w gaussian C primes tiu i x j ij 0 lt lt 1 IEUC isotropic C 1 1 2 1l w lid J i 25 tuy euclidean C I tiy itj 0 lt lt 1 LVR linear variance C 1 45 1 2 1l w 0 lt 1 7
37. 11 column 11 0 0 1 6 3304 12 mu Fault G structure header Last line read was 1 Term not found Repl 10000 ninerr6 variety id pid raw rep nloc yield lat Model specification TERM LEVELS GAMMAS MaxNonO 56 11 15 Error messages 259 variety 56 mu 1 repl 4 0 100 3 SECTIONS 224 4 2 TYPE 0 0 0 STRUCT 224 0 0 0 0 0 0 12 factors defined max 500 4 variance parameters max1500 2 special structures Final parameter values 0 10000 1 0000 Last line read was Repl 10000 Finished 11 Apr 2008 15 41 53 668 G structure header Term not found Fixing the header line we then get the error message Structure Factor mismatch This arose because repl has 4 levels but we have only declared 2 in the G struc ture model line The G structure should read repl 1 4 0 IDV 0 1 The last lines of the output with this error are displayed below 11 column 11 0 0 1 6 3304 11 12 mu 1 2 identity 0 1000 Structure for repl has 2 levels defined Fault Structure Factor mismatch Last line read was 20 IDV 0 100000 ninerr7 variety id pid raw rep nloc yield lat Model specification TERM LEVELS GAMMAS variety 56 mu 1 repl 4 0 100 3 SECTIONS 224 4 i TYPE 0 0 1002 STRUCT 224 0 0 0 0 0 2 1 0 5 0 1 12 factors defined max 500 15 Error messages 260 5 variance parameters maxi500 2 special structures Final parameter values 0 10000 1 0000 0 10000 Last line read was 20 IDV0 100000 Finished 11 Apr 2
38. 3 7 Tabulation predicted values and functions of the variance com ponents It may take several runs of ASReml to determine an appropriate model for the data that is the fixed and random effects that are important During this process you may wish to explore the data by simple tabulation Having identified an appropriate model you may then wish to form predicted values or functions of the variance components The facilities in ASReml to form predicted values and functions of the variance components are described in Chapters 10 and 13 respectively Our example only includes tabulation and prediction The statement tabulate yield variety in nin89 as results in nin89 tab as follows NIN alliance trial 1989 11 Jul 2005 13 55 21 Simple tabulation of yield variety LANCER 28 56 BRULE 26 07 REDLAND 30 50 CODY 21 21 ARAPAHOE 29 44 3 A guided tour 40 NE83404 27 39 NE83406 24 28 NE83407 22 69 CENTURA 21 65 SCOUT66 27 52 COLT 27 00 NE87522 25 00 NE87612 21 80 NE87613 29 40 NE87615 25 69 NE87619 31 26 NE87627 23 23 The predict variety statement after the model statement in nin89 as results in the nin89 pvs file displayed below some output omitted containing the 56 predicted variety means also in the order in which they first appear in the data file column 2 together with standard errors column 3 An average standard error of difference among the predicted variety means is displayed immediately after the list of
39. 9 LogL 4233 65 S2 83065 666 df 10 LogL 4233 65 S2 83100 666 df Source Model terms Gamma Component Comp SE C variety 532 532 1 06038 88117 5 2 92 OP Variance 670 666 1 00000 83100 1 8 90 OP Residual AR AutoR 67 0 685387 0 685387 16 65 OU Residual AR AutoR 10 0 265909 0 285909 3 87 OU Wald F statistics Source of Variation NumDF DenDF F_inc Prob 7 mu 1 41 7 6248 65 lt 001 3 weed 1 491 2 85 84 lt 001 The change in REML log likelihood is significant x 12 46 p lt 001 with the inclusion of the autoregressive parameter for columns Figure 16 6 presents the sample variogram of the residuals for the AR1xAR1 model There is an indication that a linear drift from column 1 to column 10 is present We include a linear regression coefficient pol column 1 in the model to account for this Note we use the 1 option in the pol term to exclude the overall constant in the regression as it is already fitted The linear regression of column number on yield is significant t 2 96 The sample variogram Figure 16 7 is more satisfactory though interpretation of variograms is often difficult particularly for unreplicated trials This is an issue for further research The abbreviated output for this model and the final model in which a nugget effect has been included is AR1xAR1 pol column 1 1 LogL 4270 99 S2 0 12730E 06 665 df 2 LogL 4258 95 52 0 11961E 06 665 df 3 LogL 4245 27 S2 0 10545E 06 665 df 4 LogL 4229 5
40. ASReml will retrieve starting values from the most recent rsv file formed by that job You can of course copy an rsv file building the new PART number into its name so that ASReml uses that particular set of values The ask file keeps track of which rsv files have been formed 7 Command file Specifying the variance structures 155 7 11 Convergence issues Revised 08 ASReml does not always converge to a satisfactory solution and this sections raises some of the issues In terms of the iteration sequence the usual case is that the REML loglikelihood increases smoothly and quadratically with each iteration to an effective maximum Convergence problems are indicated when the LogL oscillates between two values or decreases usually dramatically They are also indicated if the mixed model coefficient matrix ceases to be positive semidefinite that is has negative pivots discovers new singularities after the first iteration or generates a negative residual sum of squares Failure to converge can arise because e the variance model does not suit the data or e the initial variance parameters are too far from the REML solution and the Average Information updates overshoot When convergence failure occurs it is sometimes helpful to examine the sequence of parameter values which is reported in the res file This may indicate which parameters are the problem ASReml requires the user to supply initial values for the variance parameters
41. E where F is a matrix of loadings on the correlation scale and E is diagonal and is defined by difference the parameters are specified in the order loadings for each factor F followed by the variances diag when k is greater than 1 constraints on the ele ments of F are required see Table 7 5 FACVk models CV for covariance are an alternative formulation of FA models in which is modelled as TI W where T is a matrix of loadings on the covariance scale and W is diagonal The parameters in FACV are specified in the order loadings T followed by variances W when k is greater than 1 constraints on the elements of I are required see Table 7 5 are related to those in FA by DF and DED XFAk X for extended is the third form of the factor analytic model and has the same parameterisation as for FACV that is TT W However XFA models have parameters specified in the order diag W and vec T when kis greater than 1 constraints on the elements of I are required see Table 7 5 may not be used in R structures are used in G structures in combination with the xfa f k model term 7 Command file Specifying the variance structures 143 Revised 08 ASReml3 return the factors as well as the effects permit some elements of W to be fixed to zero are computationally faster than the FACV formulation for large problems when kis much smaller than w Special
42. If one member appears in the classify set only that member may appear in the PRESENT list For example yield region r region family entry PREDICT entry ASSOCIATE family entry PRESENT entry region Association averaging is used to form the cells in the PRESENT table and PRESENT averaging is then applied Complicated weighting with PRESENT Generally when forming a prediction table it is necessary to average over or ignore some dimensions of the hyper table By default ASReml uses equal weights 1 f for a factor with f levels More complicated weighting is achieved by using the AVERAGE qualifier to set specific unequal weights for each level of a factor However sometimes the weights need to be defined with respect to two or more factors The simplest case is when there are missing cells and weighting is equal for those cells in a multiway table that are present achieved by using the PRESENT qualifier This is further generalized by allowing the user to supply the weights to be used by the PRESENT machinery via the PRWTS qualifier The user specifies the factors in the table of weights with the PRESENT statement and then gives the table of weights using the PRWTS qualifier There may only be one PRESENT qualifier on the predict line when PRWTS is specified The order of factors in the tables of weights must correspond to the order in the PRESENT list with later factors nested within preceding factors The weights may b
43. K and L respectively For example IGYCLE Yi RT Y23 x2 I mu J When cycling is active an extra line is written to the asr file containing some details of the cycle in a form which can be extracted to form an analysis summary by searching for LogL A heading for this extra line is written in the first cycle For example LogL LogL Residual NEDF NIT Cycle Text LogL 208 97 0 703148 587 6 1466 LogL Converged The LogL line with the highest LogL value is repeated at the end of the asr file DOPATH n The qualifiers DOPART and PART have been extended in re lease 2 0 and DOPATH and PATH are thought to be more ap propriate names Both spellings can be used interchangably DOPATH allows several analyses to be coded and run sequen tially without having to edit the as file between runs Which particular lines in the as file are honoured is controlled by the argument n of the DOPATH qualifier in conjunction with PATH or PART statements The argument n is often given as 1 indicating that the actual path to use is specified as the first argument on the command line see Section 11 4 See Sections 16 7 and 16 11 for examples The default value of n is 1 DOPATH n can be located anywhere in the job but if placed on the top job control line it cannot have the form DOPATH 1 unless the arguments are on the command line as the ASReml2 DOPATH qualifier will be parsed before any job arguments on the same line are parsed
44. NIN Alliance trial 1989 variety A column 11 nin89 asd skip 1 tabulate yield variety yield mu variety r repl predict variety 0 0 1 repl 1 repl 0 IDV 0 1 cept variety fits a fixed variety effect and repl fits a random replicate effect The r qualifier tells ASReml to fit the terms that follow as random effects Prediction Prediction statements appear after the model statement and before any variance structure lines In this case the 56 variety means for yield as predicted from the fitted model would be formed and returned in the pvs output file See Chapter 10 for a detailed discussion of prediction in ASReml Variance structures The last three lines are included for exposi tory purposes and are not actually needed for this particular analysis An extensive range of variance structures can be fitted in ASReml See Chapter 7 for a lengthy discussion of vari ance modelling in ASReml In this case in dependent and identically distributed random replicate effects are specified using the iden tifier IDV in a G structure G structures are described in Section 2 1 and the list of avail NIN Alliance trial 1989 variety A column 11 nin89 asd skip 1 tabulate yield variety yield mu variety r repl predict variety 001 repl 1 repl 0 IDV 0 1 NIN Alliance trial 1989 variety A column 11 nin89 asd skip 1 tabulate yield variety yield mu variety r repl predict variety
45. Proceedings of the 28th International Biometrics Conference Smith A Cullis B R and Thompson R 2001b Analysing variety by envi ronment data using multiplicative mixed models and adjustments for spatial field trend Biometrics 57 1138 1147 Smith A Cullis B R and Thompson R 2005 The analysis of crop cul tivar breeding and evaluation trials an overview of current mixed model approaches review Journal of Agricultural Science 143 449 462 Steel R G D and Torrie J H 1960 Principles and procedures of statistics McGraw Hill Stein M L 1999 Interpolation of Spatial Data Some Theory for Kriging Springer Verlag New York Stevens M M Fox K M Warren G N Cullis B R Coombes N E and Lewin L G 1999 An image analysis technique for assessing resistance in rice cultivars to root feeding chironomid midge larvae diptera Chirono midae Field Crops Research 66 25 26 Stroup W W Baenziger P S and Mulitze D K 1994 Removing spatial variation from wheat yield trials a comparison of methods Crop Science 86 62 66 Thompson R Cullis B R Smith A and Gilmour A R 2003 A sparse implementation of the average information algorithm for factor analytic and reduced rank variance models Australian and New Zealand Journal of Statistics 45 445 459 Verbyla A P 1990 A conditional derivation of residual maximum likelihood Australian Journal of Statistics 32
46. READ qualifier in Table 5 2 After parsing the model line ASReml actually reads the data file It reads a line into a temporary vector performs the transformations in that vector and then saves the positions 5 Command file Reading the data 53 ASReml3 that relate to labelled variables to the internal data array Note that e there may be up to 10000 variables and these are internally labeled V1 V2 V10000 for transformation purposes Values from the data file ignoring any SKIPed fields are read into the leading variables alpha A integer I pedigree P and date DATE fields are converted to real numbers level codes as they are read and before any transformations are applied e transformations may be applied to any variable since every variable is nu meric but it may not be sensible to change factor level codes e transformations operate on a single variable not a G group of variables unless it is explicitly stated otherwise e transformations are performed in order for each record in turn variables that are created by transformation should be defined after below variables that are read from the data file unless it is the explicit intention to overwrite an input variable see below after completing the transformations for each record the values in the record for variables associated with a label are held for analysis or the record all values is discarded see D transformation and Section
47. The R structures are defined first so the next two lines are the R structure definition lines for e as in 3b The last two lines are the G structure definition lines for repl as in 2b In this case V 02 yrl Ec Pc Ur pr NIN Alliance Trial 1989 variety A id row 22 column 11 nin89aug asd skip 1 yield mu variety r repl if my ye 11 column AR1 0 3 22 row AR1 0 3 repl i repl O IDV 0 1 7 Command file Specifying the variance structures 125 Table 7 1 Sequence of variance structures for the NIN field trial data ASReml syntax extra random terms term G structure models 1 2 residual error term term R structure models 1 2a 2b 3a 3b 3c yield mu variety repl yield mu variety lIr repl yield mu variety lIr repl 001 repl i 40 IDV 0 1 yield mu variety If mv 120 11 column ID 22 row AR1 0 3 yield mu variety If mv 120 11 column AR1 0 3 22 row AR1 0 3 yield mu variety r units f mv 120 11 column AR1 0 3 22 row AR1 0 3 yield mu variety lIr repl f mv 121 11 column AR1 0 3 22 row AR1 0 3 repl i 40 IDV 0 1 yield mu variety Ir column row 001 column row 2 column O ARI 5 row O ARIV 0 5 0 1 repl repl units repl column row IDV IDV IDV IDV AR1 AR1V error error error column column column column error row row row row ID I
48. a dense set and a sparse set The partition is at the r point unless explicitly set with the DENSE data line qualifier or mv is included before r see Table 5 5 The special term mv is always included in sparse Thus random and sparse terms are estimated using sparse matrix methods which result in faster processing The inverse coefficient matrix is fully formed for the terms in the dense set The inverse coefficient matrix is only partially formed for terms in the sparse set Typically the sparse set is large and sparse storage results in savings in memory and computing A consequence is that the variance matrix for estimates is only available for equations in the dense portion Ordering of terms in ASReml The order in which estimates for the fixed and random effects in linear mixed model are reported will usually differ from the order the model terms are specified Solutions to the mixed model equations are obtained using the methods outlined Gilmour et al 1995 ASReml orders the equations in the sparse part to maintain as much sparsity as it can during the solution After absorbing them it absorbs the model terms associated with the dense equations in the order specified Aliassing and singularities A singularity is reported in ASReml when the diagonal element of the mixed model equations is effectively zero see the TOLERANCE qualifier during absorption It indicates there is either e no data for that fixed effect or e a line
49. fix parameters that you are confident of while getting better estimates for others that is fix variances when estimating co variances fit a simpler model reorganise the model to reduce covariance terms for example use CORUH instead of US It is best to start with a positive definite corre lation structure Maybe use a structured cor relation matrix A variance structure should be specified for this term The reported limit is hardcoded The number of variables to be read must be reduced The error could be in the variable factor name or in the number of values or the list of values 15 Error messages 269 Table 15 3 Alphabetical cause s remedies list of error messages and probable error message probable cause remedy Error in SUBGROUP label factor values Error in R structure model checks Error opening file Error reading something Error reading the data Error reading the DATA FILENAME line Error reading the model factor list Error setting constraints VCC on variance components Error setting dependent variable Error setting MBF design matrix IMBF mbf x k filename Error structures are wrong size Error when reading knot point values Failed forming R G scores Failed ordering Level labels The error could be in the variable factor name or in the number of values or the list of values the error model is not correctly specified t
50. genetic variance phenotypic variance Correlation Correlations are requested by lines in the pin F phenvar 1 3 4 6 file beginning with an R The specific form of R Phencorr 7 8 9 i R gencorr 4 6 the directive is pan R label a ab b This calculates the correlation r dab 4 0202 and the associated standard error a b and ab are integers indicating the position of the components to be used Alternatively R label a n calculates the correlation r Cab oa for all correlations in the lower tri angular row wise matrix represented by components a to n and the associated 13 Functions of variance components 218 standard errors 2 2 var r re oa var 5 var Cav doz 4o Cab 2cov 07 07 2cov o2 Sab 2cov oan 7 4020 2020p 20u07 In the example R phencorr 7 8 9 calculates the phenotypic covariance by calculating component 8 ycomponent 7 x component 9 where components 7 8 and 9 are created with the first line of the pin file and R gencorr 4 6 calculates the genotypic covariance by calculating component 5 component 4 x component 6 where components 4 5 and 6 are variance components from the analysis A more detailed example The following example is a little more com Bivariate sire model plicated and has the pin file coding inserted sire I Eei t fat in the job file for a bivariate sire model in wien bsiremod asd bsiremod
51. highlighted bold type for easy identification indicates that some of the the continuation symbol is used to original code is omitted from indicate that some of the original code is the display omitted Data examples are displayed in larger boxes in the body of the text see for example page 43 Other conventions are as follows e keyboard key names appear in SMALLCAPS for example TAB and ESC e example code within the body of the text is in this size and font and is highlighted in bold type see pages 34 and 50 e in the presentation of general ASReml syntax for example path asreml basename as arguments typewriter font is used for text that must be typed verbatim for example asreml and as after basename in the example italic font is used to name information to be supplied by the user for exam ple basename stands for the name of a file with an as filename extension square brackets indicate that the enclosed text and or arguments are not always required Do not enter these square brackets e ASReml output is in this size and font see page 36 e this font is used for all other code Some theory The linear mixed model Introduction Direct product structures Variance structures for the errors R structures Variance structures for the random effects G structures Estimation Estimation of the variance parameters Estimation prediction of fixed and random effects Wha
52. pin file A simple sample pin file is shown in the ASReml code box above The pin file specifies the functions to be calculated The pin file can be formally created as a separate file and processed by running ASReml with the P command line option specifying the pin file as the input file ASReml reads the model information from the asr and vvp files and calculates the requested functions These are reported in the pvc file Alternatively the pin file may be processed by ASReml as the final stage of an analysis run if the VPREDICT directive is included in the as file 13 2 VPREDICT PIN file processing ASReml3 Processing of a pin file is activated from within the as file by including a VPREDICT directive The VPREDICT line may appear anywhere in the as file but it is recommended it be placed after the model line It is recognised by the characters VPR in character positions 1 3 of a line It is processed after the job part cycle has finished There are four forms of the VPREDICT directive e If the pin file exists and has the same name as the jobname including any suffix appended by using RENAME just specify the VPREDICT directive e If the pin file exists but has a different name to the jobname specify the VPREDICT directive with the pin file name as its argument e If the pin file does not exist or must be reformed a name argument for the file is optional but the DEFINE qualifier should be set Then th
53. t print predictions of non estimable functions unless the PRINTALL qualifier is specified However using PRINTALL is rarely a satisfactory solution Failure to report predicted values normally means that the predict statement is averaging over some cells of the hyper table that have no information and there fore cannot be averaged in a meaningful way Appropriate use of the AVERAGE and or PRESENT qualifiers will usually resolve the problem The PRESENT qual ifier enables the construction of means by averaging only the estimable cells of the hyper table where this is appropriate Table 10 1 is a list of the prediction qualifiers with the following syntax 10 Tabulation of the data and prediction from the model 183 fis an explanatory variable which is a factor e tis a list of terms in the fitted model e nis an integer number vis a list of explanatory variables Table 10 1 List of prediction qualifiers qualifier action Controlling formation of tables ASSOCIATE v facilitates prediction when the levels of one factor are grouped by ASReml3 the levels of another in a hierarchical manner More details are given below Two independent associate lists may be specified AVERAGE f weights is used to formally include a variable in the averaging set and AVERAGE f file n to explicitly set the weights for averaging Variables that only appear in random model terms are not included in the averaging set unl
54. variance structure required is not the standard multivariate unstructured matrix is used with SECTION v and ROWFAC v to instruct ASReml to set up R structures for analysing a multi environment trial with a separable first order autoregressive model for each site environment vis the name of a factor or variate containing column numbers 1 ne where ne is the number of columns on which the data is to be sorted See SECTION for more detail is used to select particular graphic displays In spatial anal ysis of field trials four graphic displays are possible see Sec tion 14 4 Coding these 1 variogram 2 histogram 4 row and column trends 8 perspective plot of residuals set n to the sum of the codes for the desired graphics The default is 9 1 8 These graphics are only displayed in versions of ASReml linked with Winteracter that is LINUX SUN and PC ver sions Line printer versions of these graphics are written to the res file See the G command line option Section 11 3 on graphics for how to save the graphs in a file for printing Use NODISPLAY to suppress graphic displays sets hardcopy graphics file type to eps is used to set a grouping variable for plotting see X 5 Command file Reading the data 74 Table 5 4 List of occasionally used job control qualifiers qualifier action ASReml2 ASReml3 IGKRIGE p GROUPFACTOR tvp JOIN Year controls the expansion of PVAL
55. which may only be associated with the second file causes the field contents for the nominated fields from the second file only be inserted once into the merged file For example assume we want to merge two files containing data from sheep The first file has several records per animal containing fleece data from various years The second file has one record per animal containing birth and weaning weights Merging with NODUP bwt wwt will copy these traits only once into the merged file ISKIP fields is used to exclude fields from the merged file It may be specified with either or both input files SORT instructs ASReml to produce the merged file sorted on the key fields Otherwise the records are return in the order they appear in the primary file 12 Command file Merging data files 213 The merging algorithm is briefly as follows The secondary file is read in skip fields being omitted and the records are sorted on the key fields If sorted output is required the primary file is also read in and sorted The primary file or its sorted form is then processed line by line and the merged file is produced Matching of key fields is on a string basis not a value basis If there are no key fields the files are merged by interleaving If there are multiple records with the same key these are severally matched That is if 3 lines of file 1 match 4 lines of file 2 the merged file will contain all 12 combinations 12 3 Exampl
56. 0 290190E 01 3 52 3 1 06636 0 290831E 01 36 67 42 07 5 1 17407 0 433905E 01 27 06 6 2 53439 0 434880E 01 58 28 32 85 9 Trait 1 Visti 0 107933 66 13 2 21 0569 0 209095 100 71 78 16 11 Trait TEAM TO effects fitted 12 Trait TAG 1042 effects fitted SLOPES FOR LOG ABS RES on LOG PV for Section 1 1 00 1 54 10 possible outliers see res file Finished 08 Apr 2008 11 46 37 140 LogL Converged Command file Genetic analysis Introduction The command file The pedigree file Reading in the pedigree file Genetic groups GIV files The example 164 9 Command file Genetic analysis 165 9 1 Introduction In an animal model or sire model genetic analysis we have data on a set of animals that are genetically linked via a pedigree The genetic effects are there fore correlated and assuming normal modes of inheritance the correlation ex pected from additive genetic effects can be derived from the pedigree provided all the genetic links are in the pedigree The additive genetic relationship matrix sometimes called the numerator relationship matrix can be calculated from the pedigree It is actually the inverse relationship matrix that is formed by ASReml for analysis Users new to this subject might find notes by Julius van der Werf helpful http http www vsni co uk products asreml user geneticanalysis pdf titled Mixed Mod els for Genetic analysis pdf For the more general situation where the pedigree based i
57. 0 3 0 1 This is why the G structure definition line for column is specified first ASReml automatically includes and estimates an error variance parameter for each section of an R structure The variance structures defined by the user should therefore normally be correlation matrices A variance model can be specified but the S2 1 qualifier would then be required to fix the error vari ance at 1 and prevent ASReml trying to estimate two confounded parameters error variance and the parameter corresponding to the variance model speci fied see 3a on page 123 ASReml does not have an implicit scale parameter for G structures that are defined explicitly For this reason the model supplied when the G structure involves just one variance model must be a variance model an initial value must be supplied for this associated scale parameter this is discussed under additional_initial_values on page 130 when the G structure involves more than one variance model one must be either a homogeneous or a heterogeneous variance model and the rest should be correlation models if more than one are non correlation models then the IGF qualifier should be used to avoid identifiability problems that is ASReml trying to estimate both parameters when they are confounded 7 8 G structures involving more than one random term The usual case is that a variance structure applies to a particular term in the linear model and that there is no covariance b
58. 0000 7 LogL 160 369 2 1 0000 Source Model terms Gamm Residual ANTE UDU 1 0 26865 Residual ANTE UDU 1 0 62841 Residual ANTE UDU 2 0 37280 Residual ANTE UDU 2 1 4910 Residual ANTE UDU 3 0 59963 Residual ANTE UDU 3 1 2804 Residual ANTE UDU 4 0 78971 Residual ANTE UDU 4 0 96781 Residual ANTE UDU 5 0 39063 Covariance Variance Correlation M 37 20 0 5946 0 3549 23 38 41 55 0 5968 34 83 61 89 258 9 44 58 79 22 331 4 43 14 76 67 320 7 Source of Variation Trait tmt 9 Tr tmt Be 0 The iterative sequence converged 60 df 60 df 60 df a Component Comp SE C 7E O1 0 268657E 01 2 44 OU 3 0 628413 2 65 OU 1E 01 0 372801E 01 2 41 OU 8 1 49108 2 54 OU 2E 02 0 599632E 02 2 43 OU 1 1 28041 6 19 OU 3E 02 0 789713E 02 2 44 OU 5 0 967815 15 40 OU 5E 01 0 390635E 01 2 45 OU atrix ANTE UDU 0 3114 0 3040 0 5237 0 5112 0 8775 0 8565 550 8 6 9761 533 0 541 4 Wald F statistics DF F_inc 5 188 84 1 4 14 4 3 91 and the antedependence parameter estimates are printed columnwise by time the column of U and the element of D Le 0 0269 0 0373 0 0060 0 0079 0 0391 D diag U 1 0 0 0 0 0 6284 0 0 0 1 1 4911 0 0 0 1 1 2804 0 0 0 1 0 9678 0 0 0 1 Finally the input and output files for the unstructured model are presented below The REML estimate of from the yi y3 y5 y7 yi0O Trait tmt Tr tmt 120 14 S2 Tr 0 US 37 20 ANTE model is used to provide starting values 1
59. 01 0 6102E 03 Wald F statistics Source of Variation NumDF DenDF F_inc Prob 7 mu 1 4 0 169 87 lt 001 3 age 1 4 0 92 78 lt 001 5 Season 1 8 9 108 60 lt 001 16 Examples 330 200 600 1000 1400 li li li li li li 5 Marginal 200 4 AA Lo LO Trunk circumference mm 200 4 150 100 50 4 200 600 1000 1400 Time since December 31 1968 Days Figure 16 15 Trellis plot of trunk circumference for each tree at sample dates ad justed for season effects with fitted profiles across time and confidence intervals Figure 16 15 presents the predicted growth over time for individual trees and a marginal prediction for trees with approximate confidence intervals 2 stan dard error of prediction Within this figure the data is adjusted to remove the estimated seasonal effect The conclusions from this analysis are quite differ ent from those obtained by the nonlinear mixed effects analysis The individual curves for each tree are not convincingly modelled by a logistic function Fig ure 16 16 presents a plot of the residuals from the nonlinear model fitted on p340 of Pinheiro and Bates 2000 The distinct pattern in the residuals which is the same for all trees is taken up in our analysis by the season term 16 Examples 331 0o o 000 Qo oko Residual Q is o 10 o a o T T T T T T T T 200 400 600 800 1000 1200 1400 1600 age Figur
60. 050 25 53 8 lat 0 Oo 4 300 27 22 9 long 0 G 1 200 14 08 10 row 22 0 0 1 11 7321 11 column ti 0 0 1 6 3304 12 mu 1 4 identity E S Sl 0 1000 Structure for repl has 4 levels defined Forming 61 equations 57 dense Initial updates will be shrunk by factor 0 316 Notice 1 singularities detected in design matrix 1 LogL 454 807 S2 50 329 168 df 1 000 2 LogL 454 663 S2 50 120 168 df 1 000 3 LogL 454 532 S2 49 868 168 df 1 000 4 LogL 454 472 S2 49 637 168 df 1 000 5 LogL 454 469 S2 49 585 168 df 1 000 6 LogL 454 469 S2 49 582 168 df 1 000 7 LogL 454 469 S2 49 582 168 df 1 000 Final parameter values 1 0000 0 Results from analysis of yield Source Model terms Gamma Component Variance 224 168 1 00000 49 5824 repl identity 4 0 199323 9 88291 Wald F statistics Source of Variation NumDF DenDF F_inc 12 mu 1 3 0 242 05 1 variety 55 165 0 0 88 MaxNonO StndDevn 56 56 00 4156 840 0 16 20 1121 149 0 4 000 42 00 47 30 26 40 22 11 0 000 7 450 12 90 7 698 1000 1173 1463 1866 1986 1993 0 1993 19932 D oOo O oo ao Comp SE C 9 08 OP 142 OU Prob lt 001 0 708 Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using algebraic derivative 5 repl 4 effects fitted S 3 A guided tour 38 Finished 04 Apr 2008 17 00 50 296 LogL Converged The sln file The following is an extract from nin89 sln containing t
61. 1 au Trait 2 at Trait 3 at Trait 5 Residual age age age Sex sex Sex 10 vor eck 73 th 98 ae 7 62 7 28 7 23 22d grp grp grp grp grp grp grp 2 2 S2 2 2 2 goa S2 2 2 1 0000 1 0000 1 0000 1 0000 1 0000 1 0000 1 0000 1 0000 1 0000 1 0000 0000 terms 0 0 0 S 1 0 1 0 010 df df df df df df df df 3 df df df Gamma G 000 00 000 5380 48 06 5197 20000 components components components components components components components components PrRPRPePNNWN omponent Comp 49 49 49 49 0 132682E 02 0 908220E 03 0 175614E 02 0 223617E 03 49 49 49 UnStru i 49 49 49 49 1 0 902586 15 3623 0 280673 1 42136 7 47555 0 132682E 02 0 908220E 03 0 175614E 02 0 223617E 03 0 902586 15 3623 0 280673 1 42136 7 47555 Covariance Variance Correlation Matrix UnStructured Residual 18 7 476 4 768 0 1189 0 9377 0 4208 Covariance Variance Correlation 3 898 4 877 0 3029 0 49 0 81 9 1 0 29 64 54 74 0 6021E 01 0 4375 0 6154 ti 07 0 1339 0 4381 0 1056 0 2891 0 4869E 01 0 2473 0 5763 0 3689 0 1875 0 3425 0 4864 3 345 0 1333 0 3938 0 1298 i171 1 333 Matrix UnStructure 0 3899E 01 0 6148 0 1849 0 7217 0 7085E 01 0 2415E 01 0 3041 O 5027E 02 0 6117 0 4104E 01 0 1853 0 4672 0 2570 d Tr tag
62. 1 iterations Then pairs including the last are estimated until iteration 7 If AILOADINGS is not specified and CONTINUE is used and initializes the XFA model from a lower order the i parameter is set internally can be specified to force a job to continue even though a singu larity was detected in the Average Information AI matrix The AI matrix is used to give updates to the variance pa rameter estimates In release 1 if singularities were present in the AI matrix a generalized inverse was used which effec tively conditioned on whichever parameters were identified as singular ASReml now aborts processing if such singularities appear unless the AISINGULARITIES qualifier is set Which particular parameter is singular is reported in the variance component table printed in the asr file The most common reason for singularities is that the user has overspecified the model and is likely to misinterpret the results if not fully aware of the situation Overspecification will occur in a direct product of two unconstrained variance matrices see Section 2 4 when a random term is confounded with a fixed term and when there is no information in the data on a particular component The best solution is to reform the variance model so that the ambiguity is removed or to fix one of the parameters in the variance model so that the model can be fitted For in stance if ASUV is specified you may also need 2 1 Only rarely will it be r
63. 108 5000 9 1070 E 0 2_cwt Victory 89 6667 9 1070 E 0 2 cwt Golden_rain 98 5000 9 1070 E O_cwt Marvellous 86 6667 9 1070 E O_cwt Victory 71 5000 9 1070 E O_cwt Golden_rain 80 0000 9 1070 E Predicted values with SED PV 126 833 118 500 9 71503 124 833 9 71503 9 71503 117 167 7 68295 9 71503 9 71503 110 833 9 71503 7 68295 9 71503 9 71503 114 667 9 71503 9 71503 7 68295 9 71503 9 71503 108 500 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 89 6667 9 71503 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 98 5000 9 71503 9 71503 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 86 6667 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 71 5000 9 71503 7 68295 9 71503 9 1503 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 80 0000 9 71503 9 71503 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 SED Standard Error of Difference Min 7 6830 Mean 9 1608 Max 3 7150 16 3 Unbalanced nested design Rats The second example we consider is a data set which illustrates some further aspects of testing fixed effects in linear mixed models This example differs from the split plot example as it is unbalanced and so more care is required in assessing the significance of fixed effects 16 Examples 284 The experiment was reported by Dempster et al 1984 and was designed to compare the effect of three doses of an experimental compound control low and high on the maternal performance of rats Thi
64. 11 Apr 2008 15 58 39 484 32 Mbyte Windows nin89a Licensed to NSW Primary Industries permanent SECO k kk kk kkk kkk OOO 3k k kk k III A IK a A I KKK Contact support asreml co uk for licensing and support arthur gilmour dpi nsw gov au SECO OOOO OOOO ORK ARG Folder C data asr3 ug3 manex variety A QUALIFIERS SKIP 1 DISPLAY 15 QUALIFIER DOPART 1 is active Reading nin89aug asd FREE FORMAT skipping 1 lines Univariate analysis of yield Summary of 242 records retained of 242 read Model term Size miss zero MinNonO Mean MaxNonO StndDevn 1 variety 56 0 0 1 26 4545 56 2 id 0 O 1 000 26 45 56 00 17 18 3 pid 18 0 1101 2628 4156 1121 4 raw 18 O 21 00 510 5 840 0 149 0 5 repl 4 0 1 2 4132 4 6 nloc 0 O 4 000 4 000 4 000 0 000 7 yield Variate 18 0 1 050 25 53 42 00 7 450 8 lat 0 0 4 300 25 80 47 30 13 63 9 long 0 0 1 200 13 80 26 40 029 10 row 22 0 0 1 11 5000 22 11 column 11 0 0 1 6 0000 11 12 mu al 13 mv_estimates 18 11 AR AutoReg 5 5 0 5000 22 AR AutoReg 6 6 0 5000 Forming 75 equations 57 dense Initial updates will be shrunk by factor 0 316 Notice 1 singularities detected in design matrix 1 LogL 401 827 S2 42 467 168 df 1 000 0 5000 0 5000 15 Error messages 252 parameter estimates Testing fixed effects outliers NO oO F WN LogL 400 LogL 399 LogL 399 LogL 399 LogL 399 LogL 399 8 LogL 399 780 807 353 326 324 324 324 52 2 S52 S2 52 S2
65. 1409 1 4853 110 3232 1 3669 0 4753 0 2166 Lambda 0000 0000 0000 0000 0000 0000 PRPRrPRPRP RB 5 10 45 45 45 45 0000 0000 0000 0000 0000 0000 14 Description of output files 232 Conditional F statistics calculation of Denominator degrees of freedom Source Size NumDF F value Lambda F Lambda DenDF mu 1 1 327 5462 327 5462 1 0000 6 0475 variety 3 2 1 4853 1 4853 1 0000 10 0000 LinNitr 1 1 110 3232 110 3232 1 0000 45 0000 nitrogen 4 2 1 3669 1 3669 1 0000 45 0000 variety LinNitr 3 2 0 4753 0 4753 1 0000 45 0000 variety nitrogen 12 4 0 2166 0 2166 1 0000 45 0000 The asl1 file The asl file is primarily used for low level debugging It is produced when the LOGFILE qualifier is specified and contains lowlevel debugging information information when the DEBUG qualifier is given However when a job running on a Unix system crashes with a Segmentation fault the output buffers are not flushed so the output files do not reflect the latest program output In this case use the Unix script screen log command before running ASReml with the DEBUG qualifier but without the LOGFILE qualifier to capture all the debugging information in the file screen log The debug information pertains particularly to the first iteration and includes timing information reported in lines beginning gt gt gt gt gt gt gt gt gt gt gt gt These lines also mark progress through the iteration The dpr f
66. 2 2 2 1 0000 1 0000 1 0000 1 0000 1 0000 1 0000 1 0000 1 0000 2964 2964 2964 2964 2964 2964 2964 2964 0 316 df df df df df df df df 1042 levels defined 2 singularities detected in design matrix Results from analysis of GFW FDIAM 8 Command file Multivariate analysis 163 Source Model terms Gamma Component Comp SE C Residual UnStructured 1 1 0 198351 0 198351 21 94 OU Residual UnStructured 2 1 0 128890 0 128890 12 40 OU Residual UnStructured 2 2 0 440601 0 440601 21 93 Ov Trait TEAM UnStructured 1 1 0 374493 0 374493 3 89 OU Trait TEAM UnStructured 2 1 0 388740 0 388740 2 60 OU Trait TEAM UnStructured 2 2 1 36533 1 36533 3 74 OU Trait TAG UnStructured 1 1 0 257159 0 257159 12 09 OU Trait TAG UnStructured 2 1 0 219557 0 219557 5 55 OU Trait TAG UnStructured 2 2 1 92082 1 92082 14 35 OU Covariance Variance Correlation Matrix UnStructured Residual 0 1984 0 4360 0 1289 0 4406 Covariance Variance Correlation Matrix UnStructured Trait TEAM 0 3745 0 5436 0 3887 1 365 Covariance Variance Correlation Matrix UnStructured Trait TAG 0 2572 0 3124 0 2196 1 921 Wald F statistics Source of Variation NumDF DenDF F_inc Prob 9 Trait 2 33 0 5761 58 lt 001 10 Trait YEAR 4 1162 2 1094 90 lt 001 Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using numerical derivatives Estimate Standard Error T value T prev 10 Trait YEAR 2 0 102262
67. 254 error hint give away the last line read before the job was terminated an error message Error parsing nine asd SLIP 1 and other information obtained to that point In this case the program only made it to the data file definition line in the command file Since nine asd commences in column 1 ASReml checks for a file of this name in the working directory since no path is supplied Since ASReml did not find the data file it tried to interpret the line as a variable definition but is not permitted in a variable label The problem is either that the filename is misspelt or a pathname is required In this case the data file was given as nine asd rather than nin asd An unrecognised qualifier and 3 An incorrectly defined factor After supplying the correct pathname and re running the job ASReml produces the warning message WARNING Unrecognised qualifier at character 9 slip 1 followed by the fault message ERROR Reading the data The warning does not cause the job to terminate immediately but arises because slip is not a recognised data file line qualifier the correct qualifier is skip The job terminates when reading the header line of the nin asd file which is alphabetic when it is expecting numeric values The following output displays the error message produced Folder C data ex manex QUALIFIERS SLIP 1 Warning Unrecognised qualifier at character 9 SLIP 1 QUALIFIER DOPART 1 is active Reading nin asd
68. 2s H a pe Go pR a 13 Covariance Variance Correlation Matrix UnStructured at Tr 1 dam 0 9988 0 5881 0 70 24 O 7008 02 15 mii sfa 88 90 By gi 80 0 1070E 05 92 00 0 1070E 05 00 constrained constrained constrained constrained constrained constrained constrained constrained gt SE So ao 6 ad oo Si 86 c 16 Examples 355 Covariance Variance Correlation Matrix UnStructured at Tr 1 1lit 3 714 0 5511 0 1635 O G15 8 01 2 019 3 614 0 5176 0 4380 0 4506E 01 0 1407 0 2045E 01 0 3338 0 1021 0 7166 0 4108E 01 0 7407 Wald F statistics Source of Variation NumDF F_inc 15 Tr age 5 99 16 16 Te ber 15 116 52 17 Tr sex 5 59 94 19 Tr age sex 4 5 10 There is no guarantee that unstructured variance component matrices will be positive definite unless GP qualifier is set This example highlights this issue We used the GU qualifier on the maternal component to obtain the matrix 0 9988 0 5881 0 5881 0 7018 ASReml reports the correlation as 0 7024 which it obtains by ignoring the sign in 0 7018 This is the maternal component for ywt Since it is entirely reasonable to expect maternal influences on growth to have dissipated at 12 months of age it would be reasonable to refit the model omitting at Tr 2 dam and changing the dimension of the G structure Bibliography Abramowitz M and Stegun I A eds 1965 Handbook of Mathematical Func tions Dover Public
69. 30 40 ILAST lt factor gt lt levi gt lt face gt lt lev2 gt lt fac3 gt lt lev3 gt ASReml2 limits the order in which equations are solved in ASReml by Difficult forcing equations in the sparse partition involving the first lt lev gt equations of lt factor gt to be solved after all other equations in the sparse partition Is intended for use when there are multiple fixed terms in the sparse equations so that ASRemlwill be consistent in which effects are identified as singular The test example had Ir Anim Litter f HYS where genetic groups were included in the definition of Anim 5 Command file Reading the data 86 Table 5 5 List of rarely used job control qualifiers qualifier action Consequently there were 5 singularities in Anim The default reordering allows those singularities to appear anywhere in the Anim and HYS terms Since 29 genetic groups were defined in Anim LAST Anim 29 forces the genetic group equations to be absorbed last and therefore incorporate any singularities In the more general model fitting Ir Tr Anim Tr Lit f Tr HYS without LAST the location of singularities will almost surely change if the G structures for Tr Anim or Tr Lit are changed invalidating Likelihood Ratio tests between the models OUTLIER performs the outlier check described on page 18 This can ASReml3 have a large time penalty in large models OWN f supplies the name of a program supplied by the user i
70. 4 4 5 5 5 5 5 6 6 6 6 6 7 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 8 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 9 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 10 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 Column Rowblk levels Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 iL 1 1 1 1 it 11 11 11 11 21 21 21 21 21 2 2 2 2 2 2 12 12 12 12 12 22 22 22 22 22 3 3 3 3 3 3 13 13 13 13 13 23 23 23 23 23 4 4 4 4 4 4 14 14 14 14 14 24 24 24 4 4 5 5 5 5 5 5 15 15 15 15 15 25 25 25 25 25 6 6 6 6 6 6 16 16 16 16 16 26 26 26 26 26 7 Ti T T T T AG I7 I7 17 17 237 27 27 27 27 8 8 8 8 8 8 18 18 18 18 18 28 28 28 28 28 9 9 9 9 9 9 19 19 19 19 19 29 29 29 29 29 10 10 10 10 10 10 20 20 20 20 20 30 30 30 30 30 Column Colblk levels Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 I5 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 T 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 8 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 9 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 10 16 17 18 19 20 21 22 233 2x4 25 26 27 28 29 30 16 Examples 301 Abbreviated ASReml output file is presented below The iterative sequence has converged to column and row correlation parameters of 68377 45859 respec tively The plot size and orientation is not known and so it is not possible to ascertain whether these values are spatially sensible It is genera
71. 5 2 lists the qualifiers relating to data input Use the Index to check for examples or further discussion of these qualifiers Table 5 2 Qualifiers relating to data input and output qualifier action Frequently used data file qualifier SKIP n Other data file qualifiers CSV DATAFILE f FILTER v SELECT n IFOLDER s ASReml3 causes the first n records of the non binary data file to be ignored Typically these lines contain column headings for the data fields used to make consecutive commas imply a missing value this is automatically set if the file name ends with csv or CSV see Section 4 2 Warning This qualifier is ignored when reading binary data specifies the datafile name replacing the one obtained from the datafile line It is required when different PATHS see DOPATH in Table 11 3 of a job must read different files The SKIP qualifier if specified will be applied when reading the file enables a subset of the data to be analysed v is the number or name of a data field When reading data the value in field vis checked after any transformations are performed If select is omitted records with zero in field v are omitted from the analysis Otherwise records with n in field v are retained and all other records are omitted The argument n is typically an integer which is compared with the numeric value if a field after any conversion if the input field performed by the A or I data
72. 5000 1 000 0 5045 4 SIRE 34 0 0 1 17 0714 34 5 Total Weight 0 O 16 00 35 00 64 00 12 89 16 Examples 333 6 FSi 0 O 6 000 23 46 50 00 10 76 7 Fo2 0 0 3 000 10 14 30 00 5 661 8 Scald 0 13 1 000 3 071 16 00 3 458 9 Rot 0 19 1 000 1 196 4 000 1 151 10 pRot Variate 0 19 0 1754E 01 0 3606E 01 0 1818 0 3833E 01 11 mu al 12 SEX GRP 5 3 SEX 1 2 GRP 5 Forming 46 equations 12 dense Initial updates will be shrunk by factor 0 224 Notice Algebraic Denominator DF calculation is not available Numerical derivatives will be used Notice 4 singularities detected in design matrix 1 LogL 2423 41 S2 0 32397E 01 1952 df 1 components restrained 2 LogL 2431 71 S2 0 32792E 01 1952 df 0 6325E 02 1 000 3 LogL 2431 80 52 0 32737E 01 1952 df 0 9265E 02 1 000 4 LogL 2431 80 52 0 32738E 01 1952 df 0 9200E 02 1 000 Final parameter values 0 92543E 02 1 0000 Results from analysis of pRot Approximate stratum variance decomposition Stratum Degrees Freedom Variance Component Coefficients SIRE 25 70 0 506971E 01 59 7 1 0 Residual Variance 15 83 0 327367E 01 0 0 1 0 Source Model terms Gamma Component Comp SE C SIRE 34 34 0 918415E 02 0 300659E 03 0 98 22 P Variance 56 1952 1 00000 0 327367E 01 2 81 OP Wald F statistics Source of Variation NumDF DenDF F ine Prob 11 mu 1 19 9 42 79 lt 001 3 SEX 1 16 2 0 02 0 882 2 GRP 3 21 9 2 04 0 139 12 SEX GRP 3 16 1 0 39 0 763 Notice The DenDF values are calculated ignoring fixed bound
73. 55819 Source Model terms Gamma Component Comp SE C Variance 70 60 1 00000 286 310 3 65 OP Residual CORRelat 5 0 558191 0 558191 4 28 OU A more realistic model for repeated measures data would allow the correlations to decrease as the lag increases such as occurs with the first order autoregressive model However since the heights are not measured at equally spaced time points we use the EXP model The correlation function is given by plu o where wu is the time lag is weeks The coding for this is yl y3 y5 y7 y10 Trait tmt Tr tmt 120 One error structure in two dimensions 14 Outer dimension 14 plants Tr O Exe 5 is amp 7 10 Time coordinates A portion of the output is LogL 183 734 S2 435 58 60 df 1 000 0 9500 LogL 183 255 S2 370 40 60 df 1 000 0 9388 LogL 183 010 S52 321 50 60 df 1 000 0 9260 LogL 182 980 S2 298 84 60 df 1 000 0 9179 LogL 182 979 52 302 02 60 df 1 000 0 9192 Final parameter values 1 0000 0 91897 Source Model terms Gamma Component Comp SE C Variance 70 60 1 00000 302 021 Fee O P Residual POW EXP 5 0 918971 0 918971 29 53 OU When fitting power models be careful to ensure the scale of the defining variate here time does not result in an estimate of too close to 1 For example use of days in this example would result in an estimate for of about 993 The residual plot from this analysis is presented in Figure 16 4 This suggests increasing variance over time This can be modelled by
74. 7 3 of order k 6 Command file Specifying the terms in the mixed model 99 Examples ASReml code action yield mu variety yield mu variety r block yield mu time variety time variety livewt mu breed sex breed sex r sire fits a model with a constant and fixed variety effects fits a model with a constant term fixed variety effects and random block effects fits a saturated model with fixed time and variety main effects and time by va riety interaction effects fits a model with fixed breed sex and breed by sex interaction effects and ran dom sire effects 6 3 Fixed terms in the model Primary fixed terms The fixed list in the model formula e describes the fixed covariates factors and interactions including special functions to be included in the table of Wald F statistics e generally begins with the reserved word mu which fits a constant term mean or inter cept see Table 6 1 NIN Alliance Trial 1989 variety row 22 column 11 nin89 asd skip 1 mvinclude yield mu variety r repl If mv 12 11 column AR1 3 22 row AR1 3 6 Command file Specifying the terms in the mixed model 100 Sparse fixed terms The f sparse_fired terms in model formula NIN Alliance Trial 1989 variety e are the fixed covariates for example the fixed lin row covariate now included in ace the model formula factors and interac column 11 nin89 asd skip 1 iel
75. 7 and u leads to the mixed model equations Robinson 1991 which are given by X R X X R Z _ X Ry 2 11 ZROX Z R Z G l Z Rty These can be written as CB WR y where C W R W G B r uJ and _ 0 0 gali eal The solution of 2 11 requires values for y and In practice we replace y and by their REML estimates and 2 Some theory 15 Note that 7 is the best linear unbiased estimator BLUE of 7 while amp is the best linear unbiased predictor BLUP of u for known y and We also note that a e izn e 2 3 What are BLUPs Consider a balanced one way classification For data records ordered r repeats within b treatments regarded as random effects the linear mixed model is y XT Zu e where X 1 1 is the design matrix for T the overall mean Z I Q 1 is the design matrix for the b random treatment effects u and e is the error vector Assuming that the treatment effects are random implies that u N Aw o7I for some design matrix A and parameter vector w It can be shown that j roe oO a y 19 Ay 2 12 ro o ro o where y is the vector of treatment means is the grand mean The differences of the treatment means and the grand mean are the estimates of treatment effects if treatment effects are fixed The BLUP is therefore a weighted mean of the data based estimate and the prior mean Aw If Y 0 the BLUP in 2 12 becomes 2 P ro b
76. ASReml processes it If the pinfile basename differs from the basename of the output files it is processing then the basename of the output files must be specified with the P option letter Thus ASReml border pin will perform the pinfile calculations defined in border pin on the results in files border asr and border vvp ASReml Pborderwwt border pin will perform the pinfile calculations defined in border pin on the results in files borderwwt asr and borderwwt vvp Forming a job template from a data file The facility to generate a template as file has been moved to the command line and extended Normally the name of a as command file is specified on the command line If a as file does not exist and a file with file extension asd csv dat gsh txt or x1s is specified ASReml assumes the data file has field labels in the first row and generates a as file template First it seeks to convert the gsh Genstat or xls Excel see page 45 file to csv format using the ASRemload d11 utility provided by VSN In generating the as template ASReml 11 Command file Running the job 197 takes the first line of the csv or other file as providing column headings and generates field definition lines from them If some labels have appended these are defined as factors otherwise ASReml attempts to identify factors from the field contents The template needs further editing before it is ready to run but does have the field
77. Command file Specifying the variance structures 135 Table 7 3 Details of the variance models available in ASReml base description algebraic number of parameters identifier form corr homo s hetero s variance variance SPH spherical C 1 265 503 1 2 1l w ASReml2 0 lt h CIR circular Web Ci 1 1 2 1 w ASReml2 ster amp Oliver 2 Bija 1 02 sin 16 2001 p 113 0 lt dy AEXP anisotropic ex C 1 2 3 2 w onential zi zj yi yy P n C gl al gly yjl 0 lt lt 10 lt lt 1 AGAU anisotropic C 1 2 3 2 w gaussian Gi Gimes pmu 0 lt lt 10 lt lt 1 MATK Mat rn with C Mat rn see text k k 1 k w ASReml2 firt 1 lt k lt 5 gt 0 range v shape 0 5 parameters isO annist tio 1 specified by th anisotropy ratio 1 user a anisotropy angle 0 A 1 2 metric 2 Additional heterogeneous variance models DIAG diagonal IDH y p 4 50 i j w US unstructured diy Q w w 1 general covari ance matrix OWNk user explicitly k forms V and OV ANTE 1 i k order UDU zm werd ANTEk k antede D 4d D 0 i j pendence j U 1 U u Ui 0 1 gt 9 1l lt k lt w l 7 Command file Specifying the variance structures 136 Table 7 3 Details of the variance models available in ASReml base description algebraic number of parameters identifier form corr homo s hetero s variance variance CHOL 1 1 k order LDL ea CHOLK k cholesk
78. If extracting a single covariate from a large set of covariates in the file the specific field to extract can be given by FIELD s in absolute terms or relative to the key field by RFIELD r For example IMBF mbf variety 1 markers csv key 1 RFIELD 35 rename Marker35 SKIP k requests the first k lines of the file be ignored SPARSE can be used when the covariates are predominately zero Each key value is followed by as many column value pairs as required to specifiy the non zero elements of the design for that value of key The pairs should be arranged in increasing order of column within rows The rows may be continued on subsequent lines of the file provided incomplete lines end with a COMMA Restrictions The key field MUST be numeric In particular if the data field it relates to is either an A or I encoded factor the original uncoded level labels may not specified in the MBF file Rather the coded levels must be specified The MBF file is processed before the data file is read in and so the mapping to coded levels has not been defined in ASReml when the MBF file is processed although the user can must anticipate what it will be 5 Command file Reading the data 76 Table 5 4 List of occasionally used job control qualifiers qualifier action MVINCLUDE MVREMOVE NODISPLAY IPVAL v p PVAL f ulist ROWFAC v Comment If this MBF process is to be used repeatedly for example to proces
79. LOTESAN LOvEsaN E9PL8AN ET9L8AN LZSISAN VUNLNAO lt DLETESSH ZT9L8AN NISHONA AdOO SOPLSEIN ZISL8aN VNOA LOLSAN NIMSMONE LOVESN I II OL 6 8 L 9 G Vv G T Mor wumnyoo jeun PJ NIN 242 Ul SJOjd 0 salqalUeA Jo UO JedO Je pue node jel T E aIGeL 3 A guided tour 30 These data are analysed again in Chapter 7 using spatial methods of analysis see model 3a in Section 7 3 For spatial analysis using a separable error structure see Chapter 2 the data file must first be augmented to specify the complete 22 row x 11 column array of plots These are the first 20 lines of the augmented data file nin89aug asd with 242 data rows Note that repl nloc yield lat long row column variety id pid raw LANCER 1 NA NA 1 4 NA LANCER 1 NA NA 1 4 NA LANCER 1 NA NA 1 4 NA LANCER 1 NA NA 1 4 NA LANCER 1 NA NA 1 4 NA LANCER 1 NA NA 1 4 NA LANCER 1 NA NA 1 4 NA LANCER 1 NA NA 1 4 NA LANCER 1 NA NA 1 4 NA LANCER 1 NA NA 1 4 NA LANCER 1 NA NA 1 4 NA LANCER 1 NA NA 1 4 NA LANCER 1 NA NA 1 4 NA LANCER 1 NA NA 1 4 NA LANCER 1 NA NA 1 4 NA LANCER 1 NA NA 2 4 NA LANCER 1 NA NA 3 4 NA LANCER 1 NA NA 4 4 NA LANCER 1 1101 585 1 4 11 1 al 1 ad 1 1 10 3 9 1 12 10 1 13 2 11 14 4 12 15 6 13 16 8 14 o 18 15 1 Ia Tea G A 25 9 22 9 19 6 38 7 12 0 10 9 29 25 4 3 19 2 16 1 OPRNOTWAA PN ONOrFRARWND SAA DADA AA A RR AR RO errre WWWWWWWWWWWwWWwW www BRULE 2 1102 631 1 4 31 55 4 3 20 4 17 1 REDLAND 3 1103 701 1 4 35 05
80. Likelihood especially in bivariate cases where DF associated with groups may differ between traits The LAST qualifier see page 85 is designed to help as without it reorder ing may associate singularities in the A matrix with random effects which at the very least is confusing When the A matrix incorporates fixed effects the number of DF involved may not be obvious especially if there is also a sparsely fitted fixed HYS factor The number of Fixed effects degrees of freedom associated with GROUPS is taken as the declared number less twice the number of constraints applied This assumes all groups are rep resented in the data and that degrees of freedom associated with group constraints will be fitted elsewhere in the model INBRED generates pedigree for inbred lines Each cross is assumed to be selfed ASReml2 several times to stabilize as an inbred line as is usual for cereals such as wheat before being evaluated or crossed with another line Since inbreeding is usually associated with strong selection it is not obvious that a pedigree assumption of covariance of 0 5 between parent and offspring actually holds Do not use the INBRED qualifier with the MGS or SELF qualifiers 9 Command file Genetic analysis 170 List of pedigree file qualifiers qualifier description ASReml3 ASReml3 ASReml3 ASReml3 ASReml2 ASReml2 ASReml3 LONGINTEGER MAKE MEUWISSEN MGS QUAAS REPEAT
81. R header SECTIONS DIMNS GSTRUCT R structure header SITE DIM GSTRUCT Variance header SEC DIM GSTRUCT R structure error ORDER SORTCOL MODEL GAMMAS R structures are larger than number of records REQUIRE ASUV qualifier for this R structure REQUIRE I x E R structure Scratch Segmentation fault Singularity appeared in AI matrix Singularity in Average Information Matrix Sorting data by Section Row Sorting the data into field order STOP SCRATCH FILE DATA STORAGE ERROR error with the variance header line Often some other error has meant that the wrong line is being interpreted as the variance header line Commonly the model is written over sev eral lines but the incomplete lines do not all end with a comma an error reading the error model Maybe you need to include mv in the model to stop ASReml discarding records with missing values in the response variable Without the ASUV qualifier the multivariate error variance MUST be specified as US Apparently ASReml could not open a scratch file to hold the transformed data On unix check the temp directory tmp for old large scratch files this is a Unix memory error It typically oc curs when a memory address is outside the job memory The first thing to try is to increase the memory workspace using the WORKSPACE see Section 11 3 on memory command line option Otherwise you may need to send your data and the as files to Customer Support for debu
82. SE C spl age 7 5 5 0 787457E 01 3 95215 0 40 UP Variance T 5 1 00000 50 1888 1 33 OP Wald F statistics Source of Variation NumDF DenDF F_inc Prob 7 mu 1 3 8 1382 80 lt 001 3 age 1 i 217 60 lt 001 Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using algebraic derivatives Estimate Standard Error T value T prev 3 age 1 0 814772E 01 0 552336E 02 14 75 7 mu il 24 4378 5 75429 4 25 6 spl age 7 5 effects fitted Finished 19 Aug 2005 10 08 11 980 LogL Converged The REML estimate of the smoothing constant indicates that there is some non linearity The fitted cubic smoothing spline is presented in Figure 16 13 The fitted values were obtained from the pvs file The four points below the line were the spring measurements 16 Examples 326 160 on circumference 80 40 20 T T T T T T T T 200 400 600 800 1000 1200 1400 1600 age Figure 16 13 Fitted cubic smoothing spline for tree 1 We now consider the analysis of the full dataset Following Verbyla et al 1999 we consider the analysis of variance decomposition see Table 16 11 which models the overall and individual curves An overall spline is fitted as well as tree deviation splines We note however that the intercept and slope for the tree deviation splines are assumed to be random effects This is consistent with Verbyla et al 1999 In this sense the tree deviation splines
83. Symbolic description of factorial models for analysis of variance Applied Statistics 22 392 399 Wolfinger R and O Connell M 1993 Generalized linear mixed models A pseudo likelihood approach Journal of Statistical Computation and Simu lation 48 233 243 Wolfinger R D 1996 Heterogeneous variance covariance structures for re peated measures Journal of Agricultural Biological and Environmental Statistics 1 362 389 Yates F 1935 Complex experiments Journal of the Royal Statistical Society Series B 2 181 247 Index ABORTASR NOW 71 FINALASR NOW 71 47 VPREDICT directive 215 Access 45 accuracy genetic BLUP 227 advanced processing arguments 203 Al algorithm 13 AIC 18 Akaike Information Criteria 18 aliassing 114 Analysis of Deviance 110 Analysis of Variance 20 Wald F statistics 116 animal breeding data 2 arguments 5 ASReml symbols 94 44 44 H 44 44 96 96 96 96 96 96 96 96 Associated Factors 102 autoregressive 123 Average Information 2 363 balanced repeated measures 290 Bayesian Information Criteria BIC 18 binary files 45 Binomial divisor 111 BLUE 15 BLUP 15 case 95 combining variance models 16 command file 31 genetic analysis 165 multivariate 158 Command line option A ASK 199 B BRIEF 199 C CONTINUE 201 D DEBUG 199 F FINAL 201 Gg graphics 199 Hg HARDCOPY 200 IN
84. Warning Spatial mapping information for side 2 of order 22 ranges from 1 0 to 11 0 Error Failed to sort data records Sortkeys range 22 Failed at record 2 2 1 2 1 1 1 1 2 2 1 1 3 3 1 23 4 4 1 23 22 22 i 22 Fault Sorting data into field order Last line read was 22 column AR1 0 100000 ninerriO variety id pid raw rep nloc yield lat Model specification TERM LEVELS GAMMAS variety 56 mu 1 mv_estimates 18 SECTIONS 242 4 1 STRUCT 11 1 1 5 1 10 22 1 1 6 1 11 13 factors defined max 500 6 variance parameters max1500 2 special structures Final parameter values 3 6 0 0000 10000E 360 10000 0 10000 Last line read was 22 column AR1 0 100000 Finished 11 Apr 2008 20 41 46 421 Sorting data into field order 15 Error messages 263 15 5 Information Warning and Error messages ASReml prints information warning and error messages in the asr file The major information messages are in Table 15 1 A list of warning messages together with the likely meaning s is presented in Table 15 2 Error messages with their probable cause s is presented in Table 15 3 Table 15 1 Some information messages and comments information message comment Logl converged the REML log likelihood last changed less than 0 002 iteration number and variance param eter values appear stable BLUP run done A full iteration has not been completed See discussion of BLUP JOB ABORTED by USER Logl converged parameters not converged
85. an average or typical value of the covariate Omission of a covariate from the prediction model is equivalent to predicting at a zero covariate value which is often not appropriate unless the covariate is centred Before considering the syntax it is useful to consider the conceptual steps involved in the prediction process Given the explanatory variables fixed factors random factors and covariates used to define the linear mixed model the four main steps are a Choose the explanatory variable s and their respective level s value s for which predictions are required the variables involved will be referred to as the classify set and together define the multiway table to be predicted Include only one from any set of associated factors in the classify set b Note which of the remaining variables will be averaged over the averaging set and which will be ignored the ignored set The averaging set will include all remaining variables involved in the fixed model but not in the classify set Ignored variables may be explicitly added to the averaging set The combination of the classify set with these averaging variables defines a multiway hyper table Only the base factor in a set of associated factors formally appears in this hyper 10 Tabulation of the data and prediction from the model 179 table regardless of whether it is fitted as fixed or random Note that variables evaluated at only one value for example a covariate at
86. and colblk effects The precision from the spatial analyses are similar 45796 58 23 8842 1917 442 c f 8061 808 4 03145 1999 729 but slightly lower reflecting the Revised 08 gain in accuracy from the spatial analysis For further reading see Smith et al 2001 2005 16 7 Unreplicated early generation variety trial Wheat 16 Examples 306 To further illustrate the approaches presented in the previous section we con sider an unreplicated field experiment conducted at Tullibigeal situated in south western NSW The trial was an S1 early stage wheat variety evaluation trial and consisted of 525 test lines which were randomly assigned to plots in a 67 by 10 array There was a check plot variety every 6 plots within each column That is the check variety was sown on rows 1 7 138 67 of each column This variety was numbered 526 A further 6 replicated commercially available varieties numbered 527 to 532 were also randomly assigned to plots with between 3 to 5 plots of each The aim of these trials is to identify and retain the top say 20 of lines for further testing Cullis et al 1989 considered the analysis of early generation variety trials and presented a one dimensional spatial analysis which was an extension of the approach developed by Gleeson and Cullis 1987 The test line effects are assumed random while the check variety effects are consid ered fixed This may not be sensible or justifiable for most trials and ca
87. and cp is a multiplier for v m is a number bigger than the current length of v to flag the special case of adding the offset k Where matrices are to be combined the form F label a b k c d can be used as in the Coopworth data example see page 349 Assuming that the pin file in the ASReml code box corresponds to a simple sire model and that variance component 1 is the sire variance and variance component 2 is the residual variance then F phenvar 1 2 13 Functions of variance components 217 gives a third component which is the sum of the variance components that is the phenotypic variance and F genvar 1 4 gives a fourth component which is the sire variance component multiplied by 4 that is the genotypic variance Heritability Heritabilities are requested by lines in the F phenvar 1 2 pheno var pin file beginning with an H The specific F genvar 1 4 geno var i A H herit 4 3 heritabilit form of the directive in this case is r H label nd This calculates 02 07 and se o2 c where n and d are integers pointing to com ponents v and vg that are to be used as the numerator and denominator respec tively in the heritability calculation 2 4 4 pp oF on Oo oTa Var 24 2 2 Var on Var 3 2Cov n a In the example H herit 4 3 calculates the heritability by calculating component 4 from second line of pin component 3 from first line of pin that is
88. and modify the data so that they are omitted or consistently detected One possibility is to centre and scale covariates involved in interac tions so that their standard deviation is close to 1 15 Error messages 268 Table 15 3 Alphabetical cause s remedies list of error messages and probable error message probable cause remedy PRINT Cannot open output file AINV GIV matrix undefined or wrong size ASReml command file is EMPTY ASReml failed in Continue from rsv file Convergence failed Correlation structure is not positive definite Define structure for Error The indicated number of input fields exceeds the limit Error in CONTRAST label factor values Check filename Check the size of the factor associated with the AINV GIV structure The job file should be in ASCII format Try running the job with increased workspace or using a simpler model Otherwise send the job to VSN mailto support asreml co uk for investigation Try running without the CONTINUE qualifier the program did not proceed to convergence because the REML log likelihood was fluctuat ing wildly One possible reason is that some singular terms in the model are not being de tected consistently Otherwise the updated G structures are not positive definite There are some things to try define US structures as positive definite by using GP supply better starting values
89. are also printed in the asr file with their standard error a t statistic for testing that effect and a t statistic for testing it against the preceding effect in that factor heritability pvc file placed in the pvc file when postprocessing with a pin file histogram of residu res file and graphics file als intermediate results asl file given if the DL command line option is used 14 Description of output files 244 Table 14 2 Table of output objects and where to find them ASReml output object found in comment mean variance rela tionship observed variance covariance matrix formed from BLUPs and residuals phenotypic variance plot of residuals against field position possible outliers predicted fitted val ues at the data points predicted values REML log likelihood res file res file pvc file graphics file res file yht file pvs file asr file for non spatial analyses ASReml prints the slope of the regression of log abs residual against log predicted value This regression is ex pected to be near zero if the variance is inde pendent of the mean A power of the mean data transformation might be indicated otherwise The suggested power is approximately 1 b where b is the slope A slope of 1 suggests a log transfor mation This is indicative only and should not be blindly applied Weighted analysis or identi fying the cause of the heterogeneity
90. are few parameters this can be done as follows xfa dTrial 1 Family 2 7 Command file Specifying the variance structures 153 Revised 08 ASReml3 5 O XFA1 GPFPFP ABCDEFGH 0 72631 0 000 242713 0 000 882465 846305 04419 743393 Family O GIV1 xfa dTrial 1 Entry 2 5 O XFA1 GPFPFP ABCDEFGH 0 72631 0 000 242713 0 000 882465 846305 04419 743393 Entry 0 GIV2 However for a larger term there may not be enough letters in the alphabet and so VCC is required as in IVCC 1 xfa dTrial 1 Family 2 5 O XFA1 GPFPFP 0 72631 0 000 242713 0 000 882465 846305 04419 743393 Family 0 GIV1 xfa dTrial 1 Entry 2 5 O XFA1 GPFPFP 0 72631 0 000 242713 0 000 882465 846305 04419 743393 Entry 0 GIV2 21 29 BLOCKSIZE 8 parameters 21 28 are equal to parameters 29 36 pairwise Better still in this case we can use just one structure twice xfa dTrial 1 Family 2 5 0 XFA1 GPFPFP NAME FIVE 0 72631 0 000 242713 0 000 882465 846305 04419 743393 Family O GIV1i xfa dTrial 1 Entry 2 USE FIVE Model and Initial parameters are given above Entry 0 GIV2 associates the model definition labeled FIVE with the second structure 7 Command file Specifying the variance structures 154 7 10 Model building using the CONTINUE qualifier difficult Revised 08 In complex models the Average Information algorithm can have difficulty max imising the REML log likelihood when starting value
91. as shown in the code box to the ywt gat Trait r Trait sire right IPIN define F phenvar 1 3 4 6 z F addvar 4 6 4 Numbering the parameters reported in Eert 40 7 bsiremod asr and bsiremod vvp H heritB 12 9 1 error variance for ywt M PARETE F E R gencor 4 6 2 error covariance for ywt and fat 3 error variance for fat 121 4 sire variance component for ywt O ASReml will count units 5 sire covariance for ywt and fat S wee 6 sire variance for fat e E S then Trait 0 US 3 0 F phenvar 1 3 4 6 sire creates new components 7 1 4 8 2 5 13 Functions of variance components 219 The first 6 lines are copied from the asr file and 9 3 6 F addvar 4 6 4 creates new components 10 4 x 4 11 5 x 4and 12 6 x 4 H heritA 10 7 forms 10 7 to give the heritability for ywt H heritB 12 9 forms 12 9 to give the heritability for fat R phencorr 7 8 9 forms 8 7 x 9 that is the phenotypic correlation between ywt and fat R gencorr 4 6 forms 5 4x6 that is the genetic correlation between ywt and fat The resulting pvc file contains we fae 1 Residual 26 2191 2 Residual 2 85058 3 Residual 1 71554 4 Tr sire 16 5244 5 Tr sire 1 14335 6 Tr sire 0 132734 7 phenvar 1 42 75 6 297 8 phenvar 2 3 995 0 6761 9 phenvar 3 1 848 0 1183 10 addvar 4 66 10 24 58 11 addvar 5 4 577 2 354 12 addvar 6 0 5314 0 2831 h2ywt addvar 10 phenvar T 1 5465 0 3574 h2fat addvar 12 ph
92. asreml exe in a PC environment In a UNIX environment ASReml is usually run through a shell script called ASRem1 if the ASReml program is in the search path then path is not required and the word ASRem1 will suffice for example ASReml nin89 as will run the NIN analysis assuming it is in the current working folder if asreml exe ASRem1 is not in the search path then path is required for example if asreml exe is in the usual place then C Program Files ASRem13 bin Asreml nin89 as will run nin89 as e ASRem1 invokes the ASReml program e basename is the name of the as c command file The basic command line can be extended with options and arguments to path ASReml options basename as c arguments 11 Command file Running the job 196 ASReml2 e options is a string preceded by a minus sign Its components control several operations batch graphic workspace at run time for example the command line ASReml w128 rat as tells ASReml to run the job rat as with workspace allocation of 128mb e arguments provide a mechanism mostly for advanced users to modify a job at run time for example the command line ASReml rat as alpha beta tells ASReml to process the job in rat as as if it read alpha wherever 1 ap pears in the file rat as beta wherever 2 appears and 0 wherever 3 appears see below Processing a pin file If the filename argument is a pin file see Chapter 13 then
93. be linked to ConText or accessed directly ASRem1 chm There is a User Area on the website http www VSNi co uk select ASRem1l and then User Area which contains contributed material that may be of assistance It includes an ASReml tutorial in the form of sixteen sets of slides with audio mp3 discussion The sessions last about 20 minutes each Users with a support contract with VSN should email support asreml co uk for assistance with installation and running ASReml When requesting help please send the input command file the data file and the corresponding primary output 1 Introduction 5 file along with a description of the problem There is an ASReml forum which all ASReml users including unsupported users ASReml forum are encouraged to join Register now at http www vsni co uk forum 1 6 Typographic conventions A hands on approach is the best way to develop a working understanding of a new computing package We therefore begin by presenting a guided tour of ASReml using a sample data set for demonstration see Chapter 3 Throughout the guide new concepts are demonstrated by example wherever possible In this guide you will find framed sample An example ASReml code box boxes to the right of the page as shown here 4034 kena Iighlduhee seii These contain ASReml command file sample of code currently under code Note that discussion remaining code is not the code under discussion is highlighted in ian
94. been included to document the file In this case there are 11 space separated data fields variety column and the complete file has 224 data lines one for each variety in each replicate variety id pid raw repl nloc yield lat long row column optional field labels LANCER 1 1101 585 1 4 29 25 4 3 19 2 16 1 data for sampling unit 1 BRULE 2 1102 631 1 4 31 55 4 3 20 4 17 1 data for sampling unit 2 REDLAND 3 1103 701 1 4 35 05 4 3 21 6 18 1 CODY 4 1104 602 1 4 30 1 4 3 22 8 19 1 ARAPAHOE 5 1105 661 1 4 33 05 4 3 24 20 1 NE83404 6 1106 605 1 4 30 25 4 3 25 2 21 1 NE83406 7 1107 704 1 4 35 2 4 3 26 4 22 1 NE83407 8 1108 388 1 4 19 4 8 6 1 2 1 2 CENTURA 9 1109 487 1 4 24 35 8 6 2 4 2 2 SCOUT66 10 1110 511 1 4 25 55 8 6 3 6 3 2 COLT 11 1111 502 1 4 25 1 8 6 4 8 4 2 NE83498 12 1112 492 1 4 24 6 8 6 65 2 NE84557 13 1113 509 1 4 25 45 8 6 7 2 6 2 NE83432 14 1114 268 1 4 13 4 8 6 8 4 7 2 NE85556 15 1115 633 1 4 31 65 8 6 9 6 8 2 NE85623 16 1116 513 1 4 25 65 8 6 10 8 9 2 CENTURAK78 17 1117 632 1 4 31 6 8 6 12 10 2 NORKAN 18 1118 446 1 4 22 3 8 6 13 2 11 2 KS831374 19 1119 684 1 4 34 2 8 6 14 4 12 2 dvaLsaNou VLOONVI GNVTXNOIS ataya Z8t9I8AN EISL8AN TOS98AN aNv1dq4u SESLEAN ANNAAADHO 9068AN ZZ LOTNVL 60S98aN 109984N 909984N OT TLSAN VLOONVT CAVaLSaNOH LOTINVL ETSL8AN LOTNVL rOrEscIN IZ LS9V89 N LSVL80N 90vE85N amp 9TLSAN YAON VI L09984N ANVTIXNOIS UAONV T ISLESIN 60899841N MOHVdIVUV oz ZZSL8AN 909985N UAONVI 6LOLSAN ADVD
95. binary data Biometrical Journal 2 141 154 Engel B and Buist W 1998 Bias reduction of approximate maximum like lihood estimates for heritability in threshold models Biometrics 54 1155 1164 Engel B and Keen A 1994 A simple approach for the analysis of generalized linear mixed models Statistica Neerlandica 48 1 1 22 Fernando R and Grossman M 1990 Genetic evaluation with autosomal and x chromosomal inheritance Theoretical and Applied Genetics 80 75 80 Fischer T M Gilmour A R and van der Werf J 2004 Computing approxi mate standard errors for genetic parameters derived from random regression models fitted by average information reml Genetics Selection and Evolution 36 3 363 369 Bibliography 358 Gilmour A R 2007 Mixed model regression mapping for qtl detection in experimental crosses Computational Statistics and Data Analysis 51 3749 3764 Gilmour A R Anderson R D and Rae A L 1985 The analysis of binomial data by a generalised linear mixed model Biometrika 72 593 599 Gilmour A R Anderson R D and Rae A L 1987 Variance components on an underlying scale for ordered multiple threshold categorical data using a generalized linear mixed model Journal of Animal Breeding and Genetics 39 917 934 Gilmour A R Cullis B R and Verbyla A P 1997 Accounting for natural and extraneous variation in the analysis of field experiments Journal of
96. by the job and there may be mul tiple MERGE directives Indeed the job may just consist of a title line and MERGE directives The MERGE qualifier on the other hand combines information from two files into the internal data set which ASReml uses for analysis and does not save it to file It has very limited in functionality The files to be merged must conform to the following basic structure e the data fields must be TAB COMMA or SPACE separated e there will be one heading line that names the columns in the file e the names may not have embedded spaces e the number of fields is determined from the number of names e missing values are implied by adjacent commas in comma delimited files Otherwise they are indicated by NA or as in normal ASReml files e the merged file will be TAB separated if a txt file COMMA separated if a csv file and SPACE separated otherwise 12 2 Merge Syntax The basic merge command is MERGE filel WITH file2 to newfile Typically files to be merged will have common key fields In the basic merge KEY not specified any fields having the same names are taken as the key fields and if the files have no fields in common they are assumed to match on row number Fields are referenced by name case sensitive 12 Command file Merging data files 212 The full command is MERGE filel IKEY keyfzelds KEEP ISKIP fields WITH file2 IKEY keyfields f KEEP ll NODUP al SKIP fie
97. can also contain qualifiers that control other aspects of the analysis These qualifiers are presented in Section 5 8 Tabulation Optional tabulate statements provide a sim ple way of exploring the structure of a data They should appear immediately before the model line In this case the 56 simple variety means for yield are formed and written to a tab output file See Chapter 10 for a discus sion of tabulation NIN Alliance trial 1989 variety A id pid raw repl 4 nloc yield lat long row 22 column 11 nin89 asd skip 1 NIN Alliance trial 1989 variety A id pid row 22 column 11 nin89 asd skip 1 tabulate yield variety yield mu variety r repl predict variety 001 repl repl 0 IDV 0 1 column 11 nin89 asd skip 1 tabulate yield variety yield mu variety r repl predict variety 3 A guided tour 33 See Chapter 6 See Chapter 10 See Chapter 7 Specifying the terms in the mixed model The linear mixed model is specified as a list of model terms and qualifiers All elements must be space separated ASReml accommo dates a wide range of analyses See Section 2 1 for a brief discussion and general algebraic formulation of the linear mixed model The model specified here for the NIN data is a sim ple random effects RCB model having fixed va riety effects and random replicate effects The reserved word mu fits a constant term inter
98. can be calculated as 0 tan 1 lij1 lij2 choosing 0 lt 6 lt 180 if lij2 gt 0 and 180 lt i lt 0 if lij lt 0 Note that the variogram has angular symmetry in that vij vj dij dji and 0 6 180 The variogram presented averages the vj within 12 distance classes and 4 6 or 8 sectors selected using a VGSECTORS qualifier centred on an angle of i 1 180 s i 1 s A figure is produced which reports the trends in v with increasing distance for each sector ASReml also computes the variogram from predictors of random effects which appear to have a variance structures defined in terms of distance The variogram details are reported in the res file 2 Some theory 20 2 6 ASReml2 Inference Fixed effects Introduction Inference for fixed effects in linear mixed models introduces some difficulties In general the methods used to construct F tests in analysis of variance and regression cannot be used for the diversity of applications of the general linear mixed model available in ASReml One approach would be to use likelihood ratio methods see Welham and Thompson 1997 although their approach is not easily implemented Wald type test procedures are generally favoured for conducting tests concerning T The traditional Wald statistic to test the hypothesis Hp Lr l for given L r xp and l r x 1 is given by W L 1 L X H 1X L Y HL l 2 17 and asymptotically this sta
99. component is meaningful and in fact necessary and obtained by use of the GU option in this context since it should be considered as part of the variance structure for the combined variety main effects and treatment by variety interactions That is 2 2 2 oj a o var 12 Q u1 u2 1 p 2c 2 fe Q Ig4 16 8 Using the estimates from table 16 8 this structure is estimated as 3 84 2 33 233 1 96 ET Thus the variance of the variety effects in the control group also known as the genetic variance for this group is 3 84 The genetic variance for the treated group 16 Examples 317 Table 16 9 Equivalence of random effects in bivariate and univariate analyses bivariate univariate effects model 16 10 model 16 7 trait variety Uy 1 9 u u trait run Ur l 8 U U trait pair e 1 u e is much lower 1 96 The genetic correlation is 2 33 V 3 84 x 1 96 0 85 which is strong supporting earlier indications of the dependence between the treated and control root area Figure 16 8 A multivariate approach In this simple case in which the variance heterogeneity is associated with the two level factor tmt the analysis is equivalent to a bivariate analysis in which the two traits correspond to the two levels of tmt namely sqrt rootwt for control and treated The model for each trait is given by Yj XTj Zvw Zrur e J 6 t 16 9 where y is a vector of length n 132 containing the sqrtroot value
100. consideration is required when using the XFAk model The SSP must be expanded to have room to hold the k factors This is achieved by using the xfa f k model term in place of fin the model For example y site r geno xfa site 2 0 0 7 geno xfa site 2 2 geno xfa site 2 0 XFA2 With multiple factors some constraints are required to maintain identifiablity Traditionally this has simply been to set the leading loadings of new factors to zero Loadings then need to be rotated to orthogonality In ASReml 3 if no loadings are fixed i e GP ASReml will rotate the loadings to orthogonality and hold the leading loadings of lower factors fixed They are however updated in the orthogonalization process which occurs at the beginning of each iteration so the final returned values have not been formally rotated Finding the REML solutions for multifactor Factor Analytic models can be dif ficult The first problem is specifying initial values When using CONTINUE and progressing XFA k to XFA k 1 ASReml3 initialises the factor k 1 at W x 0 2 changing the sign of the relatively largest loading to negative One strategy which sometimes works in this context is to hold the previously estimated factor loadings fixed for one a few iterations so that the factor k 1 initally aims to explain variation previously incorporated in w Then allow all loadings to be updated in the remaining rounds A second problem at present unresolved i
101. constructed as a direct 2 Some theory 10 product of matrices corresponding to underlying factors is called the assumption of separability and assumes that any correlation process across levels of a factor is independent of any other factors in the term Multivariate data and repeated measures data usually satisfy the assumption of separability In particular if the data are indexed by factors units and traits for multivariate data or times for repeated measures data then the R structure may be written as units traits or units times This assumption is sometimes required to make the estimation process computationally feasible though it can be relaxed for certain applications for example fitting isotropic covariance models to irregularly spaced spatial data Variance structures for the random effects G structures The q x 1 vector of random effects is often composed of b subvectors u u wy us where the subvectors u are of length q and these subvectors are usually assumed independent normally distributed with variance matrices 0Gi Thus just like R we have Gy 0 0 0 0 Go 0 0 G 0_1Gi Co 4 l 0 0O Gnu 0 0 O sus 0 Gp There is a corresponding partition in Z Z Z1 Z2 Z As before each submatrix G is assumed to be the direct product of one two or three component matrices These matrices are indexed for each of the factors constituting the term in the linear model For example the term site gen
102. correlation matrix of order 22 for rows AR1 and the variance scale parameter 2 e a2 is implicit Note the following e placing column and row in the second position on lines 1 and 2 respectively tells ASReml to internally sort the data rows within columns before processing the job This is to ensure that the data matches the direct product structure specified If column and row were replaced with O in these two lines ASReml would assume that the data were already sorted in this order which is not true in this case e the 0 3 on line 2 is a starting value for the autoregressive row correlation Note that for spatial analysis in two dimensions using a separable model a complete matrix or array of plots must be present To achieve this we augmented the data with the 18 records for the missing yields as shown on page 30 In the 7 Command file Specifying the variance structures 123 See Chapter 14 See Sections 6 3 and 6 10 See Sections 2 1 and 7 5 See Section 7 7 augmented data file the yield data for the missing plots have all been made NA one of the missing value indicators in ASReml and variety has been arbitrarily coded LANCER for all of the missing plots any of the variety names could have been used f mv is now included in the model specification This tells ASReml to estimate the missing values The f before mv indicates that the missing values are fixed effects in the sparse set of terms e u
103. curs after several iterations it is likely that the variance components are very small Try sim plifying the model In multivariate analyses it arises if the error variance is becomes nega tive definite Try specifying GP on the struc ture line for the error variance too many terms are being defined 15 Error messages 273 Table 15 3 Alphabetical cause s remedies list of error messages and probable error message probable cause remedy No giv file for No residual variation Out of Out of memory Out of memory forming design Overflow structure table Pedigree coding errors Pedigree factor has wrong size Pedigree too big or in error POWER model setup error Fix the argument to giv after fitting the model the residual variation is essentially zero that is the model fully ex plains the data If this is intended use the BLUP 1 qualifier so that you can see the es timates Otherwise check that the dependent values are what you intend and then identify which variables explain it Again the BLUP 1 qualifier might help A program limit has been breached Try sim plifying the model use WORKSPACE qualifier to increase the workspace allocation It may be possible to revise the models to increase sparsity factors are probably not declared properly Check the number of levels Possibly use the WORKSPACE qualifier occurs when space allocated for the structure
104. ef fect Thus to form a direct maternal genetic and maternal environment model the maternal environment is defined as a second animal effect coded the same as dams viz r animal dam ide dam forms the reciprocal of v r This may also be used to transform the response variable leg v n forms n 1 Legendre polynomials of order 0 intercept 1 linear n from the values in v the intercept polynomial is omitted if n is preceded by the negative sign The actual values of the coefficients are written to the res file This is similar to the pol function described below lin f takes the coding of factor f as a covariate The function is defined for f 1 f being a simple factor Trait and units The lin f function does not centre or scale the variable Motivation Sometimes you may wish to fit a covariate as a random factor as well If the coding is say 1 n then you should define the field as a factor in the field definition and use the lin function to include it as a covariate in the model Do not centre the field in this case If the covariate values are irregular you would leave the field as a covariate and use the fac function to derive a factor version 6 Command file Specifying the terms in the mixed model 105 Table 6 2 Alphabetic list of model functions and descriptions model function action log v 7r forms the natural log of v r This may also be used to transform the response variable
105. effect plus heterogeneous tmt variety interaction variance structure 16 8 in the univariate analysis Similarly the unstructured form for trait run is equivalent to the run main effect plus heterogeneous tmt run interaction variance structure The unstructured form for the errors trait pair in the bivariate analysis is equivalent to the pair plus heteroge neous error tmt pair variance in the univariate analysis This bivariate analysis is achieved in ASReml as follows noting that the tmt factor here is equivalent to traits this is for the paired data id pair 132 run 66 variety 44 A yc ye ricem asd skip 1 X syc Y sye sqrt yc sqrt ye Trait r Tr variety Tr run 122 132 2 Tr 0 US 2 21 1 1 2 427 Tr variety 2 20 US 1 401 1 1 477 4400 Tx kum 2 20 US T9 45 2 8987 66 0 0 predict variety A portion of the output from this analysis is 7 LogL 343 220 S2 1 0000 262 df 8 LogL 343 220 S2 1 0000 262 df Source Model terms Gamma Component Comp SE C Residual UnStruct 1 2 14373 2 14373 4 44 OU Residual UnStruct 1 0 987401 0 987401 2 59 OUY 16 Examples 319 Residual UnStruct 2 2 34751 2 34751 4 62 0 y Tr variety UnStruct 1 3 83959 3 83959 3 47 OU Tr variety UnStruct 1 2 33394 2 33394 2 01 Q U Tr variety UnStruct 2 1 96173 1 96173 2 69 0 y Tr run UnStruct 1 1 70788 1 70788 2 62 O U Tr run UnStruct 1 0 319145 0 319145 0 59 0U Tr run UnStruct 2 2 54326 2 54326 3 20 oU Covariance Variance Correlation
106. field qualifiers However n may be a quoted string in which case to is compared to the character value of the field as it is read and before any conversion to numeric value Warning If the filter column contains a missing value the value from the previous non missing record is assumed in that position specifies an alternative folder for ASReml to find input files This qualifier is usually placed on a separate line BEFORE the data filename line and any pedigree giv grm file name lines For example FOLDER Data data asd SKIP 1 is equivalent to Data data asd SKIP 1 5 Command file Reading the data 65 Table 5 2 Qualifiers relating to data input and output qualifier action FORMAT s supplies a Fortran like FORMAT statement for reading fixed for mat files A simple example is FORMAT 314 5F6 2 which reads 3 integer fields and 5 floating point fields from the first 42 characters of each data line A format statement is en closed in parentheses and may include 1 level of nested paren theses for example e g FORMAT 4x 3 14 8 2 Field descriptors are e rX to skip r character positions e rAw to define r consecutive fields of w characters width e riw to define r consecutive fields of w characters width and e rFw d to define r consecutive fields of w characters width d indicates where to insert the decimal point if it is not explicitly present in the field where r is an optional repe
107. for explicit times 1 10 data sorted date within plot O date EXP 0 2 SUBSECTION plot USE f requests ASReml use the variance structure previously declared and ASReml3 named f see page 152 7 7 Rules for combining variance models As noted in Section 2 1 under Combining variance models variance structures are sometimes formed as a direct product of variance models For example the variance structure for a a two factor interaction is typically formed as the direct product of two variance models one for each of the two factors in the interaction Some of the rules for combining variance models in direct products differ for R structures and G structures because R structures usually have an implicit scaling parameter while G structures never do 7 Command file Specifying the variance structures 148 See Sections 2 1 and 7 5 A summary of the rules is as follows NIN Alliance Trial 1989 variety A e when combining variance models in both R i and G structures the resulting direct prod uct structure must match the ordered ef row 22 fects with the outer factor first for example column 11 i I i the G structure in the example opposite is ae Ep yield mu variety r repl for column row which tells ASReml that the bolumn row direct product structure matches the effects 0 0 1 ordered rows within columns The variance pases erg ia 2 column model can be written as o I Uc AzR Zos 0 ARV
108. in e N 0 R The focus of this discussion is on e changes to u and e and the assumptions about these terms e the impact this has on the specification of the G structures for u and the R structures for e 7 Command file Specifying the variance structures 120 See Section 6 4 1 Traditional randomised complete block RCB analysis The only random term in a traditional RCB analysis of these data is the residual error term e N 0 o2I The model therefore involves just one R structure and no G struc tures u 0 In ASReml e the error term is implicit in the model and is not formally specified on the model line e the IID variance structure R 07I is the default for error NIN Alliance Trial 1989 variety A id pid raw repl 4 row 22 column 11 nin89 asd skip 1 yield mu variety repl Important The error term is always present in the model but its variance structure does not need to be formally declared when it has the default IID structure 2a Random effects RCB analysis The random effects RCB model has 2 random terms to indicate that the total variation in the data is comprised of 2 components a ran dom replicate effect up N 0 7 02 where yr 02 02 and error as in 1 This model in volves both the original implicit IID R struc ture and an implicit IID G structure for the random replicates In ASReml e IID variance structure is the default for ran dom terms in t
109. in the second set of models We begin by modelling the variance matrix for the intercept and slope for each tree X as a diagonal matrix as there is no point including a covariance com ponent between the intercept and slope if the variance component s for one or both is zero Model 1 also does not include a non smooth component at the overall level that is fac age Abbreviated output is shown below 16 Examples 328 Table 16 12 Sequence of models fitted to the Orange data model term 1 2 3 4 5 6 tree y y y y y y age tree y y y y y y covariance n n n n n y spl age 7 y y y y n y tree spl age 7 y y y n y y fac age n y y n n n season n n y y y y REML log likelihood 97 78 94 07 87 95 91 22 90 18 87 43 12 LogL 97 7788 S2 6 3550 33 df Source Model terms Gamma Component Comp SE C Tree 5 5 4 79025 30 4420 1 24 OP Tree age 5 5 0 939436E 04 0 597011E 03 1 41 0 P spl age 7 5 5 100 513 638 759 1 55 oF spl age 7 Tree 25 25 1 11728 7 10033 1 44 OP Variance 35 33 1 00000 6 35500 1 74 OP Wald F statistics Source of Variation NumDF DenDF F_inc Prob 7 mu 1 4 0 47 04 0 002 3 age 1 4 0 95 00 lt 001 A quick look suggests this is fine until we look at the predicted curves in Fig ure 16 14 The fit is unacceptable because the spline has picked up too much curvature and suggests that there may be systematic non smooth variation at the overall level This can be formally examined by including the fac age term as a rand
110. is implied by the length of the list Thus if the analysis involves 5 traits CONTRAST Time Trait 1 3 5 10 20 IDDF i requests computation of the approximate denominator ASReml2 degrees of freedom according to Kenward and Roger 1997 for the testing of fixed effects terms in the dense part of the linear mixed model There are three options for i i 1 suppresses computation i 1 and i 2 compute the denominator d f using numerical and algebraic methods respectively If 7 is omitted then 7 2 is assumed If DDF i is omitted i 1 is assumed except for small jobs lt 10 parameters lt 500 fixed effects lt 10 000 equations and lt 100 Mbyte workspace when i 2 5 Command file Reading the data 70 Table 5 3 List of commonly used job control qualifiers qualifier action ASReml2 FCON IMAXIT n Calculation of the denominator degrees of freedom is compu tationally expensive Numerical derivatives require an extra evaluation of the mixed model equations for every variance parameter Algebraic derivatives require a large dense ma trix potentially of order number of equations plus number of records and is not available when MAXIT is 1 or for multivari ate analysis adds a conditional Wald F statistic column to the Wald F Statistics table It enables inference for fixed effects in the dense part of the linear mixed model to be conducted so as to respect both structural and intrinsic
111. mai creates a first differenced by rows design matrix which when defining a mal f random effect is equivalent to fitting a moving average variance structure in one dimension In the mai form the first difference operator is coded across all data points assuming they are in time space order Otherwise the coding is based on the codes in the field indicated mbf f c is a term that is predefined by using the MBF qualifier see page 75 mbf f mu is used to fit the intercept constant term It is normally present and listed first in the model It should be present in the model if there are no other fixed factors or if all fixed terms are covariates or contrasts except in the special case of regression through the origin mv is used to estimate missing values in the response variable Formally this creates a model term with a column for each missing value Each column contains zeros except for a solitary 1 in the record containing the corre sponding missing value This is used in spatial analyses so that computing advantages arising from a balanced spatial layout can be exploited The equations for mv and any terms that follow are always included in the sparse set of equations Missing values are handled in three possible ways during analysis see Section 6 9 In the simplest case records containing missing values in the response variable are deleted For multivariate including some re peated measures analysis records with missing
112. missing 3 will change missing values to 3 e multiple arithmetic operations cannot be expressed in a complex expression but must be given as separate operations that are performed in sequence as they appear for example yield 120 0 0333 would calculate 0 0333 yield 120 e Most transformations only operate on a single field and will not therefore be performed on all variables in a G factor set The only transformations that apply to the whole set are DOM MM and RESCALE ASReml code action yield MO changes the zero entries in yield to missing values yield 0 takes natural logarithms of the yield data score 5 subtracts 5 from all values in score score ISET 0 5 1 5 2 5 replaces data values of 1 2 and 3 with 0 5 1 5 and 2 5 respectively 5 Command file Reading the data 62 ASReml code action score 5SUB 0 5 1 5 2 5 block 8 variety 20 yield plot variety SEQ Var 3 Nit 4 VxN 12 Var 1 4 4 Nit YA V98 YA NA O YB V99 YB NA O V98 DO replaces data values of 0 5 1 5 and 2 5 with 1 2 and 3 respectively a data value of 1 51 would be replaced by 0 since it is not in the list or very close to a number in the list in the case where there are multiple units per plot contiguous plots have different treatments and the records are sorted units within plots within blocks this code generates a plot factor assuming a new plot whenever t
113. mu variety r repl predict variety 00414 repl 1 repl 0 IDV 0 1 ter any tabulate statements or after the R and G structure lines The syntax is predict factors qualifiers e predict must be the first element of the predict statement commencing in column 1 in upper or lower case e factors is a list of the variables defining a multiway table to be predicted each variable may be followed by a list of specific levels values to be predicted or the name of the file that contains those values the qualifiers listed in Table 10 1 modify the predictions in some way e apredict statement may be continued on subsequent lines by terminating the current line with a comma 10 Tabulation of the data and prediction from the model 180 e several predict statements may be specified ASReml parses each predict statement before fitting the model If any syntax problems are encountered these are reported in the pvs file after which the statement is ignored the job is completed as if the erroneous prediction statement did not exist The predictions are formed as an extra process in the final iteration and are reported to the pvs file Consequently aborting a run by creating the ABORTASR NOW file see page 70 will cause any predict statements to be ignored Create FINALASR NOW instead of ABORTASR NOW to make the next iteration the final iteration in which prediction is performed By default factors are predicted at each
114. name used on the top job control line Detailed descriptions follow 11 Command file Running the job 198 Table 11 1 Command line options option qualifier type action Frequently used command line options Cc N Ww Other command line options Bb Gg Hg Rr Ss Yv CONTINUE FINAL LOGFILE NOGRAPHS WORKSPACE w ARGS a ASK IBRIEF b DEBUG DEBUG 2 GRAPHICS g HARDCOPY g INTERACTIVE JOIN ONERUN NA QUIET RENAME NA YVAR v NA job control job control screen output graphics workspace job control job control output control debug debug graphics graphics graphics output control job control post processing graphics job control workspace job control license continue iterations using previous esti mates as initial values continue for one more iteration using previous estimates as initial values copy screen output to basename asl suppress interactive graphics set workspace size to w Mbyte to set arguments a in job rather than on command line prompt for options and arguments reduce output to asr file invoke debug mode invoke extended debug mode set interactive graphics device set interactive graphics device graphics screens not displayed display graphics screen concatenate CYCLE output files override rerunning requested by RENAME calculation of functions of v
115. names in v may optionally be followed by a list of levels for inclusion if such a list has not been supplied in the specification of the classify set ASReml works out what combi nations are present from the design matrix It may have trouble with complicated models such as those involving and terms A second PRESENT qualifier is allowed on a predict statement but not with PRWTS The two lists must not overlap PRWTS v is used in conjunction with the first PRESENT v list to specify the weights that ASReml will use for averaging that PRESENT table More details are given below Controlling inclusion of model terms EXCEPT t causes the prediction to include all fitted model terms not in t IGNORE t causes ASReml to set up a prediction model based on the default rules and then removes the terms in t This might be used to omit the spline Lack of fit term IGNORE fac x from predictions as in yield mu x variety r spl x fac x predict x IGNORE fac x which would predict points on the spline curve averaging over variety ONLYUSE t causes the prediction to include only model terms in t It can be used for example to form a table of slopes as in HI mu X variety X variety predict variety X 1 onlyuse X X variety IUSE t causes ASReml to set up a prediction model based on the default rules and then adds the terms listed in t Printing IDEC n gives the user control of the number of decimal places reported in the
116. negative The size may be set in the third argument by setting the second argument to zero uni f k n creates a factor with a level for every record subject to the factor level of f equalling k i e a new level is created for the factor whenever a new record is encountered whose integer truncated data value from data field fis k Thus uni site 2 would be used to create an independent error term for site 2 in a multi environment trial and is equivalent to at site 2 units The default size of this model term is the number of data records The user may specify a lower number as the third argument There is little computational penalty from the default but the s1n file may be substantially larger than needed However if the units vector is full size the effects are mapped by record number and added back to the fitted residual for creating residual plots vect v is used in a multivariate analysis on a multivariate set of covariates v ASReml3 to pair them with the variates The test example included signal G 93 93 slides background G 93 dart asd ASUV signal Trait Trait vect background to fit a slide specific regression of signal on background In this ex ample signal is a multivariate set of 93 variates and background is a set of 93 covariates The signal values relate to either the Red or Green channels So for each slide and channel we need to fit a simple regres sion of signal mu background But the data for the 93
117. not appear to adequately cover the data values prevents the automatic reversal of the order of the fixed terms in the dense equations and possible reordering of terms in the sparse equations forces ASReml to hold the data in memory ASReml will usu ally hold the data on a scratch file rather than in memory In large jobs the system area where scratch files are held may not be large enough A Unix system may put this file in the tmp directory which may not have enough space to hold it affects the number of distinct points recognised by the pol model function Table 6 1 The default value of n is 1000 so that points closer than 0 1 of the range are regarded as the same point influences the number of points used when predicting splines and polynomials The design matrix generated by the leg pol and sp1 functions are modified to include extra rows that are accessed by the PREDICT directive The default value of n is 21 if there is no PPOINTS qualifier The range of the data is divided by n 1 to give a step size i For each point p in the list a predict point is inserted at p i if there is no data value in the interval p p 1 1x i PPOINTS is ignored if PVAL is specified for the variable This process also effects the number of levels identified by the fac model term forces ASReml to attempt to produce the standard output re port when there is a failure of the iteration algorithm Usu ally no report is produced
118. number of levels in the term or the name of a factor that has the same number of levels as the component key is usually zero but for power models EXP GAU provides the distance data needed to construct the model model is the ASReml variance model identifier acronym selected for the term variance models are listed in Table 7 3 these models have associated variance parameters initial_values are initial or starting values for the variance parameters the values for initial values are as described above for R structure definition lines qualifier tells ASReml to modify the variance model in some way the qualifiers are described in Table 7 4 7 Command file Specifying the variance structures 132 7 5 Variance model description Table 7 3 presents the full range of variance models that is correlation homo geneous variance and heterogeneous variance models available in ASReml The table contains the model identifier a brief description its algebraic form and the number of parameters The first section defines BASE correlation models and in the next section we show how to extend them to form variance models The second section defines some models parameterized as variance covariance matri ces rather than as correlation matrices The third section covers some special cases where the covariance structure is known except for the scale Note that in Important many cases the variance or scaling parameter will actua
119. oa TOR BRL U S 11 column AR1 0 3 e sis used to code the number of independent repli 1 sections in the error term repl 0 IDV 0 1 if s 0 the default IID R structure is assumed and no R structure definition lines are required as in examples 2b and 5 if s gt 0 s R structure definitions are required one for each of the s sections as in examples 3a 3b 3c and 4 for the analysis of multi section data s can be replaced by the name of a factor with the appropriate number of levels one for each section e cis the number of component variance models involved in the variance struc ture for the error term for each section for example 3a 3b and 3c have column row as the error term and the variance structure for column row in volves 2 variance models the first for column and the second for row c has a default value of 2 when s is not specified as zero 7 Command file Specifying the variance structures 129 See Table 7 3 See Section 7 7 e g is the number of variance structures G structures that will be explicitly specified for the random terms in the model R and G structures are now discussed with reference to s c and g As already noted each variance structure may involve several variance models which relate to the individual terms involved in the random effect or error For example a two factor interaction may have a variance model for each of the two factors involved in the interaction Varianc
120. of a each has the size of b For example if site and geno are factors with 3 and 10 lev els respectively then for at site geno ASReml constructs 3 model terms at site 1 geno at site 2 geno at site 3 geno each with 10 levels this is similar to forming an interaction except that a separate model term is created for each level of the first factor this is useful for random terms when each component can have a different variance The same effect is achieved by using an interaction e g site geno and associating a DIAG variance structure with the first component see Section 7 5 any at term to be expanded MUST be the FIRST component of the interaction geno at site will not work at site 1 at year geno will not work but at year at site 1 geno is OK the at factor must be declared with the correct number of levels because the model line is expanded BEFORE the data is read Thus if site is declared as site or site A in the data definitions at site geno will expand to at site 01 geno at site 02 geno regardless of the actual number of sites Associated Factors Sometimes there is a hierarchical structure to factors which should be recognised as it aids formulation of prediction tables see ASSOCIATE qualifier on page 188 Common examples are Genotypes grouped into Families and Locations grouped by Region We call these associated factors The key characteristic of associated factors is that they are coded
121. on these messages 15 2 Common problems Common problems in coding ASReml are as follows a variable name has been misspelt variable names are case sensitive a model term has been misspelt model term functions and reserved words mu Trait mv units are case sensitive 15 Error messages 248 the data file name is misspelt or the wrong path has been given enclose the pathname in quotes if it includes embedded blanks a qualifier has been misspelt or is in the wrong place there is an inconsistency between the variance header line and the structure definition lines presented failure to use commas appropriately in model definition lines there is an error in the R structure definition lines there is an error in the G structure definition lines there is a factor name error there is a missing parameter there are too many few initial values there is an error in the predict statement model term mv not included in the model when there are missing values in the data and the model fitted assumes all data is present The most common problem in running ASReml is that a variable label is misspelt The primary file to examine for diagnostic messages is the asr file When ASReml finds something atypical or inconsistent it prints an diagnostic message If it fails to successfully parse the input it dumps the current information to the asr file Below is the output for a job that has been terminated due to
122. one parameter The initial values for the variance parameters are listed after 7 Command file Specifying the variance structures 138 ASReml2 the initial values for the correlation parameters For example in AR1IV 0 3 0 5 0 3 is the initial spatial correlation parameter and 0 5 is the initial variance parameter value wxw Similarly if X then is the heterogeneous variance matrix corresponding to C 5 DCD where D diag o In this case there are an additional w parameters For example the heterogeneous variance model corresponding to ID is specified 2 2 IDH in the ASReml command file see below involves the w parameters of og and is the variance matrix o 0 0 0 o 0 un 0 0 o Notes on the variance models These notes provide additional information on the variance models defined in Table 7 3 e the IDH and DIAG models fit the same diagonal variance structure the CORGH and US models fit the same completely general variance structure parameterized differently e in CHOLk models LDI where L is lower triangular with ones on the diagonal D is diagonal and k is the number of non zero off diagonals in L e in CHOLKC models LDL where L is lower triangular with ones on the diagonal D is diagonal and k is the number of non zero sub diagonal columns in L This is somewhat similar to the factor analytic model e in ANTEk models Xt U DU where U is upper triangul
123. play a role in modelling the conditional curves for each tree and variance modelling The intercept and slope for each tree are included as random coefficients denoted by RC in Table 16 11 Thus if U is the matrix of intercepts column 1 and slopes column 2 for each tree then we assume that var vec U X I where is a 2 x 2 symmetric positive definite matrix Non smooth variation can be modelled at the overall mean across trees level and this is achieved in ASReml by inclusion of fac age as a random term 16 Examples 327 Table 16 11 Orange data AOV decomposition stratum decomposition type df or ne constant 1 F 1 age age F 1 spl age 7 R 5 fac age R T tree tree RC 5 age tree x tree RC 5 spl age 7 tree R 25 error R An extract of the ASReml input file is circ mu age r Tree 4 6 Tree age 000094 spl age 7 1 spl age 7 Tree 2 3 fac age 13 9 oO 2 Tree 2 2 0 US 4 6 00001 000094 50 0 predict age Tree IGNORE fac age We stress the importance of model building in these settings where we generally commence with relatively simple variance models and update to more complex variance models if appropriate Table 16 12 presents the sequence of fitted mod els we have used Note that the REML log likelihoods for models 1 and 2 are comparable and likewise for models 3 to 6 The REML log likelihoods are not comparable between these groups due to the inclusion of the fixed season term
124. sites to produce variety predictions 11 Command file Running the job Introduction The command line Normal run Processing a pin file Forming a job template Command line options Prompt for arguments Output control command line options Debug command line options Graphics command line options Job control command line options Workspace command line options Menu command line options Non graphics command line options Examples Advanced processing arguments Standard use of arguments Prompting for input Paths and Loops 194 11 Command file Running the job 195 11 1 Introduction The command line its options and arguments are discussed in this chapter Com mand line options enable more workspace to be accessed to run the job control some graphics output and control advanced processing options Command line arguments are substituted into the job at run time As Windows likes to hide the command line most command line options can be set on an optional initial line of the as file we call the top job control line to distinguish it from the other job control lines discussed in Chapter 6 If the first line of the as file contains a qualifier other than DOPATH it is interpreted as setting command line options and the Title is taken as the next line 11 2 The command line Normal run The basic command to run ASReml is path ASRem1 basename as c e path provides the path to the ASReml program usually called
125. square parentheses indicate elements that might be omitted lt basename gt is the name portion of the as file lt args gt is any argument strings built into the output names by use of the RENAME qualifier lt type gt indicates the contents of the figure as given in the following table lt pass gt is inserted when the job is repeated RENAME or CYCLE to ensure filenames are unique across repeats lt section gt is inserted to distinquish files produced from different sections of data for example from multisite spatial analysis and lt ezt gt indicates the file graphics format lt type gt file contents R marginal means of residuals from spatial analysis of a section V variogram of residuals from spatial analysis for a section S_ residuals in field plan for a section H histogram of residuals for a section _RvE residuals plotted against expected values XYGi figure produced by X Y and G qualifiers PV_i Predicted values plotted for PREDICT directive 7 The graphics file format is specified by following the G or H option by a number g or specifying the appropriate qualifier on the top job control line as follows 11 Command file Running the job 201 ASReml2 ASReml2 g qualifier description lt ext gt 1 HPGL HP GL pgl IPS Postscript default ps 6 BMP BMP bmp 10 WPM Windows Print Manager 11 WMF Windows Meta File wmf 12 HPGL 2 HP GL2 hgl 21 PNG PNG png 22 EPS EncapsulatedPostScript eps
126. such that the levels of one are uniquely nested in the levels of another If one is unknown coded as missing all associated factors must 6 Command file Specifying the terms in the mixed model 103 be unknown for that data record It is typically unnecessary to interact associated factors except when required to adequately define the variance structure 6 6 Alphabetic list of model functions Table 6 2 presents detailed descriptions of the model functions discussed above Note that some three letter function names may be abbreviated to the first letter Table 6 2 Alphabetic list of model functions and descriptions model function action and t r overlays adds r times the design matrix for model term t to the existing a t r design matrix Specifically if the model up to this point has p effects and t has a effects the a columns of the design matrix for t are multiplied by the scalar r default value 1 0 and added to the last a of the p columns already defined The overlaid term must agree in size with the term it overlays This can be used to force a correlation of 1 between two terms as in a diallel analysis male and female assuming the ith male is the same individual as the ith female Note that if the overlaid term is complex it must be predefined e g Tr male Tr female and Tr female at f n defines a binary variable which is 1 if the factor f has level n for the Cf n record For example to fit a row factor onl
127. table is exceeded There is room for three structures for each model term for which G structures are explicitly declared The error might occur when ASReml needs to construct rows of the table for structured terms when the user has not formally declared the struc tures Increasing g on the variance header line for the number of G structures see page 128 will increase the space allocated for the table You will need to add extra explicit declara tions also check the pedigree file and see any messages in the output Check that identifiers and pedi grees are in chronological order the A inverse factors are not the same size as the A inverse Delete the ainverse bin file and rerun the job Typically this arises when there is a problem processing the pedigree file Check the details for the distance based vari ance structure 15 Error messages 274 Table 15 3 Alphabetical cause s remedies list of error messages and probable error message probable cause remedy POWER Model Unique points disagree with size PROGRAM failed in PROGRAMMING error reading SELF option Reading distances for POWER structure Reading factor names reading Overdispersion factor READING OWN structures Reading the data Reading Update step size Residual Variance is Zero Check the distances specified for the distance based variance structure Try increasing workspace Otherwise send prob
128. table of predicted values where n is 0 9 The default is 4 G15 9 format is used if n exceeds 9 When VVP or SED are used the values are displayed with 6 significant digits unless n is specified and even then the values are displayed with 9 significant digits 10 Tabulation of the data and prediction from the model 185 Table 10 1 List of prediction qualifiers qualifier action PLOT a instructs ASReml to attempt a plot of the predicted values This ASReml2 qualifier is only applicable in versions of ASReml linked with the Winteracter Graphics library If there is no argument ASReml produces a figure of the predicted values as best it can The user can modify the appearance by typing lt Esc gt to expose a menu or with the plot arguments listed in Table 10 2 PRINTALL instructs ASReml to print the predicted value even if it is not of an estimable function By default ASReml only prints predic tions that are of estimable functions SED requests all standard errors of difference be printed Normally only an average value is printed Note that the default average SED is actually an SED calculated from the average variance if the predicted values and the average covariance among the predicted values rather than being the average of the individual SED values However when SED is specified the average of the individual SED values is reported TDIFF requests t statistics be printed for all combinations of predicted
129. tells ASReml that the variance model for replicates is IDV of order 4 o7 The 0 1 is a starting value for yr 02 02 a starting value must be specified Finally the second element 0 on the last line of the file indicates that the effects are in standard order There is almost always a O no sorting in this position for G structures The following points should be noted the 4 on the final line could have been written as rep1 to give repl 0 IDV 0 1 This would tell ASReml that the order or dimension of the IDV variance model is equal to the number of levels in rep1 4 in this case when specifying G structures the user should ensure that one scale parameter is present ASReml does not automatically include and estimate a scale param eter for a G structure when the explicit G structure does not include one For this reason the model supplied when the G structure involves just one variance model must not be a correlation model all diagonal elements equal 1 all but one of the models supplied when the G structure involves more than one variance model must be correlation models the other must be either an homogeneous or a heterogeneous variance model see Section 7 5 for the distinction between these models see also 5 for an example an initial value must be supplied for all parameters in G structure definitions ASReml expects initial values immediately after the variance model identifier 7 Command file Specifying the varia
130. the figure 1 indicates the proportion of TotalVar explained by the first load ing 2 indicates the proportion explained by first and second provided it plots right of 1 Consequently the distance from 2 to the right margin represents PsiVar expl reports the percentage of TotalVar explained by all loadings The last row contains column averages The rsv file The rsv file contains the variance parameters from the most recent iteration of a model The primary use of the rsv file is to supply the values for the CONTINUE qualifier see Table 5 4 and the C command line option see Table 11 1 It contains sufficient information to match terms so that it can be used when the variance model has been changed This is nin89a rsv 76 6 1690 120 0 000000 0 000000 0 000000 1 000000 0 6555046 0 4374830 RSTRUCTURE 1 2 VARIANCE 1 1 0 1 00000 STRUCTURE 22 1 1 0 655505 STRUCTURE 11 1 1 0 437483 The tab file The tab file contains the simple variety means and cell frequencies Below is a cut down version of nin89 tab nin alliance trial 10 Sep 2002 04 20 15 14 Description of output files 241 Simple tabulation of yield variety LANCER 28 56 4 BRULE 26 07 4 REDLAND 30 50 4 CODY 2120 4 ARAPAHOE 29 44 4 NE83404 27 39 4 NE83406 24 28 4 NE83407 22 69 4 CENTURA 21 65 4 SCOUT66 27 52 4 COLT 27 00 4 NE87615 25 69 4 NE87619 31 20 4 NE87627 23 23 4 The vrb file The vrb file contains the estimates of the effects together with
131. the next line You have probably mis specified the number of levels in the factor or omitted the I qual ifier see Section 5 4 on data field definition syntax ASReml corrects the number of lev els the term did not appear in the model the term did not appear in the model 15 Error messages 265 Table 15 2 List of warning messages and likely meaning s warning message likely meaning Warning term is ignored for prediction Warning Check if you need the RECODE qualifier Warning Code B fixed at a boundary GP Warning Dropped records were not evenly distributed across Warning Eigen analysis check of US matrix skipped WARNING Extra lines on the end of the input file Warning Failed to find header blocks to skip Warning Fewer levels found in term Warning FIELD DEFINITION lines should be INDENTED Warning Fixed levels for factor Warning Initial gamma value is Zero Warning Invalid argument Warning It is usual to include Trait in the model Warning LogL Converged Parameters Not Converged Warning LogL not converged terms like units and mv cannot be included in prediction RECODE may be needed when using a pedigree and reading data from a binary file that was not prepared with ASReml suggest drop the term and refit the model MVREMOVE has been used to delete records which have a missing value in design vari ables This has resulted in multi
132. the processing time when compared to the alternative of using MAXIT 1 rather than a tt BLUP n qual ifier However MAXIT 1 does result in complete and correct output sets the number of equations solved densely up to a maximum of 5000 By default sparse matrix methods are applied to the random effects and any fixed effects listed after random fac tors or whose equation numbers exceed 800 Use DENSE n to apply sparse methods to effects listed before the r reduc ing the size of the DENSE block or if you have large fixed model terms and want Wald F statistics calculated for them Individual model terms will not be split so that only part is in the dense section n should be kept small lt 100 for faster processing alters the error degrees of freedom from v to v n This qualifier might be used when analysing pre adjusted data to reduce the degrees of freedom n negative or when weights are used in lieu of actual data records to supply error infor mation n positive The degrees of freedom is only used in the calculation of the residual variance in a univariate single site analysis The option will have no effect in analyses with multiple error variances for sites or traits other than in the reported degrees of freedom Use ADJUST r rather than DF n if r is not a whole number Use with YSS r to supply variance when data fully fitted 5 Command file Reading the data 82 Table 5 5 List of rarely used job control qual
133. to manually cover a grid of v values We note that there is non uniqueness in the anisotropy parameters of this metric d since inverting and adding 5 to a gives the same distance This non uniqueness can be removed by considering 0 lt a lt 5 and 6 gt 0 or by considering 0 lt a lt q7andeither0 lt 6 lt 1ord gt 1 With 2 isotropy occurs when 6 1 and then the rotation angle a is irrelevant correlation contours are circles compared with ellipses in general With A 1 correlation contours are diamonds 7 Command file Specifying the variance structures 141 Notes on power models Power models rely on the definition of distance for the associated term for ex ample the distance between time points in a one dimensional longitudinal analysis the spatial distance between plot coordinates in a two dimensional field trial analysis Information for determining distances is supplied by the key argument on the structure line For one dimensional cases key may be the name of a data field containing the coordinate values when it relates to an R structure 0 in which case a vector of coordinates of length order must be supplied after all R and G structure lines fac x when it relates to model term fac z In two directions IEXP IGAU IEUC AEXP AGAU MATn the key argument also depends on whether it relates to an R or G structure For an R structure use the form rrcc where rr is the number of
134. to consider the two component terms as a single term which gives rise to a single G structure This concept is discussed later 2 2 Estimation Estimation involves two processes that are closely linked They are performed within the engine of ASReml One process involves estimation of 7 and predic tion of u although the latter may not always be of interest for given 0 and y The other process involves estimation of these variance parameters Note that in the following sections we have set 0 1 to simplify the presentation of results Estimation of the variance parameters Estimation of the variance parameters is carried out using residual or restricted maximum likelihood REML developed by Patterson and Thompson 1971 An historical development of the theory can be found in Searle et al 1992 Note firstly that y N X7 H 2 3 2 Some theory 12 where H R ZGZ REML does not use 2 3 for estimation of variance parameters but rather uses a distribution free of 7 essentially based on error contrasts or residuals The derivation given below is presented in Verbyla 1990 We transform y using a non singular matrix L L L such that LX l LhX 0 v on 7 LHL LAL Yo 0 LHL LLHL The full distribution of L y can be partitioned into a conditional distribution namely y Yyo for estimation of T and a marginal distribution based on y for estimation of y and the latter is the basis of
135. to in a transformation Vi always refers to field variable i in a transformation statement Variables that are not initialized from the data file are initialized to missing value for the first record and otherwise to the values from the preceding record after transformation Thus A B LagA V4 V4 A reads two fields A and B and constructs LagA as the value of A from the previous record by extracting a value for LagA from working variable V4 before loading V4 with the current value of A Transformation syntax Transformation qualifiers have one of seven forms namely operator to perform an operation on the current field for example absY ABS to take absolute values operator value to perform an operation involving an argument on the current field for example logY Y 0 copies Y and then takes logs operator V field to perform an operation on the current field us ing the data in another field for example V2 to subtract field 2 from the current field Warning 5 Command file Reading the data 55 ASReml3 1V target to reset the focus for subsequent transformations to field number target TARGET target to reset the focus for subsequent transformations to the previously named field target Vtarget value to change all of the data in a target field to a given value 1V target V field to overwrite the data in a target field by the data values of another field a special case is when field
136. to the gaussian correlation function The metric parameter A is not estimated by ASReml it is usually set to 2 for Euclidean distance Setting A 1 provides the cityblock metric which together with v 0 5 models a separable AR1xAR1 process Cityblock metric may be appropriate when the dominant spatial processes are aligned with rows columns as occurs in field experiments Geometric anisotropy is discussed in most geo statistical books Webster and Oliver 2001 Diggle et al 2003 but rarely are the anisotropy angle or ratio estimated from the data Similarly the smoothness parameter v is often set a priori Kammann and Wand 2003 Diggle et al 2003 However Stein 1999 and Haskard 2006 demonstrate that v can be reliably esti mated even for modest sized data sets subject to caveats regarding the sampling design The syntax for the Mat rn class in ASReml is given by MATk where k is the number of parameters to be specified the remaining parameters take their default values Use the G qualifier to control whether a specified parameter is estimated or fixed The order of the parameters in ASReml with their defaults is v 0 5 6 1 a 0 A 2 For example if we wish to fit a Mat rn model with only og estimated and the other parameters set at their defaults then we use MAT1 MAT2 allows v to be estimated or fixed at some other value for example MAT2 2 1 GPF The parameters and v are highly correlated so it may be better
137. trial ASAVE region location while predict mu ASSOC region location trial ASAVE region gives a value of 11 58 being the average of region means 11 83 and 11 33 obtained by averaging trials within regions from Table 10 4 and predict mu ASSOCIATE region location trial ASAVE location predicts mu as 11 38 the average of the 8 location means in Table 10 5 Further discussion of associated factors The user may specify their own weights using file input if necessary Thus predict region ASAVERAGE location 1 2 3 6 1 1 1 2 1 6 would give region predictions of 11 67 and 10 84 respectively derived from the location predictions in Table 10 5 Note that because location is nested in region the location weights should sum to 1 0 within levels of region when forming region means The AVERAGE ASAVERAGE qualifier allows the weights to be read from a file which the user can create elsewhere Thus the code ASAVERAGE trial Tweight csv 2 will read the weights from the second field of file Tweight csv The user must ensure the weights are in the coding order ASReml uses trial order in this instance given in the s1n file or by using the TABULATE command It was noted that it is the base ASSOCIATE factor that is formally included in the hyper table If the lowest stratum is random it may be appropriate to ignore it Omitting it from the ASSOCIATE list will allow it to reenter the Ignore set Specifying it with the IGNORE qualif
138. using the EXPH model which models by y D 5CD 16 Examples 294 Residuals plotted against Row and Column position 1 1 34 86 Range 45 1 g le Q 8 Q 8 f i fe g 8 ie o o o Lel 0 O 8 le SEN 8 aa hae 8 A 4 g g gor omy EN ay Sy i Q ie Figure 16 4 Residual plots for the EXP variance model for the plant data where D is a diagonal matrix of variances and C is a correlation matrix with elements given by cj glti til The coding for this is yl y3 y5 y7 y10 Trait tmt Tr tmt 129 14 82 Tr O EXPH 5 100 200 300 300 300 135 7 10 Note that it is necessary to fix the scale parameter to 1 S2 1 to ensure that the elements of D are identifiable Abbreviated output from this analysis is OANDOAFWNH RH p e Source Residual Residual LogL 195 LogL 179 LogL 175 LogL 173 LogL 171 LogL 171 LogL 171 LogL 171 LogL 171 LogL 171 598 036 483 128 980 615 527 504 498 496 S52 S52 S52 S52 2 S2 S52 S2 S52 S2 Model POW EXP POW EXP PRPRPRPPRPRPRRP RE 0000 60 0000 60 0000 60 0000 60 0000 60 0000 60 0000 60 0000 60 0000 60 0000 60 terms Gamma 6 0 906917 5 60 9599 af df af df df af df ar df df 1 components constrained Component 0 906917 60 9599 Comp SE 21 89 2 12 6 OU oU 16 Examples 295 Residual POW EXP 5 72 9904 Residual POW EXP 5 309 259 Re
139. using the OWN structure rep blcol blrow variety 25 yield barley asd skip 1 OWN MYOWN EXE y variety 12 10 O AR1 1 15 0 OWN2 2 1 TRR The file written by ASReml has extension own and looks like 15 2 1 0 6025860D 000 1164403D 00 This file was written by asreml for reading by your program MYOWNGDG asreml writes this file runs your program and then reads shfown gdg which it presumes has the following format The first lines should agree with the top of this file specifying the order of the matrices C 15 the number of variance parameters 2 and a control parameter you can specify 1 These are written in 315 format They are followed by the list of variance parameters written in 6D13 7 format 7 Command file Specifying the variance structures 145 Follow this with 3 matrices written in 6D13 7 format These are to be each of 120 elements being lower triangle row wise of the G matrix and its derivatives with respect to the parameters in turn This file contains details about what is expected in the file written by your pro gram The filename used has the same basename as the job you are running with extension own for the file written by ASReml and gdg for the file your program writes The type of the parameters is set with the T qualifier described below The control parameter is set using the F qualifier F2 applies to OWN models With OWN the argument of F is passed to the MYOWNGDG progr
140. variance parameters The constraint lines occur after the G structures are defined The constraints are described in Section 7 9 The variance header line Section 7 4 must be present even ifonly 0 0 0 indicating there are no explicit R or G structures see Section 7 9 5 Command file Reading the data 89 Table 5 5 List of rarely used job control qualifiers qualifier action VGSECTORS s requests that the variogram formed with radial coordinates see page 19 be based on s 4 6 or 8 sectors of size 180 s degrees The default is 4 sectors if VGSECTORS is omitted and 6 sectors if it is specified without an argument The first sector is centred on the X direction Figure 5 1 is the variogram using radial coordinates obtained using predictors of random effects fitted as fac xsca ysca It shows low semivariance in xsca direction high semivari ance in the ysca direction with intermediate values in the 45 and 135 degrees directions controls the form of the yht file YHTFORM 1 suppresses formation of the yht file YHTFORM 1 is TAB separated yht becomes _yht txt YHTFORM 2 is COMMA separated yht becomes _yht csv YHTFORM 3 is Ampersand separated yht becomes yht tex adds r to the total Sum of Squares This might be used with DF to add some variance to the analysis when analysing summarised data Table 5 6 List of very rarely used job control qualifiers action ASReml2 YHTFORM f
141. 0 S2 78387 665 df 5 LogL 4226 02 S2 75375 665 df 6 LogL 4225 64 S2 77373 665 df 7 LogL 4225 60 S2 77710 665 df 8 LogL 4225 60 52 77786 665 df 9 LogL 4225 60 S2 77806 665 df Source Model terms Gamma Component Comp SE C variety 532 532 1 14370 88986 3 9 91 OP Variance 670 665 1 00000 77806 0 8 79 O P Residual AR AutoR 67 0 671436 0 671436 15 66 OU Residual AR AutoR 10 0 266088 0 266088 3 538 OU Outer displacement Mher displacement Figure 16 6 Sample variogram of the residuals from the AR1xAR1 model for the Tullibigeal data Outer displacement Aer displacement Figure 16 7 Sample variogram of the residuals from the ARIxXAR1 pol column 1 model for the Tullibigeal data 16 Examples 310 Wald F statistics Source of Variation NumDF DenDF 7 mu 1 42 5 3 weed 1 457 4 8 pol column 1 1 50 8 AR1xAR1 units pol column 1 1 LogL 4272 74 S2 0 11683E 06 665 df 2 LogL 4266 07 S2 50207 665 df 3 LogL 4228 96 S2 76724 665 df 4 LogL 4220 63 S2 55858 665 df 5 LogL 4220 19 S2 54431 665 df 6 LogL 4220 18 S2 54732 665 df 7 LogL 4220 18 S2 54717 665 df 8 LogL 4220 18 S2 54715 665 df Source Model terms Gamma C variety 532 532 1 34824 units 670 670 0 556400 Variance 670 665 1 00000 Residual AR AutoR 67 0 837503 Residual AR AutoR 10 0 375382 Source of Variation 7 mu 3 weed 8 pol column 1 F_inc TO73 7 0 91 91 6 73 Prob lt 001 lt 001 0 005
142. 007 S2 0 52814E 01 255 df LogL 203 240 S2 0 51278E 01 255 df LogL 203 242 S2 0 51141E 01 255 di LogL 203 242 S2 0 51140E 01 255 df Source Model terms Gamma Component Comp SE C setstat 10 10 0 233418 0 119371E 01 1 35 OP setstat regulatr 80 64 0 601817 0 307771E 01 3 64 OP teststat 4 4 0 642752E 01 0 328706E 02 0 98 Q P setstat teststat 40 40 0 100000E 08 0 511404E 10 0 00 OB Variance 256 255 1 00000 0 511404E 01 9 72 OP Warning Code B fixed at a boundary GP F fixed by user liable to change from P to B P positive definite C Constrained by user VCC U unbounded S Singular Information matrix The convergence criteria has been satisfied after six iterations A warning message in printed below the summary of the variance components because the variance component for the setstat teststat term has been fixed near the boundary The default constraint for variance components GP is to ensure that the REML estimate remains positive Under this constraint if an update for any variance component results in a negative value then ASReml sets that variance component to a small positive value If this occurs in subsequent iterations the parameter is fixed to a small positive value and the code B replaces P in the C column of the summary table The default constraint can be overridden using the GU qualifier but it is not generally recommended for standard analyses Figure 16 2 presents the residual plot which indicates two unusua
143. 008 16 21 52 609 Structure Factor mismatch 8 A misspelt factor name in the predict statement The final error in the job is that a factor name is misspelt in the predict state ment This is a non fatal error The asr file contains the messages Notice Invalid argument unrecognised qualifier or vector space exhausted at voriety Warning Extra lines on the end of the input file are ignored from predict voriety see Chapter 14 The faulty statement is otherwise ignored by ASReml and no pvs file is pro duced To rectify this statement correct voriety to variety 9 Forgetting mv in a spatial analysis The first error message from running part 2 of the job is R structures imply 0 242 records only 224 exist Checking the seventh line of the output below we see that there were 242 records read but only 224 were retained for analysis There are three reasons records are dropped 1 the FILTER qualifier has been specified 2 the D transformation qualifier has been specified and 3 there are missing values in the response variable and the user has not specified that they be estimated The last applies here so we must change the model line to read yield mu variety mv Folder C data ex manex variety A QUALIFIERS SKIP 1 QUALIFIER DOPART 2 is active Reading nin asd FREE FORMAT skipping 1 lines Univariate analysis of yield Using 224 records of 242 read 15 Error messages 261 Model term Size miss zero M
144. 02 452 0 2465 0 08907 0 083022 100101 16 3 0 2917D 01 452 0 2642 0 02384 0 01736 010101 17 3 0 2248D 01 452 0 2657 0 01838 0 01187 0 O 1 1 0 1 18 3 0 1111D 02 452 0 2460 0 09088 0 08484 101001 19 3 0 1746D 01 452 0 2668 0 01427 0 00773 0O 1 1 0 0 1 20 3 0 1030D 02 452 0 2478 0 08423 0 07815 1 1 0001 21 3 0 1279D 02 452 0 2423 0 10454 0 09860 1 0 000 1 22 3 0 8086D 01 452 0 2527 0 06609 0 05989 0 10001 23 3 0 7437D 01 452 0 2542 0 06079 0 05456 0 0 1 0 0 1 24 3 0 1071D 02 452 0 2469 0 08755 0 08149 0 0 O 1 0 1 25 3 0 1370D 02 452 0 2403 0 11200 0 10611 000011 FORK RK 26 3 0 1511D 02 452 0 2372 0 12351 0 11770 100010 FORK RK 27 3 0 1353D 02 452 0 2407 0 11064 0 10473 0 10010 680 3 0 1057D 02 452 0 2472 0 08641 0 08035 1 1 0 0 0 0 The sln file fitted fitted fitted fitted fitted 33 32 31 0 0 o ooo eeereerOoOOCOOCOOOCOODOOCOODOOODOOO 0 0 oob eaooocnoon ooo ooo 9 D S 0 ooo eoooooooc ooo Ceo oSs C OQARA O OCOOON GUO 30 29 28 0 0 ooo CE E A E E E E AEE 0 coo SSeoooooocoooeooooe 3 0 ao 2 CE E E E E E E E E T I oo 6 So s08 08 42 04 J09 50 12 03 40 st J01 26 1 44 w w w w w w w w w w w w B 7 are zero 672 are zero 2199 singular 2198 singular 0 154 OTTI 0 518 0 838 0 929 0 088 0 613 0 234 27 26 25 24 23 000 0 0 ooo ooo ooo emo ooo oko momo me 00 0 0 0 0 0 ae e SSGooeo
145. 1 at Trait 1 age grp 0024 at Trait 2 age grp 0019 at Trait 4 age grp 0020 at Trait 5 age grp 00026 at Trait 1 sex grp 93 at Trait 2 sex grp 16 0 at Trait 3 sex grp 28 at Trait 5 sex grp 1 18 tf Tr grp 16 Examples 345 123 0 0 0 Tr US 15 0 TY sire 2 PATH 1 Tr 0 DIAG 0 608 1 298 0 015 0 197 0 035 PATH 2 Tr 0 FAL GP 0 5 0 5 08 2 01 0 1 0 608 1 296 0 015 0 197 0 035 PATH 3 Te 9 US 0 6199 0 6939 1 602 1 R structure with 2 dimensions and 3 G structures Independent across animals General structure across traits Asreml will estimate some starting values Sire effects Initial analysis ignoring genetic correlations Specified diagonal variance structure Initial sire variances Factor Analytic model Correlation factors Variances Unstructured variance model Lower triangle row wise 0 003219 0 007424 0 01509 0 02532 0 05840 0 0002709 0 1807 0 06013 0 1387 PATH sire 0 0006433 0 005061 0 03487 Maternal structure covers the 3 model terms ae at Tr 1 dam 2 PATH 1 3 0 CORGH GU Aal 2 2 4 14 0 018 IPATH 2 3 0 CORGH GU wie gt 2 2 4 14 0 018 IPATH 3 3 0 US GU i 2 2 4 14 0 018 PATH dam at Tr 1 dam at Tr 2 dam at Tr 3 dam Maternal effects Equivalent to Unstructured 16 Examples 346 Litter structure covers the 4 model terms at Tr 1 lit at Tr 2 1lit fae Ts 3 lit at Tr 4 lit
146. 1 exp x 2 3 where y is the trunk circumference x is the tree age in days since December 31 1968 1 is the asymptotic height 2 is the inflection point or the time at which the tree reaches 0 5 1 3 is the time elapsed between trees reaching half and about 3 4 of 1 y 16 11 The datafile consists of 5 columns viz Tree a factor with 5 levels age tree age in days since 31st December 1968 circ the trunk circumference and season The last column season was added after noting that tree age spans several years and if 16 Examples 324 this is the orange data circ age Tree 4 a 5 1 2 3 Figure 16 12 Trellis plot of trunk circumference for each tree converted to day of year measurements were taken in either Spring April May or Autumn September October First we demonstrate the fitting of a cubic spline in ASReml by restricting the dataset to tree 1 only The model includes the intercept and linear regression of trunk circumference on age and an additional random term spl age 7 which instructs ASReml to include a random term with a special design matrix with 7 2 5 columns which relate to the vector 6 whose elements 6 7 2 6 are the second differentials of the cubic spline at the knot points The second differentials of a natural cubic spline are zero at the first and last knot points Green and Silverman 1994 The ASReml job is this is the orange data for tree 1 seq record numb
147. 2 0 114 SIRE_2 0 1 5 175 375 2522 115 SIRE_2 0 115 SIRE 2 0 1 5 171 382 1722 116 SIRE_2 0 116 SIRE_2 0 1 5 168 417 2752 117 SIRE_3 0 117 SIRE_3 0 1 3 154 389 2383 118 SIRE_3 0 118 SIRE 3 0 1 4 184 414 2463 119 SIRE_3 0 119 SIRE 3 0 1 5 174 483 2293 120 SIRE_3 0 120 SIRE_3 0 1 5 170 430 2303 9 Command file Genetic analysis 167 9 4 Reading in the pedigree file The syntax for specifying a pedigree file in the ASReml command file is pedigree_file qualifiers the qualifiers are listed in Table 9 1 the identities individual male_parent female_parent are merged into a single list and the inverse relationship is formed before the data file is read when the data file is read data fields with the P qualifier are recoded according to the combined identity list the inverse relationship matrix is automatically associated with factors coded from the pedigree file unless some other covariance structure is specified The inverse relationship matrix is specified with the variance model name AINV the inverse relationship matrix is written to ainverse bin if ainverse bin already exists ASReml assumes it was formed in a previous run and has the correct inverse ainverse bin is read rather than the inverse being reformed unless MAKE is specified this saves time when performing repeated analyses based on a particular pedigree delete ainverse bin or specify MAKE if the pedigree is changed between runs i
148. 227 230 Bibliography 362 Verbyla A P Cullis B R and Thompson R 2007 The analysis of qtl by simultaneous use of the full linkage map Theoretical and Applied Genetics 116 95 111 Verbyla A P Cullis B R Kenward M G and Welham S J 1999 The analysis of designed experiments and longitudinal data by using smoothing splines with discussion Applied Statistics 48 269 311 Waddington D Welham S J Gilmour A R and Thompson R 1994 Com parisons of some glmm estimators for a simple binomial model Genstat Newsletter 30 13 24 Webster R and Oliver M A 2001 Geostatistics for Environmental Scientists John Wiley and Sons Chichester Welham S J 1993 Genstat 5 Procedure Library manual R W Payne G M Arnold and G W Morgan eds release 2 3 edn Numerical Algorithms Group Oxford Welham S J 2005 Glmm fits a generalized linear mixed model in R Payne and P Lane eds GenStat Reference Manual 3 Procedure Library PL17 VSN International Hemel Hempstead UK pp 260 265 Welham S J Cullis B R Gogel B J Gilmour A R and Thompson R 2004 Prediction in linear mixed models Australian and New Zealand Journal of Statistics 46 325 347 White I M S Thompson R and Brotherstone S 1999 Genetic and environ mental smoothing of lactation curves with cubic splines Journal of Dairy Science 82 632 638 Wilkinson G N and Rogers C E 1973
149. 243 LogL 4240 LogL 4240 LogL 4239 LogL 4239 LogL 4239 LogL 4239 75 57 89 76 59 01 91 88 88 88 OANDOFRWN RH 10 Final parameter values Source variety Variance Residual Source of Variation 7 mu 3 weed S2 0 12850E 06 666 df 0 1000 1 000 0 1000 S2 0 12138E 06 666 df 0 1516 1 000 0 1799 S2 0 10968E 06 666 df 0 2977 1 000 0 2980 S2 88033 666 df 0 7398 1 000 0 4939 S2 84420 666 df 0 9125 1 000 0 6016 S2 85617 666 df 0 9344 1 000 0 6428 S2 86032 666 df 0 9474 1 000 0 6596 S2 86189 666 df 0 9540 1 000 0 6668 S2 86253 666 df 0 9571 1 000 0 6700 S2 86280 666 df 0 9585 1 000 0 6714 0 95918 1 0000 0 67205 Model terms Gamma Component Comp SE C 532 532 0 959184 82758 6 3 98 OP 670 666 1 00000 86280 2 Bele 0 P AR AutoR 67 0 672052 0 672052 16 04 1y Wald F statistics NumDF DenDF F_inc Prob 1 83 6 9799 18 lt 001 1 477 0 109 33 lt 001 The iterative sequence converged the REML estimate of the autoregressive pa rameter indicating substantial within column heterogeneity The abbreviated output from the two dimensional AR1xAR1 spatial model is 1 LogL 4277 99 2 LogL 4266 13 3 LogL 4253 05 4 LogL 4238 72 S2 S2 S52 S2 0 12850E 06 0 12097E 06 0 10777E 06 83156 666 df 666 df 666 df 666 df 16 Examples 308 5 LogL 4234 53 S2 79868 666 df 6 LogL 4233 78 S2 82024 666 df 7 LogL 4233 67 S2 82725 666 df 8 LogL 4233 65 S2 82975 666 df
150. 33 SEX GRP a 1 16 0 487 Deviance from GLM fit 48 37 96 Variance heterogeneity factor Deviance DF 0 79 16 Examples 336 The Deviance is the deviance calculated from the binomial part of the log likelihood This is distinct from the log likelihood obtained by the REML algo rithm which pertains to the working variable Since the working variable changes with the model fitted the LogL values are not comparable between models The heterogeneity factor is the Deviance df and gives some indication as to how well the discrete distribution fits the data A value greater than 1 suggests the data is over dispersed that is the data values are more variable than expected under the chosen distribution There is also a DISPERSION d qualifier If d is supplied it serves as a scal ing factor for the weights in the analysis changing the reported variances and standard deviations If d is not supplied it is estimated from the residual as the model is fitted to the working variable ASReml solves for the linear effects twice see the GLMM qualifier each iteration of the variance components so that the variance component updates are based on solutions obtained using the same variance parameters I e We start with a set of solutions and some parameters We use these to update the solutions Then use the updated solutions to update the variance parameter Bivariate analysis of Foot score The data file BINNOR txt contains the expanded versio
151. 378 2 334 tmt variety 0 492 1 505 0 372 run 0 321 0 319 tmt run 1 748 1 388 2 223 variety run pair 0 976 0 987 tmt pair 1 315 1 156 1 359 REML log likelihood 345 256 343 22 Wald F statistics Source of Variation NumDF DenDF F_inc Prob 7 mu 1 53 5 1484 27 lt 001 4 tmt 1 60 4 469 36 lt 001 The estimated variance components from this analysis are given in column a of table 16 8 The variance component for the variety main effects is large There is evidence of tmt variety interactions so we may expect some discrimination between varieties in terms of tolerance to bloodworms Given the large difference p lt 0 001 between tmt means we may wish to allow for heterogeneity of variance associated with tmt Thus we fit a separate variety variance for each level of tmt so that instead of assuming var u2 o3Igg we assume 2 yar u2 2 0 0 of amp I4 where o2 and o3 are the tmt variety interaction variances for control and treated respectively This model can be achieved using a diagonal variance struc ture for the treatment part of the interaction We also fit a separate run variance for each level of tmt and heterogeneity at the residual level by including the uni tmt 2 term We have chosen level 2 of tmt as we expect more variation for the exposed treatment and thus the extra variance component for this term 16 Examples 316 should be positive Had we mistakenly specified level 1 then ASReml would hav
152. 38757 125 df 1 000 0 6838 0 4586 Final parameter values 1 0000 0 68377 0 45861 Source Model terms Gamma Component Comp SE C Variance 150 125 1 00000 38756 6 5 00 0P Residual AR AutoR 15 0 683767 0 683767 10 80 OU Residual AR AutoR 10 0 458607 0 458607 5 55 OU Wald F statistics Source of Variation NumDF DenDF F_inc Prob 8 mu 1 12 8 850 88 lt 001 6 variety 24 80 0 13 04 lt 001 ARI x AR1 units 1 LogL 740 735 S2 33225 125 df 2 components constrained 2 LogL 723 595 52 11661 125 df 7 1 components constrained 3 LogL 698 498 S2 46239 125 df 4 LogL 696 847 S2 44725 125 df 5 LogL 696 823 S2 45563 125 df 6 LogL 696 823 S2 45753 125 df 7 LogL 696 823 S2 45796 125 df Source Model terms Gamma Component Comp SE C units 150 150 0 106154 4861 48 2of2 QP Variance 150 125 1 00000 45796 3 2 74 OP Residual AR AutoR 15 0 843795 0 843795 12 33 OU Residual AR AutoR 10 0 682686 0 682686 6 68 0U Wald F statistics Source of Variation NumDF DenDF Fane Prob 8 mu 1 3 5 259 81 lt 001 6 variety 24 T T 10 21 lt 001 The lattice analysis with recovery of between block information is presented below This variance model is not competitive with the preceding spatial models The models can be formally compared using the BIC values for example IB analysis 16 Examples 303 NOOR WNPR LogL 734 LogL 720 LogL 711 LogL 707 LogL 707 LogL 707 LogL 707 184 060 119 937 786 786 786 S52 S2 S52 S
153. 4 0 393626E 4 0 363341E 4 0 000000E 4 0 362019E 00 00 01 01 00 01 F01 00 Fot O1 O1 O1 01 00 01 0 801579E 01 0 298660E 01 0 456648E 01 0 476546E 01 0 389620E 01 0 377176E 01 0 129013E 01 0 316915E 01 0 376637E 01 0 378585E 01 0 442457E 01 0 502071E 01 0 430512E 01 0 444776E 01 0 351386E 01 0 352370E 01 0 475935E 01 0 000000E 00 0 886687E 01 0 876708E 01 0 416124E 01 0 428109E 01 0 000000E 00 0 412130E 01 0 419780E 01 0 985202E O1 0 439485E 01 0 901191E 01 0 423753E 01 0 527289E O1 0 369983E 01 0 359516E 01 0 000000E 00 The first 5 rows of the lower triangular matrix in this case are 48 6802 0 2 98660 4 70711 0 313123 oe o eo o gt The vvp file 8 07551 4 56648 8 86687 4 10031 4 76546 8 76708 The vvp file contains the inverse of the average information matrix on the com ponents scale The file is formatted for reading back under the control of the pin file described in Chapter 13 The matrix is lower triangular row wise in the order the parameters are printed in the asr file This is nin89a vvp with the parameter estimates in the order error variance spatial row correlation spatial column correlation Variance of Variance components 3 51 0852 0 217089 0 318058E 02 0 677748E 01 0 201181E 02 0 649355E 02 14 Description of output files 243 14 5 ASReml outp
154. 4 z pq where z 0 0758 is the ordinate of a Normal 0 1 corre sponding to p 1 q 0 034 The preceding Wald F Statistics pertain to the working variable created as part of the PQL analysis The SEX GRP interaction is clearly not significant even though ASReml was not able to calculate a plausible value for the Denominator DF for this summarized data The predicted means shown below are not that different from those obtained from analysis on the 0 1 scale but the standard errors are very different These predicted means have been backtransformed by ASReml from the underlying logistic scale to the probablity scale The initial analysis on the 0 1 probability scale ignores the variance differences associated with binomial data Sex PxP 1980 BRxP 1980 BxR 1980 BRxP 1981 0 0 0180 0 0070 0 0430 0 0124 0 0748 0 0323 0 0281 0 0083 1 0 0151 0 0063 0 0373 0 0110 0 0592 0 0257 0 0401 0 0103 ASReml has an Analysis of Deviance option which we now demonstrate In a mixed model the variance components will change depending on which fixed terms are in the model This will invalidate the Analysis of Deviance unless the variance components are fixed at the full model solution So fitting the model line Rot bin TOT Total AODEV mu SEX GRP SEX GRP r SIRE 2632 GF produces the Analysis of Deviance Analysis of Deviance Table for Rot Source of Variation df Deviance Derived F SEX d 0 02 0 021 GRP 3 4 35 1 8
155. 4 3 21 6 18 1 CODY 4 1104 602 1 4 30 1 4 3 22 8 19 1 optional field labels file augmented by missing values for first 15 plots and 3 buffer plots and variety coded LANCER to complete 22x11 array buffer plots between reps original data e the pid raw repl and yield data for the missing plots have all been made NA one of the three missing value indicators in ASReml see Section 4 2 e variety is coded LANCER for all missing plots one of the variety names must be used but the particular choice is arbitrary 3 A guided tour 31 3 4 The ASReml command file See Chapters 5 By convention an ASReml command file has a as extension The file defines 6 and 7 for de saili e a title line to describe the job e labels for the data fields in the data file and the name of the data file e the linear mixed model and the variance model s if required e output options including directives for tabulation and prediction Below is the ASReml command file for an RCB analysis of the NIN field trial data highlighting the main sections Note the order of the main sections title line gt data field definition gt data field definition gt data file name and qualifiers gt tabulate statement linear mixed model definition gt predict statement gt variance model specification gt The title line The first text non blank non control line in an ASReml command file is taken as the ti
156. 5064 E CODY 23 1728 2 4970 E ARAPAHOE 27 0431 2 4417 E NE83404 25 7197 2 4424 E NE83406 25 3797 2 5028 E NE83407 24 3982 2 6882 E CENTURA 26 3532 2 4763 E SCOUT66 29 1743 2 4361 E NE87615 25 1238 2 4434 E NE87619 30 0267 2 4666 E NE87627 19 7126 2 4833 E SED Overall Standard Error of Difference 2 925 The res file The res file contains miscellaneous supplementary information including a list of unique values of x formed by using the fac model term a list of unique x y combinations formed by using the fac z y model term legandre polynomials produced by leg model term orthogonal polynomials produced by pol model term the design matrix formed for the sp1 model term 14 Description of output files 234 predicted values of the curvature component of cubic smoothing splines the empirical variance covariance matrix based on the BLUPs when a X amp J or I gt structure is used this may be used to obtain starting values for another run of ASReml a table showing the variance components for each iteration a figure and table showing the variance partitioning for any XFA structures fitted some statistics derived from the residuals from two dimensional data multi variate repeated measures or spatial the residuals from a spatial analysis will have the units part added to them defined as the combined residual unless the data records were sorted within ASReml in which case the units and the corr
157. 52 S52 S52 S2 26778 16591 11173 8562 4 3091 2 8061 8 8061 8 125 125 125 125 125 126 125 df df df df df df df Results from analysis of yield Approximate stratum variance decomposition Component Coefficients Stratum Degrees Freedom Variance Rep 5 00 266657 RowBlk 24 00 74887 8 Co1lB1lk 23 66 41358 5 Residual Variance 72 34 8061 81 Source Model terms Gamma Rep 6 6 0 528714 RowBlk 30 30 1 93444 ColBlk 30 30 1 83725 Variance 150 125 1 00000 Source of Variation 8 mu 6 variety 2 5 0 5 0 0 0 4 3 0 0 0 0 0 0 0 0 Component 4262 39 15595 1 14811 6 8061 81 Wald F statistics NumDF 1 24 DenDF F_inc 5 0 1216 29 79 3 8 84 5 0 0 0 4 3 0 0 Comp SE 0 62 3 06 3 04 6 01 errre ao OGOGO AG OP OP OP oP Prob lt 001 lt 001 Finally we present portions of the pvs files to illustrate the prediction facility of ASReml The first five and last three variety means are presented for illustration The overall SED printed is the square root of the average variance of difference between the variety means The two spatial analyses have a range of SEDs which are available if the SED qualifier is used All variety comparisons have the same SED from the third analysis as the design is a balanced lattice square The Wald F statistic statistics for the spatial models are greater than for the lattice analysis We note the Wald F statistic for the AR1xAR1 u
158. 6 9 Thus variables form three classes those read from the data file possibly modified normally labelled and available for subsequent use in analysis those created and labelled available for subsequent use in the analysis and those created but not labelled intermediate calculations not required for subsequent analysis When listing variables in the field definitions list those read from the data file first After them list and define the variables that are to be created and labelled but not read The number of variables read can be explicitly set using the READ qualifier described in Table 5 5 Otherwise if the first transformation on a field overwrites its contents for instance using ASReml recognises that the field does not need to be read in unless a subsequent field does need to be read For example A B C A B reads two fields A and B and constructs C as A B All three are available for analysis However A B 5 Command file Reading the data 54 C A B D E D B reads four fields A B C and D because the fourth field is not obviously created and must therefore be read even though the third field C is overwritten The fifth field is not read but just created E Variables that have an explicit label may be referenced by their explicit label or their internal label Therefore to avoid confusion do not use explicit labels of the form Vi where 7 is a number for variables to be referred
159. 6 Examples 297 23 38 41 55 34 83 61 89 44 58 79 22 43 14 76 67 LogL 160 368 LogL 159 027 LogL 158 247 LogL 158 040 LogL 158 036 oP WN Pe Source Model Residual US UnStr Residual US UnStr Residual US UnStr Residual US UnStr Residual US UnStr Residual US UnStr Residual US UnStr Residual US UnStr Residual US UnStr Residual US UnStr Residual US UnStr Residual US UnStr Residual US UnStr Residual US UnStr Residual US UnStr 258 9 331 4 550 8 320 7 533 0 541 4 2 1 0000 60 df 2 1 0000 60 df 2 1 0000 60 df 2 1 0000 60 df S2 1 0000 60 dt terms Gamma Component 1 37 2202 37 2262 1 23 3935 23 3935 2 41 5195 41 5195 ill 51 6524 51 6524 2 61 9169 61 9169 3 259 121 259 121 i 70 8113 70 S113 2 57 6146 57 6146 3 331 807 331 807 4 651 507 551 507 1 73 7857 73 7857 2 62 5691 62 5691 3 330 851 330 851 4 533 1796 533 756 5 542 175 542 175 Covariance Variance Correlation Matrix US UnStructu 37 23 0 5950 0 5259 0 4942 0 5194 23 39 41 52 0 5969 0 3807 0 4170 51 85 61 92 259 1 OSTIT 0 8827 10 81 Bh wd 331 8 551 5 0 9761 Tau 09 62 57 330 9 533 8 542 2 NNONFPRPFNNRFPYPNFP PDN BE Comp SE 2 ee 45 mogl s18 45 54 nae 229 45 60 33 29 42 45 45 m Oe OO CO Oo fe Oo Oo CO CO fe SO 2 Sea Se amp Se ae ee Se SS Ss a eh The antedependence model of order 1 is clearly more parsimonious than the unstructured model Table 16 5 presents the incremental Wald F statistics for e
160. 6785 52 1 0000 48 df Dev DF 0 7908 Final parameter values 0 26321 1 0000 Deviance from GLM fit 48 37 96 Variance heterogeneity factor Deviance DF 0 79 Results from analysis of Rot Notice While convergence of the LogL value indicates that the model has stabilized its value CANNOT be used to formally test differences between Generalized Linear Mixed Models Approximate stratum variance decomposition Stratum Degrees Freedom Variance Component Coefficients SIRE 3 10 0 263207 1 0 Source Model terms Gamma Component Comp SE C SIRE 34 34 0 263207 0 263207 1 25 0P Variance 56 48 1 00000 1 00000 0 00 OF Wald F statistics Source of Variation NumDF DenDF F_inc Prob 11 mu A 20 2 418 38 lt 001 3 SEX 1 48 0 0 02 0 881 2 GRP 3 21 5 1 99 0 146 12 SEX GRP 3 NA 0 36 NA The effects in this analysis are on a logistic scale with a variance of 3 28987 17 3 16 Examples 335 4x 0 2632 and so the heritability on the underlying logistic scale is 0 296 33808710 26321 This can be calculated in ASReml with the pin file commands F GenVar 1 4 F TotVar 1 4 3 28987 H heritability 3 4 Repeating the analysis on the Probit scale by inserting PROBIT after BIN in the model line produces a Sire component of 0 0514 on the Probit scale which has an underlying variance of 1 0 The heritabily estimate is then 0 196 Given the incidence 0 034 the heritability on the probit scale is expected to be around 0 215 0 036
161. 9 FIELD 75 FILTER 64 FINAL 198 FOLDER 64 FORMAT 65 FOWN 24 84 GAMMA GLM 110 IGF 146 IGIV 169 GKRIGE 74 GLMM 85 GOFFSET 169 IGP 146 GRAPHICS 198 GROUPFACTOR 74 GROUPSDF 173 GROUPS 169 IGU 146 IGZ 146 1G 50 71 73 HARDCOPY 198 HOLD 85 HPGL 85 IDENTITY link 110 INBRED 169 INCLUDE 67 INTERACTIVE 198 1I 50 JOIN 71 74 198 Jddm 57 Jmmd 57 Jyyd 57 KEEP 212 IKEY 75 212 KNOTS 90 ILAST 85 169 LOGARITHM 110 LOGFILE 198 LOGIT 109 LOGIT link 109 ILOG link 109 LONGINTEGER 170 IL 49 IMAKE 170 MATCH 66 IMAXIT 70 IMAX 57 IMBF 75 I MERGE 66 I MEUWISSEN 170 IMGS 170 IMIN 57 MM transformation 57 60 MOD 57 IMVREMOVE 76 IM 57 INAME 146 152 153 INA 57 IND 172 NEGBIN GLM 110 NOCHECK 90 NODUP 212 NOGRAPHS 198 Index 369 NOKEY 75 NOREORDER 90 NORMAL 58 NORMAL GLM 109 NOSCRATCH 90 INSD 172 OFFSET variable 111 ONERUN 198 OUTLIER 18 OWN 86 PEARSON residuals 111 PLOT 185 PNG 86 POISSON GLM 110 POLPOINTS 90 PPOINTS 90 PRINTALL 185 PRINT 86 PROBIT 109 PROBIT 109 PSD 172 IPS 86 PVAL 76 PVR GLM fitted values 111 PVSFORM 86 PVW GLM fitted values 111 IP 50 QUASS 170 QUIET 198 READ 66 RECODE 66 IRENAME 75 198 REPEAT 170 REPLACE 58 REPORT 90 RESCALE 58 RE
162. 9PVL8AN aOHVdVuV 667L85N LOSISAN Adoo 61 OOZINVL LZ9L80N LIOO 8S98AN IStL8HN 999L98AN vOvesaN LZ9L8AN 89TLSAN 80S98IN GNWIGEY SI TOS98AN 8LAVUNLNAO 80PL8AN 80S98AN ANVTXNOIS e19L8GN 86VE8AN e19L8GN LSVLSAN 108984N a144 LI eT9L8aN ZILESAN SOS98AN totsgaN ANNAAAHO ZI9L8AN 209984N 60VL8AN TS7L8AN VLOONVT YAONWT 91 S6VE8aN eTSL8GN VUNLNAIO dVALSANOH ZEGLEIN TTAN AINNAATHO ZILESAN 9YYL8AN QAYVALSAWOH z GT 619L84N 99LN008 9bPL89N 9GGG8AN TOS9STN Z8ST98SAN 667L8AN 8LAVUNLNAD 6OTLSSIN Z8tI8SAN p ZevesaNn NVMUON ZISL8GN 60S98AIN ST9LSAN 0S984N 619L84N ZEvEsaN 80tL8AN 00 WVL gf anv1dqa4u 660280 N e0vL8aN 86 9S8AN 999LISAN WLOONV I ADVO TSPL8GN E0tL8AN LETESSJH 3 ZI ANNAATHO Z8998AN 999 L984N E0tL8AN LZIL8AN OOZINVL DLETESSM 807L8AN 999LISAN NVMUON II AOHVAVUV E9PL8AN I9LNOOS SLMVYNLNAO 99998AN L99089N Z8S98aN LLESAN SLMVUNLNAO OI ST9L8AN AdOO S6FESAN AOHVdIVUV LOTAVL ST9L8GN 909984N AdOO ADVO 869SSAN 5 6 LOvE8aN vOvesaN YACINHDNOU amp L9LSAN VNOA NVMUON 609984 N 79S8GN ANVTXNOIS 9898AN gt 8 aDVD VNOA ZISLSAN o0z WYVL LEG98HN ZZSL8AN 99LNO00S VUNLNAO VNOA ZETESAN z L 60PL84N UACIMHDNOU ZETESAN LOS9SEIN LIOO LIOO 229989 N YaCIMHDAOU LSS TSN 9 TSPL8GN 209989 N VUNLNIO LLESAN TLETESSM 90PE8SAN UFCIMHDNOU LEILAN LO998EIN 86FESAN G LZ9984N ataua 66tL8AN LSST8AN AN V Ida L90L80N NIMSMONG 6L9LSAN 909985N L102 S i4 EZ9IS8AN 99998AN 60tL8AN LSTLSAN NVMUON 0PL8aN L0S980N STIL8AN 8998GIN 99LQOOS 5 Z8P98AN NIMsMONnd 90TESAN I9LSAN
163. A o o o o o o 0 5 o fo o o o o o T T T T T T 2 1 o 1 2 3 control BLUP Figure 16 10 Estimated deviations from regression of treated on control for each variety plotted against estimate for control 16 Examples 322 An alternative definition of tolerance is the simple difference between treated and control BLUPs for each variety namely 6 uy Uy Unless 8 1 the two measures and 6 have very different interpretations The key difference is that e is a measure which is independent of inherent vigour whereas 6 is not To see this consider cov uy COV Uy BUvo Wy Ovet 2 Ova 3 Iwe Iss Tie 0 whereas cov up cov ty Uv Uy a z Ti Is O O O 6 fo 14 o o o a a o E Q o O o 2 7 a a 8 a e 2 o o 5 S o0 e oo O O O o O oO Tao e O T T T T T T 2 A o 1 2 3 control BLUP Figure 16 11 Estimated difference between control and treated for each variety plotted against estimate for control 16 Examples 323 The independence of and u and dependence between 6 and wy is clearly illustrated in Figures 16 10 and 16 11 In this example the two measures have provided very different rankings of the varieties The choice of tolerance mea sure depends on the aim of the experiment In this experiment the aim was to identify tolerance which is independent of inherent vigour so the deviations from regression measure i
164. AR1 424 22 row AR1 904 coded 0 except in the record where the par ticular missing value occurs where it is coded 1 The action when mv is omitted from the model depends on whether a univariate or multivariate analysis is being performed For a univariate analysis ASReml discards records which have a missing response In multivariate analyses all records are retained and the R matrix is modified to reflect the missing value pattern Missing values in the explanatory variables ASReml will abort the analysis if it finds missing values in the design matrix unless MVINCLUDE or MVREMOVE is specified see Section 5 8 MVINCLUDE causes the missing value to be treated as a zero MVREMOVE causes ASReml to discard the whole record Records with missing values in particular fields can be explicitly dropped using the DV transformation Table 5 1 Covariates Treating missing values as zero in covariates is usually only sensible if the covariate is centred has mean of zero Design factors Where the factor level is zero or missing and the MVINCLUDE qualifier is specified no level is assigned to the factor for that record These effectively defines an extra level class in the factor which becomes a reference level 6 Command file Specifying the terms in the mixed model 114 6 10 Some technical details about model fitting in ASReml Sparse versus dense ASReml partitions the terms in the linear model into two parts
165. ASReml User Guide Release 3 0 2009 A R Gilmour NSW Department of Primary Industries Orange Australia B J Gogel University of Adelaide Adelaide Australia B R Cullis NSW Department of Primary Industries Wagga Wagga Australia R Thompson School of Mathematical Sciences Queen Mary University of London Mile End Road London E1 4NS and Centre for Mathematical and Computational Biology and Department of Biomathematics and Bioinformatics Rothamsted Research Harpenden AL5 2JQ United Kingdom ASReml User Guide Release 3 0 ASReml is a statistical package that fits linear mixed models using Residual Maximum Likelihood REML It is a joint venture between the Biometrics Pro gram of NSW Department of Primary Industries and the Biomathematics Unit of Rothamsted Research Statisticians in Britain and Australia have collaborated in its development Main authors A R Gilmour B J Gogel B R Cullis and R Thompson Other contributors D Butler M Cherry D Collins G Dutkowski S A Harding K Haskard A Kelly S G Nielsen A Smith A P Verbyla S J Welham and I M S White Author email addresses Arthur Gilmour cargovale com au Beverley Gogel adelaide edu au Brian Cullis dpi industry gov au Robin Thompson bbsrc ac uk Copyright Notice Copyright 2009 NSW Department of Industry and Investment All rights reserved Except as permitted under the Copyright Act 1968 Commonwealth of Aus tra
166. Agricultural Biological and Environmental Statistics 2 269 293 Gilmour A R Cullis B R Welham S J Gogel B J and Thompson R 2004 An efficient computing strategy for prediction in mixed linear mod els Computational Statistics and Data Analysis 44 571 586 Gilmour A R Thompson R and Cullis B R 1995 AI an efficient algorithm for REML estimation in linear mixed models Biometrics 51 1440 1450 Gleeson A C and Cullis B R 1987 Residual maximum likelihood REML estimation of a neighbour model for field experiments Biometrics 43 277 288 Gogel B J 1997 Spatial analysis of multi environment variety trials PhD thesis Department of Statistics University of Adelaide South Australia Goldstein H and Rasbash J 1996 Improved approximations for multilevel models with binary response Journal of the Royal Statistical Society A General 159 505 513 Goldstein H Rasbash J Plewis I Draper D Browne W Yang M Wood house G and Healy M 1998 A user s guide to MLwiN Institute of Education London Green P J and Silverman B W 1994 Nonparametric regression and gener alized linear models London Chapman and Hall Harvey W R 1977 Users guide to LSML76 The Ohio State University Columbus Harville D A 1997 Matrix algebra from a statisticians perspective Springer Verlag New York Bibliography 359 Harville D and Mee R 1984
167. CIM ignores variety sow when calculating DenDF for the test of water and ignores water sow when calculating DenDF for the test of variety When DenDF is not 2 Some theory 25 available it is often possible though anti conservative to use the residual degrees of freedom for the denominator Kenward and Roger 1997 pursued the concept of construction of Wald type test statistics through an adjusted variance matrix of 7 They argued that it is useful to consider an improved estimator of the variance matrix of 7 which has less bias and accounts for the variability in estimation of the variance parameters There are two reasons for this Firstly the small sample distribution of Wald F statistics is simplified when the adjusted variance matrix is used Secondly if measures of precision are required for 7 or effects therein those obtained from the adjusted variance matrix will generally be preferred Unfortunately the Wald statistics are currently computed using an unadjusted variance matrix Approximate stratum variances ASReml reports approximate stratum variances and degrees of freedom for sim ple variance components models For the linear mixed effects model with vari ance components setting oF 1 where G SHIR bj it is often possible to consider a natural ordering of the variance component parameters including a Based on an idea due to Thompson 1980 ASReml computes approximate stratum degrees of freedom and stratum variances b
168. D ID ID AR1 AR1 AR1 ID AR1 AR1 AR1 AR1 7 Command file Specifying the variance structures 126 See Section 7 7 Important 5 Two dimensional separable autoregressive spatial model defined as a G structure This model is equivalent to 3c but with the NIN Alliance Trial 1989 spatial model defined as a G structure rather variety 76 l d than an R structure As discussed in 2b one t and only one of the component models must gt b i del and all oth t be oY 7 e a variance model and all others must be HOAT correlation models nin89 asd skip 1 yield mu variety Ir row column BENA 00a AR1 to a variance model and the second initial column 2 value 0 1 is for the variance ratio That row 0 AR1V 0 5 0 1 is V o2 ee Eel pe Erl pr a4 column 0 AR1 0 5 The V in AR1V converts the correlation model Try starting this model with initial correlations of 0 3 it fails to converge Use of row column as a G structure is a useful approach for analysing incomplete spatial arrays it will often run faster for large trials but requires more memory Note that we have used the original version of the data and f mv is omitted from this analysis since row column is fitted as a G structure If we had used the augmented data nin89aug asd we would still omit f mv and ASReml would discard the records with missing yield 7 4 Variance structures Revised 08 The previ
169. FREE FORMAT skipping 0 lines Univariate analysis of yield Error at field 1 wariety of record 1 line 1 Since this is the first data record you may need to skip some header lines see SKIP or append the A qualifier to the definition of factor variety Fault Missing faulty SKIP or A needed for variety Last line read was variety id pid raw rep nloc yield lat long row column Currently defined structures COLS and LEVELS 1 variety 1 56 56 0 0 2 id 1 1 1 15 Error messages 255 hint raw repl nloc yield lat Oo ON DO fF WwW e e re re PP FP be e e re re BP PB long o onOne WD 22 22 14 11 10 row a e 11 column 12 mu OF FP Be RP Be Be BP Be eB oOo oO 2 2 52 2 2 o O O O O O 2 Oo 2 j m ninerr2 nin asd Model specification TERM LEVELS GAMMAS mu 0 variety 0 12 factors defined max 500 O variance parameters maxi500 2 special structures Last line read was variety id pid raw rep nloc yield lat long row column Finished 27 Jul 2005 15 41 40 068 Missing faulty SKIP or A needed for variety Fixing the error by changing slip to skip however still produces the fault message Missing faulty SKIP or A needed for variety The portion of output given below shows that ASReml has baulked at the name LANCER in the first field on the first data line This alphabetic data field is not declared as alphabetic The correct data field definition for variety is variety A to indi
170. GET sqrtA 70 5 Udat 0 Uniform 4 5 is equivalent to Udat Uniform 4 5 1V3 2 5 1V10 V3 1V11 block gt V12 V0 QTL marker transformations ASReml2 IMM s associates marker positions in the vector s based on the Haldane mapping function with marker variables and replaces missing values in a vector of marker states with expected values calculated using distances to non missing flanking markers This transformation will normally be used on a G n factor where the n variables are the marker states for n markers in a linkage group in map order and coded 1 1 backcross or 1 0 1 F2 design s length n 1 should be the n marker positions relative to a left telomere position of zero and an extra value being the length of the linkage group the position of the right telomere 5 Command file Reading the data 60 ASReml2 ASReml3 The length right telomere may be omitted in which case the last marker is taken as the end of the linkage group The positions may be given in Morgans or centiMorgans if the length is greater than 10 it will be divided by 100 to convert to Morgans The recombination rate between markers at sz and spg L is left and R is right of some putative QTL at Q is brr l e sr s1 2 Consequently for 3 markers L Q R OLR LQ QR 20LQOQR The expected value of a missing marker at Q between L and R depends on the marker states at L and R E q 1 1 1
171. Gi 0 0 G2 00 G3 0 0 SIRE_1 SIRE_2 SIRE_3 SIRE_4 SIRE_5 SIRE_6 SIRE_7 SIRE_8 SIRE_9 101 SIRE_1 G1 102 SIRE_1 G1 103 SIRE_1 G1 163 SIRE_9 G3 164 SIRE_9 G3 165 SIRE_9 G3 G1 G1 G1 G2 G2 G3 G3 G3 G3 G1 G1 G1 G2 G2 G3 G3 G3 G3 It is usually appropriate to allocate a genetic group identifier where the parent is unknown Table 9 1 List of pedigree file qualifiers qualifier description ALPHA indicates that the identities are alphanumeric with up to 225 characters otherwise by default they are numeric whole numbers lt 200 000 000 If using long alphabetic identities use SLNFORM to see the full identity in the sln file IDIAG causes the pedigree identifiers the diagonal elements of the Inverse of the Relationship and the inbreeding coefficients for the individuals calculated as the diagonal of A I to be written to basename aif 9 Command file Genetic analysis 169 List of pedigree file qualifiers qualifier description FGEN f indicates the pedigree file contains a fourth field indicating the level of ASReml3 selfing or the level of inbreeding in a base individual In the fourth field 0 indicates a simple cross 1 indicates selfed once 2 indicates selfed twice etc A value between 0 and 1 for a base individual is taken as its inbreeding value If the pedigree has implicit individuals they appear as parents but not in the first field of the pedigree file the
172. Matrix UnStructured 2 144 0 4402 0 9874 2 348 Covariance Variance Correlation Matrix UnStructured 3 840 0 8504 2 334 1 962 Covariance Variance Correlation Matrix UnStructured 1 708 0 1531 0 3191 2 543 The resultant REML log likelihood is identical to that of the heterogeneous uni variate analysis column b of table 16 8 The estimated variance parameters are given in Table 16 10 The predicted variety means in the pvs file are used in the following section on interpretation of results A portion of the file is presented below There is a wide range in SED reflecting the imbalance of the variety concurrence within runs Assuming Power transformation was Y 0 000 0 500 run is ignored in the prediction except where specifically included Trait variety Power_value Stand_Error Ecode Retransformed approx_SE sqrt yc A1iCombo 14 9532 0 9181 E 223 5982 27 4571 sqrt ye A1iCombo 7 9941 0 7993 E 63 9054 12 7790 sqrt yc Bluebelle 13 1033 0 9310 E 171 6969 24 3980 sqrt ye Bluebelle 6 6299 0 8062 E 43 9559 10 6901 Table 16 10 Estimated variance parameters from bivariate analysis of bloodworm data control treated source variance variance covariance us trait variety 3 84 1 96 2 33 us trait run 1 71 2 54 0 32 us trait pair 2 14 2 35 0 99 16 Examples 320 sqrt yc C22 16 6679 0 9181 E 277 8192 30 6057 sqrt ye C22 8 9543 0 7993 E 80 1798 14 3140 sqrt yc YRK1i 15 1859 0 9549 E 230 6103 29 0012 sqrt y
173. N LOG PV for section 1 0 99 2 01 4 34 produced from a trivariate analysis reports the slopes A slope of b suggests 14 Description of output files 235 that y might have less mean variance relationship If there is no mean variance relation a slope of zero is expected A slope of suggests a SQRT transformation might resolve the dependence a slope of 1 means a LOG trans formation might be appropriate So for the 3 traits log y1 yz 1 and Yz 3 are indicated This diagnostic strategy works better when based on grouped data regressing log standard deviation on log mean Also SIND RES 16 2 35 6 58 5 64 indicates that for the 16th data record the residuals are 2 35 6 58 and 5 64 times the respective standard deviations The standard deviation used in this test is calculated directly from the residuals rather than from the analysis They are intended to flag the records with large residuals rather than to pre cisely quantify their relative size They are not studentised residuals and are generally not relevant when the user has fitted heterogeneous variances This is nin89a res Convergence sequence of variance parameters Iteration 1 2 3 4 5 6 LogL 401 827 400 780 399 807 399 353 399 326 399 324 Change 59 80 83 21 5 1 Adjusted 0 0 0 0 0 0 StepSz 0 316 0 562 1 000 1 000 1 000 1 000 5 0 500000 0 538787 0 589519 0 639457 0 651397 0 654445 0 5 6 0 500000 0 487564 0 469768 0 448895 0 440861 0 438406 0 6 Plo
174. O ORK ARG Folder C data asr3 ug3 manex TAG 1I BloodLine I QUALIFIERS SKIP 1 Reading wether dat FREE FORMAT skipping 1 lines Bivariate analysis of GFW and FDIAM Summary of 1485 records retained of 1485 read Model term Size miss zero MinNonO Mean MaxNonO StndDevn 8 Command file Multivariate analysis 162 1 TAG 521 0 0 1 261 0956 521 2 TRIAL 0 0 3 000 3 000 3 000 0 000 3 BloodLine 27 0 0 t 13 4323 27 4 TEAM 35 0 0 al 18 0067 35 5 YEAR 3 0 0 i 2 0391 3 6 GFW Variate 0 O 4 100 7 478 11 20 1 050 7 YLD 0 60 30 T511 88 60 4 379 8 FDIAM Variate 0 15 90 22 29 30 60 2 190 9 Trait 2 10 Trait YEAR 6 9 Trait 2 5 YEAR 3 11 Trait TEAM 70 9 Trait 2 4 TEAM 35 12 Trait TAG 1042 9 Trait 2 1 TAG S21 1485 identity 2 UnStructure 9 11 0 2000 0 2000 0 4000 2970 records assumed pre sorted 2 within 1485 Trait TEAM variance structure is 2 UnStructure 12 14 0 4000 0 3000 1 3000 35 identity Structure for Trait TEAM has 70 levels defined Trait TAG variance structure is 2 UnStructure 15 17 0 2000 0 2000 2 0000 Forming Initial updates will be shrunk by factor Notice Algebraic Denominator DF calculation is not available Notice il ON Do F WN 521 identity Structure for Trait TAG has 1120 equations 8 dense Numerical derivatives will be used LogL 886 LogL 818 LogL 755 LogL 725 LogL 723 LogL 723 LogL 723 LogL 723 521 508 911 374 475 462 462 462 2 2 2 2 2
175. Oro 9gr 1 rR E q 1 1 PQr rQ 0Lr Elq 1 1 Oro PQR OLR and E q 1 1 1 819 E 8a Let Az E q 1 1 E ql1 1 2 2220 Pen rg OLR 1 OLR and Az E ql 1 1 E q 1 1 2 e Han Then E q rL R ALTE AR R Where there is no marker on one side E q er 1 0gr r 0Qr TR trR 1 209r This qualifier facilitates the QTL method discussed in Gilmour 2007 IDOM A is used to form dominance covariables from a set of additive marker covariables previously declared with the MM marker map qualifier It assumes the argument A is an existing group of marker variables relating to a linkage group defined using MM which represents additive marker variation coded 1 0 1 representing marker states aa aA and AA respectively It is a group transformation which takes the 1 1 interval values and calculates X 0 5 2 i e 1 and 1 become one 0 becomes 1 The marker map is also copied and applied to this model term so it can be the argument in a qt1 term page 106 IDO ENDDO provides a mechanism to repeat transformations on a set of variables All tranformations except DOM and RESCALE operate once on a sin gle field unless preceded by a DO qualifier The DO qualifier has three arguments n ttJiv n is the number of times the following transformations are to be per formed i default 1 is the increment applied to the targe
176. R 0 0 0 0 R 0 0 R O34Rj i oc 2 i 0 0 Ry 0 0 Oo sz 0 Rs so that each section has its own variance structure which is assumed to be inde pendent of the structures in other sections A structure for the residual variance for the spatial analysis of multi environment trials Cullis et al 1998 is given by Ry Rj Qj 2 aj p Each section represents a trial and this model accounts for between trial error variance heterogeneity a and possibly a different spatial variance model for each trial In the simplest case the matrix R could be known and proportional to an identity matrix Each component matrix R or R itself for one section is assumed to be the direct product see Searle 1982 of one two or three component matrices The component matrices are related to the underlying structure of the data If the structure is defined by factors for example replicates rows and columns then the matrix R can be constructed as a direct product of three matrices describing the nature of the correlation across replicates rows and columns These factors must completely describe the structure of the data which means that 1 the number of combined levels of the factors must equal the number of data points 2 each factor combination must uniquely specify a single data point These conditions are necessary to ensure the expression var e OR is valid The assumption that the overall variance structure can be
177. S2 48 708 168 df 1 000 0 6554 0 4375 Final parameter values 1 0000 0 65550 0 43748 Results from analysis of yield Source Model terms Gamma Component Comp SE C parameter Variance 242 168 1 00000 48 7085 6 81 OP estimates Residual AR AutoR 22 0 655505 0 655505 11 63 OU Residual AR AutoR 11 0 437483 0 437483 5 43 OU testing Wald F statistics fixed effects Source of Variation NumDF DenDF F_inc Prob 12 mu 1 25 0 331 85 lt 001 1 variety 55 2110 8 2522 lt 001 Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using algebraic derivatives 13 mv_estimates 18 effects fitted 6 possible outliers in section 1 see res file Finished 10 Apr 2008 16 47 47 765 LogL Converged Following is a table of Wald F statistics augmented with a portion of Regression Screen output The qualifier was SCREEN 3 SMX 3 Source Model terms Gamma Component Comp SE C idsize 92 92 0 581102 0 136683 3 31 0P expt idsize 828 828 0 121231 0 285153E 01 1 12 OF Variance 504 438 1 00000 0 235214 12 70 OP Wald F statistics Source of Variation NumDF DenDF_con F_inc F_con M P_con 113 mu di 72 4 65452 25 56223 68 lt 001 2 expt 6 37 6 5 27 0 64 A 0 695 4 type 4 63 8 22 95 3 01 A 0 024 114 expt type 10 T93 1 31 0 93 B 0 508 23 X20 i 65 1 4 33 2 37 B 0 130 24 x21 ik 63 3 1 91 0 87 B 0 355 25 x23 1 68 3 23 93 0 11 B 0 745 26 x39 1 TAT 1 85 0 35 B 0 556 14 Description of output files 226 27 28 29 30
178. SIDUALS 86 87 RESPONSE residuals 111 RFIELD 75 ROWFAC 73 76 RREC 67 IRSKIP 67 1 2 1 147 1S 2 r 147 SARGOLZAEI 170 ISAVEGIV 172 SAVE 87 SCALE 90 SCORE 91 SCREEN 87 SECTION 77 SED 185 SEED 58 SELECT 64 SELF 170 SEQ 59 SETN 58 SETU 58 SET 58 ISIN 56 ISKIP 64 75 170 212 SLNFORM 88 SLOW 91 SMX 87 SORT 170 212 SPARSE 75 SPATIAL 88 SPLINE 77 SQRT link 110 ISTEP 78 SUBGROUP 78 SUBSECTION 147 SUBSET 78 SUB 58 SUM 71 TABFORM 88 TARGET 52 59 THRESHOLD GLM 109 TOLERANCE 91 ITOTAL 109 111 370 TWOSTAGEWEIGHTS 185 TWOWAY 88 TXTFORM 88 UNIFORM 59 USE 147 152 IVCC 88 VGSECTORS 89 VPV 185 VRB 91 IV 59 IWMF 78 WORKSPACE 198 WORK residuals 111 IXLINK 170 1X 71 YHTFORM 89 LYSS 81 89 332 YVAR 198 Y 71 TDIFF 185 qualifiers datafile line 64 genetic 165 job control 68 variance model 146 R structure 118 definition 129 definition lines 127 random effects 7 correlated 15 regressions model 11 terms multivariate 159 random regressions 149 random terms 94 100 RCB 31 analysis 119 design 28 reading the data 32 48 REML i 2 11 17 REMLRT 17 repeated measures 2 290 reserved terms 96 Trait 96 106 a t r 103 and t 7r 97 103 at 103 at f n 96 103 cos v 7
179. Single local PXEM EMFLAG 7 Standard EM plus 1 local EM step EMFLAG 8 Standard EM plus 10 local EM steps Options 3 and 4 cause all US structures to be updated by PX EM if any particular one requires EM updates 5 Command file Reading the data 83 Table 5 5 List of rarely used job control qualifiers qualifier action ASReml2 EQORDER o EXTRA n The test of whether the AI updated matrix is positive defini tite is based on absorbing the matrix to check all pivots are positive Repeated EM updates may bring the matrix closer to being singular This is assessed by dividing the pivot of the first element with the first diagonal element of the ma trix If it is less than 1077 this value is consistent with the multiple partial correlation of the first variable with the rest being greater than 0 9999999 ASReml fixes the matrix at that point and estimates any other parameters conditional on these values To preceed with further iterations without fixing the matrix values would ultimately make the matrix such that it would be judged singular resulting the analysis being aborted modifies the algorithm used for choosing the order for solv ing the mixed model equations A new algorithm devised for release 2 is now the default and is formally selected by EQORDER 3 The algorithm used for release 1 is essentially that selected by EQORDER 1 The new order is generally su perior EQORDER 1 instructs ASReml to pr
180. TERACT 199 J JOIN 199 N NoGraphs 199 O ONERUN 201 Q QUIET 200 R RENAME 201 S WorkSpace 202 W WorkSpace 202 command line options 197 commonly used functions 96 conditional distribution 12 Conditional F Statistics 20 conditional factors 101 constraining variance parameters 150 Index 364 constraints on variance parameters 127 contrasts 69 Convergence criterion 70 Convergence issues 155 correlated effects 15 correlation 217 between traits 158 model 10 covariance model 11 isotropic 10 covariates 43 62 113 cubic splines 106 data field syntax 49 data file 28 42 43 binary format 45 fixed format 45 free format 43 using Excel 45 data file line 32 datafile line 63 qualifiers 64 syntax 63 datasets barley asd 299 coop fmt 342 grass asd 290 harvey dat 165 nin89 asd 28 oats asd 280 orange asd 324 rat dat 158 rats asd 284 ricem asd 318 voltage asd 287 wether dat 161 wheat asd 306 debug options 199 Denominator Degrees of Freedom 20 dense 114 design factors 113 Deviance 336 diagnostics 18 diallal analysis 103 direct product 7 9 118 direct sum 9 discussion list 4 Dispersion parameter 110 distribution conditional 12 marginal 12 double slash 47 Ecode 40 Eigen analysis 243 Eigen analysis example 348 EM update 146 environment variable job control 68 equations mixed model 14 error variance heterogeneity 9 errors 248 E
181. Thy glory above all the earth Psalm 108 5 Contents Preface i List of Tables xxi List of Figures xxiii 1 Introduction 1 1 1 What ASReml can do 200 000000 doni iddu 2 1 2 Installation oaa aa 2 1 3 User Interface aoaaa aa aa 3 ASReml W 2 a 3 CONTEXT siaaa din ee BE ee a ee ee Se ae 3 1 4 Howto use this guide 0 200200004 4 1 5 Getting assistance and the ASReml forum 4 1 6 Typographic conventions 2 00 00 000 2G 5 2 Some theory 6 2 1 The linear mixed model 0 0 00 0 0 0 0 00 0 0 0 0 0 0008 4 T Contents vi Introductions 2 44 ee 4 ne be ee wee eee a Ge 7 Direct product structures ooo 002005 7 Variance structures for the errors R structures 9 Variance structures for the random effects G structures 10 22 Estimation 2 i 244 4 844585288 bo 2 G4 bd Gas 11 Estimation of the variance parameters 11 Estimation prediction of the fixed and random effects 14 2 3 What are BLUPs 2 02 0 00 000000 15 2 4 Combining variance models 0 0 0 2000000 16 2 5 Inference Random effects 200000005 17 Tests of hypotheses variance parameters 17 DIAGNOSTICS 2084 04 oe eee oS See wee ee ee ee 18 2 6 Inference Fixed effects 2 02000 000020 e 20 Introduction as 4 sae ey ee awl ale kd ee eR ee aS 20 Incremental and Conditional Wald F Statistics
182. a data field containing the coordinates for the first dimension and cc is the number of a data field containing the coordinates for the second direction For example in the analysis of spatial data if the x coordinate was in field 3 and the y coordinate was in field 4 the second argument would be 304 For a G structure relating to the model term fac z y use fac z y For example y a mi slr facla y fac x y 1 fac x y fac x y IEUCV 7 1 3 7 Command file Specifying the variance structures 142 difficult Notes on Factor Analytic models FAk FACVk and XFAk are different parameterizations of the factor analytic model in which X is modelled as TI Y where T is a matrix of loadings on the covariance scale and W is a diagonal vector of specific variances See Smith et al 2001 and Thompson et al 2003 for examples of factor analytic models in multi environment trials The general limitations are that may not include zeros except in the XFAk formulation constraints are required in I for k gt 1 for identifiability Typically one zero is placed in the second column two zeros in the third column etc The total number of parameters fitted kw w k k 1 2 may not exceed w w 1 2 wXw In FAk models the variance covariance matrix X is modelled on the corre lation scale as amp DCD where D is diagonal such that DD diag CX is a correlation matrix of the form F F
183. ach of the variance models There is a surprising level of discrepancy between models for the Wald F statistics The main effect of treatment is significant for the uniform power and antedependence models 16 Examples 298 Table 16 5 Summary of Wald F statistics for fixed effects for variance models fitted to the plant data treatment treatment time model df 1 df 4 Uniform 9 41 5 10 Power 6 86 6 13 Heterogeneous power 0 00 4 81 Antedependence order 1 4 14 3 96 Unstructured 1 71 4 46 16 6 Spatial analysis of a field experiment Barley In this section we illustrate the ASReml syntax for performing spatial and in complete block analysis of a field experiment There has been a large amount of interest in developing techniques for the analysis of spatial data both in the context of field experiments and geostatistical data see for example Cullis and Gleeson 1991 Cressie 1991 Gilmour et al 1997 This example illustrates the analysis of so called regular spatial data in which the data is observed on a lattice or regular grid This is typical of most small plot designed field exper iments Spatial data is often irregularly spaced either by design or because of the observational nature of the study The techniques we present in the following can be extended for the analysis of irregularly spaced spatial data though larger spatial data sets may be computationally challenging depending on the degree of
184. actual model are ignored without flagging an error e Any model terms which are omitted from FOWN statements are tested with the usual conditional test e If any model terms are listed twice only the first test is per formed F con tests specified in FOWN statements are given model codes 0 P The FOWN statements are parsed by the routine that parses the model line and so accepts the same model syntax options Care should be taken to ensure term names are spelt exactly as they appear in the model GLMM n sets the number of inner iterations performed when a iter ASReml3 atively weighted least squares analysis is performed Inner iterations are iterations to estimate the effects in the linear model for the current set of variance parameters Outer it erations are the AI updates to the variance parameters The default is to perform 4 inner iterations in the first round and 2 in subsequent rounds of the outer iteration Set n to 2 or more to increase the number of inner iterations HPGL 2 sets hardcopy graphics file type to HP GL An argument of 2 sets the hardcopy graphics file type to HP GL 2 HOLD list allows the user to temporarily fix the parameters listed Pa ASReml3 rameter numbers have been added to the reporting of input values to facilitate use of this and other parameter number dependent qualifiers The list should be in increasing order using colon to indicate a sequence step size is 1 For example HOLD 1 20
185. ae res 11 Trait i 1 54993 0 200125 7 74 2 3 82051 0 216314 17 66 ar12 4 SIRE 34 effects fitted Finished 18 Jun 2008 12 35 09 062 LogL Converged 16 11 Multivariate animal genetics data Sheep The analysis of incomplete or unbalanced multivariate data often presents com putational difficulties These difficulties are exacerbated by either the number of random effects in the linear mixed model the number of traits the complexity of the variance models being fitted to the random effects or the size of the problem In this section we illustrate two approaches to the analysis of a complex set of incomplete multivariate data Much of the difficulty in conducting such analyses in ASReml centres on obtaining good starting values Derivative based algorithms such as the Al algorithm can be unreliable when fitting complex variance structures unless good starting values are available Poor starting values may result in divergence of the algorithm or slow convergence A particular problem with fitting unstructured variance models is keeping the estimated variance matrix positive definite These are not simple issues and in the following we present a pragmatic approach to them The data are taken from a large genetic study on Coopworth lambs A total of 5 traits namely weaning weight wwt yearling weight ywt greasy fleece weight gfw fibre diameter fdm and ultrasound fat depth at the C site fat were measured on 7043 lambs The lambs we
186. ailable such as ASReml W and ConText described in section 1 3 3 2 Nebraska Intrastate Nursery NIN field experiment The yield data from an advanced Nebraska Intrastate Nursery NIN breeding trial conducted at Alliance in 1988 89 will be used for demonstration see Stroup 3 A guided tour 28 et al 1994 for details Four replicates of 19 released cultivars 35 experimen tal wheat lines and 2 additional triticale lines were laid out in a 22 row by 11 column rectangular array of plots the varieties were allocated to the plots using a randomised complete block RCB design In field trials complete replicates are typically allocated to consecutive groups of whole columns or rows In this trial the replicates were not allocated to groups of whole columns but rather overlapped columns Table 3 1 gives the allocation of varieties to plots in field plan order with replicates 1 and 3 in ITALICS and replicates 2 and 4 in BOLD 3 3 The ASReml data file See Chapter 4 The standard format of an ASReml data file is to have the data arranged in for details space TAB or comma separated columns fields with a line for each sampling unit The columns contain covariates factors response variates traits and weight variables in any convenient order This is the first 30 lines of the file nin89 asd containing the data for the NIN variety trial The data are in field order rows within columns and an optional heading first line of the file has
187. always check the data summary to ensure that the correct number of records have been detected and the data values match the names appropriately Folder C data ex manex variety A QUALIFIERS SKIP 1 QUALIFIER DOPART Reading nin asd FREE FORMAT skipping 1 is active Univariate analysis of yield Summary of 224 records retained of 242 read 1 lines Model term Size miss zero MinNonO Mean MaxNonO StndDevn 1 variety 56 0 0 1 28 5000 56 2 id 0 0 1 000 28 50 56 00 16 20 3 pid 0 O 110l 2628 4156 1121 4 raw 0 Oo 21 00 510 5 840 0 149 0 5 repl 4 0 0 1 2 5000 4 15 Error messages 257 6 nloc 0 O 4 000 4 000 4 000 0 000 7 yield Variate 0 1 060 25 53 42 00 7 450 8 lat 0 O 4 300 ates 47 30 12 90 9 long 0 1 200 14 08 26 40 7 698 10 row 22 0 0 1 11 7321 22 11 column aA 0 0 1 6 3304 T4 12 mu 1 QUALIFIERS R Repl Fault Error in variance header line IR Repl Last line read was IR Repl 0000 ninerr4 variety id pid raw rep nloc yield lat Model specification TERM LEVELS GAMMAS variety 56 mu 1 12 factors defined max 500 O variance parameters max1500 2 special structures Final parameter values 2 0 Last line read was IR Repl 0000 Finished 11 Apr 2008 16 21 43 968 Error in variance header line R Repl Inserting a comma on the end of the first line of the model to give yield mu variety Ir Repl solves that problem but produces the error message Error reading model terms because Repl should have
188. alysis 164 9 1 Introduction 0 00000 ee 165 9 2 The command file 2 00000 00 2 eee 165 93 The pedigree fille sa ac osora ccie 02000200 eee ee 166 9 4 Reading in the pedigree file 004 167 9 5 Genetic groups aooaa a 168 9 6 Reading a user defined inverse relationship matrix 171 Genetic groups in GIV matrices 04 173 The example continued 0 0 0200002 2 ae 173 10 Tabulation of the data and prediction from the model 175 10 1 Introduction 2 2 0 02 00 2 176 10 2 Vabulation 4 2 2 2 6 e 2 Yee 2 oe aR Oe ee ee We oe Gee 176 10 3 Prediction 2 2 0 0 00 0 2 177 Underlying principles ooo 020002200 2G 177 Predict Syntax s 4 a lt ave ate 2 OS ba See eG SE Bee 179 Predict failure 2 a a 182 Associated factors 0 0000 eee ee ee 188 Contents xiii Complicated weighting with IPRESENT 191 Examples 2 0 46 4 64 eine 26 d w Ghee ee SE ee eS 193 11 Command file Running the job 194 11 1 introduction s s sora we we Yee a ee eR eR a ee 195 11 2 The command line 0 0 00000 ee 195 Normal tit 4 2462440 pauk i i540 wh dg dha id bed 195 Processing a pinfile 02004 196 Forming a job template from a datafile 196 11 3 Command line options 2 2 197 Prompt for arguments A 0 0000020 ea 199 Output control B J 2 4 4 944 Poe b PA hg RSLS eS 199 Debug command lin
189. am as an argument the program can access This is the mech anism that allows several OWN models to be fitted in a single run Ts is used to set the type of the parameters It is primarily used in conjunc tion with the OWN structure as ASReml knows the type in other cases The valid type codes are as follows code description action if GP is set V variance forced positive G variance ratio forced positive R correlation l lt r lt l C covariance P positive correlation 0 lt r lt 1 L loading This coding also affects whether the parameter is scaled by g in the output 7 Command file Specifying the variance structures 146 7 6 Variance structure qualifiers Table 7 4 describes the R and G structure line qualifiers Table 7 4 List of R and G structure qualifiers qualifier action ASReml3 s IGP GU GF IGZ INAME f used to constrain parameters within variance structures see Section 7 9 modify the updating of the variance parameters The exact action of these codes in setting bounds for parameters depends on the particular model IGP the default in most cases attempts to keep the parameter in the theoretical parameter space and is activated when the update of a parameter would take it outside its space For example if an update would make a variance negative the negative value is replaced by a small positive value Under the GP condition repeated attempts to make a variance negati
190. an coding error If a job has an error you should read the whole asr file looking at all messages to see whether they identify the problem focus particularly on any error message in the Fault line and the text of the Last line read this line appears twice in the file to make it easier to find check that all labels have been defined and are in the correct case some errors arise from conflicting information the error may point to some thing that appears valid but is inconsistent with something earlier in the file reduce to a simpler model and gradually build up to the desired analysis this should help to identify the exact location of the problem check that lines which must start in column 1 like PREDICT TABULATE and the data filename line do start in column 1 15 Error messages 249 See Chapter 11 memory info working folder If the problem is not resolved after these checks you may need to email Customer Support at support asreml co uk Please send the as file a sample of the data the asr file and the as1 file produced by the debug options d1 running asreml dl basename as In this chapter we show some of the common coding problems The code box on the right shows our familiar job modified to generate 8 coding problems tempts to fit an inappropriate model are often harder to resolve In this chapter we use this example to discuss code debugging in detail Errors arising from at
191. analysis 161 Revised 08 e the variance component matrices for the TEAM and SheepID strata are specified as Trait 0 US GP with starting values 3 0 on the next line The size of the US structure is taken from the number of traits 2 here Since the initial values are given as 3 0 ASReml will plug in values derived from the observed phenotypic variance matrix GP requests that the resulting estimated matrix be kept within the parameter space i e it is to be positive definite the special qualifiers relating to multivariate analysis are ASUV and ASMV 1 see Table 5 4 for detail to use an error structure other than US for the residual stratum you must also specify ASUV see Table 5 4 and include mv in the model if there are missing values to perform a multivariate analysis when the data have already been ex panded use ASMV t see Table 5 4 tis the number of traits that ASReml should expect the data file must have t records for each multivariate record although some may be coded missing 8 4 The output for a multivariate analysis Below is the output returned in the asr file for this analysis ASReml 3 01d 01 Apr 2008 Orange Wether Trial 1984 88 Build e 01 Apr 2008 32 bit 08 Apr 2008 11 46 33 968 32 Mbyte Windows wether Licensed to NSW Primary Industries permanent FEAR BOAR IORI kk kk kkk IA Contact support asreml co uk for licensing and support arthur gilmour dpi nsw gov au FEO OOOO OOO
192. ar dependence in the design matrix means there is no information left to estimate the effect ASReml handles singularities by using a generalized inverse in which the singular row column is zero and the associated fixed effect is zero Which equations are singular depends on the order the equations are processed This is controlled by ASReml for the sparse terms but by the user for the dense terms They should be specified with main effects before interactions so that the table of Wald F statistics has correct marginalization Since ASReml processes the dense terms from the bottom up the first level the last level processed is often singular 6 Command file Specifying the terms in the mixed model 115 Warning The number of singularities is reported in the asr file immediately prior to the REML log likelihood LogL line for that iteration see Section 14 3 The effects and associated standard or prediction error which correspond to these singularities are zero in the sln file Singularities in the sparse_fixed terms of the model may change with changes in the random terms included in the model If this happens it will mean that changes in the REML log likelihood are not valid for testing the changes made to the random model This situation is not easily detected as the only evidence will be in the sln file where different fixed effects are singular A likelihood ratio test is not valid if the fixed model has changed Examples of al
193. ar with ones on the diagonal D is diagonal and k is the number of non zero off diagonals in U the CHOLk and ANTEk models are equivalent to the US structure that is the full variance structure when kis w 1 initial values for US CHOL and ANTE structures are given in the form of a US matrix which is specified lower triangle row wise viz 7 Command file Specifying the variance structures 139 ASReml2 On Oo O29 Ox Oy O 31 32 33 that is initial values are given in the order 1 2 0 3 Oy5 e the US model is associated with several special features of ASReml When used in the R structure for multivariate data ASReml automatically recognises patterns of missing values in the responses see Chapter 8 Also there is an option to update its values by EM rather than Al when its Al updates make the matrix non positive definite Notes on Mat rn The Mat rn class of isotropic covariance models is now described ASReml uses an extended Mat rn class which accomodates geometric anisotropy and a choice of metrics for random fields observed in two dimensions This extension described in detail in Haskard 2006 is given by p h pu d h 4 a v where h he hy is the spatial separation vector 6 a governs geometric anisotropy A specifies the choice of metric and v are the parameters of the Mat rn correlation function The function is pm d v forirwy S x 5 7 1
194. ariance components suppress screen output repeat run for each argument renaming output filenames set workspace size over ride y variate specified in the com mand file with variate number v reports current license details 11 Command file Running the job 199 ASReml2 ASReml2 Prompt for arguments A A ASK makes it easier to specify command line options in Windows Explorer One of the options available when right clicking a as file invokes ASReml with this option ASReml then prompts for the options and arguments allowing these to be set interactively at run time With ASK on the top job control line it is assumed that no other qualifiers are set on the line For example a response of H22r 1 23 would be equivalent to ASReml h22r basename 1 2 3 Output control B J B b BRIEF b suppresses some of the information written to the asr file The data summary and regression coefficient estimates are suppressed by the options B B1 or B2 This option should not be used for initial runs of a job before you have confirmed by checking the data summary that ASReml has read the data as you intended Use B2 to also have the predicted values written to the asr file instead of the pvs file Use B 1 to get BLUE estimates reported in asr file J JOIN was used in association with the CYCLE qualifier to put the output from a set of runs into single files see CYCLE list JOIN on page 205 but is no longer r
195. ariety 2 10 0 1 49 0 272 2 nitrogen 3 45 0 37 69 lt 001 8 variety nitrogen 6 45 0 0 30 0 932 For simple variance component models such as the above the default parame terisation for the variance component parameters is as the ratio to the residual variance Thus ASReml prints the variance component ratio and variance com ponent for each term in the random model in the columns labelled Gamma and Component respectively A table of Wald F statistics is printed below this summary The usual decompo sition has three strata with treatment effects separating into different strata as a consequence of the balanced design and the allocation of variety to whole plots In this balanced case it is straightforward to derive the ANOVA estimates of the stratum variances from the REML estimates of the variance components That is blocks 12624462 6 3175 1 blocks wplots 467 601 3 residual 177 1 The default output for testing fixed effects used by ASReml is a table of so called incremental Wald F statistics These Wald F statistics are described in Section 6 11 The statistics are simply the appropriate Wald test statistics divided by the number of estimable effects for that term In this example there are four terms included in the summary The overall mean denoted by mu is of no interest for these data The tests are sequential that is the effect of each term is assessed by the change in sums of squares achieved by adding the ter
196. ary singular variance parameters using numerical derivatives 4 SIRE 34 effects fitted 6 are zero Two things stand out in this analysis From a genetic perspective the heritability estimate is 0 0364 C0003007 4 0327367 This can be calculated in ASReml with the pin file commands F GenVar 1 4 F TotVar 1 2 H heritability 3 4 Secondly there is little evidence of significant difference between classes The predicted values are 16 Examples 334 Sex PxP 1980 BRxP 1980 BxR 1980 BRxP 1981 0 0 0183 0 0130 0 0432 0 0126 0 0758 0 0268 0 0305 0 0111 1 0 0152 0 0132 0 0375 0 0124 0 0603 0 0244 0 0425 0 0108 An analysis of footrot as a binomial variable using the logistic link is performed by the model line and dropping the DF qualifier Rot bin TOTAL Total mu SEX GRP SEX GRP r SIRE 16783 The pertinant results are Distribution and link Binomial Logit Mu P 1 1 exp XB V Mu 1 Mu N Warning The LogL value is unsuitable for comparing GLM models Notice 4 singularities detected in design matrix 1 LogL 28 1544 S2 1 0000 48 df Dev DF 0 9060 2 LogL 28 7417 S2 1 0000 48 df Dev DF 0 8897 3 LogL 28 7186 S2 1 0000 48 df Dev DF 0 8805 4 LogL 28 6705 S2 1 0000 48 df Dev DF 0 8551 5 LogL 28 6494 S2 1 0000 48 df Dev DF 0 8238 6 LogL 28 6687 S2 1 0000 48 df Dev DF 0 7959 7 LogL 28 6774 S2 1 0000 48 df Dev DF 0 7915 8 LogL 28 6784 52 1 0000 48 df Dev DF 0 7909 9 LogL 28
197. associated with one location and each location is associated with only one region If a level code is missing for one component it must be missing for all Averaging of associated factors will generally give differing results depending on the order in which the averaging is performed We explore this with the following extended example Consider the mean yields from 15 trials classified by region and location in Table 10 4 Table 10 3 Trials classified by region and location location Region L1 L2 L3 L4 L5 L6 L7 L8 Rl T1 T2 T3 T4 T5 T6 R2 T7 T8 T9 T10 T11 T12 T13 T14 T15 Table 10 4 Trial means Tl T2 T3 T4 T5 T6 T7 T8 TI T10 T11 T12 T13 T14 T15 10 12 11 12 13 13 11 43 11 12 13 10 12 10 10 Assuming a simplified linear model yield mu region location trial the predict statement predict trial ASSOCIATE region location trial will reconstruct the 15 trial means from the fitted mu region location and trial effects Given these trial means it is fairly natural to form location means by averaging the trials in each location to get the location means in Table 10 5 10 Tabulation of the data and prediction from the model 189 Table 10 5 Location means L1 L2 L3 L4 L5 L6 L7 L8 11 12 13 12 12 11 10 10 These are given by predict location ASSOCIATE region location trial ASAVERAGE trial or equivalently predict location ASSOCIATE region location trial since the default is to average the ba
198. at count In ASReml the A and I field descriptors are treated identi cally and simply set the field width Whether the field is interpreted alphabetically or as a number is controlled by the A qualifier Other legal components of a format statement are e the character required to separate fields blanks are not permitted in the format e the character indicates the next field is to be read from the next line However a on the end of a format to skip a line is not honoured e BZ the default action is to read blank fields as missing values and NA are also honoured as missing values If you wish to read blank fields as zeros include the string BZ e the string BM switches back to blank missing mode e the string Tc moves the last character read pointer to line position c so that the next field starts at position c 1 For example TO goes back to the beginning of the line e the string D invokes debug mode A format showing these components is FORMAT D 314 8X A6 3 2x F5 2 4x BZ 2011 and is suitable for reading 27 fields from 2 data records such as 111122223333xxxxxxxxALPHAFxx 4 12xx 5 32xx 6 32 xxxx123 567 901 345 7890 5 Command file Reading the data 66 Table 5 2 Qualifiers relating to data input and output qualifier action ASReml3 IMERGE c f SKIP n MATCH a b may be specified on a line following the datafile line READ n RECODE The purpose is to combine
199. ata records have been sorted into field order because the residuals are not in the same order that the data is stored The residual from a spatial analysis will have the units part added to it when units is also fitted The drs file could be renamed with extension db1 and used for input in a subsequent run instructs ASReml to write the data to a binary file The file asrdata bin is written in single precision if the argument n is 1 or 3 asrdata dbl is written in double precision if the argument nis 2 or 4 the data values are written before trans formation if the argument is 1 or 2 and after transformation if the argument is 3 or 4 The default is single precision after transformation see Section 4 2 When either SAVE or RESIDUALS is specified ASReml saves the factor level labels to a basename v1l and attempts to read them back when data input is from a binary file Note that if the job basename changes between runs the v11 file will need to be copied to the new basename If the v11 file does not match the factor structure i e the same factors in the same order reading the v11 file is aborted performs a Regression Screen a form of all subsets regres sion For d model terms in the DENSE equations there are 2f 1 possible submodels Since for d gt 8 2f 1 is large the submodels explored are reduced by the parameters n and m so that only models with at least n default 1 terms but no more than m default 6
200. ate lines The t2 syntax for specifying the model is 11 column AR1 3 22 row AR1 3 response wt weight fixed r random f sparse_fixed response is the label for the response variable s to be analysed multivariate analysis is discussed in Chapter 8 weight is a label of a variable containing weights weighted analysis is discussed in Section 6 7 separates response from the list of fixed and random terms fixed represents the list of primary fixed explanatory terms that is variates factors interactions and special terms for which Wald F statistics are required See Table 6 1 for a brief definition of reserved model terms operators and commonly used functions The full definition is in Section 6 6 random represents the list of explanatory terms to be fitted as random effects see Table 6 1 sparse_fized are additional fixed terms not included in the table of Wald F statistics General rules The following general rules apply in specifying the linear mixed model all elements in the model must be space separated elements in the model may also be separated by which is ignored 6 Command file Specifying the terms in the mixed model 95 e the character separates the response variables s from the explanatory vari ables in the model Choose labels e data fields are identified in the model by their labels oe ee ANOR labels are case sensitive fusi eee labels may be abbreviated tru
201. ates of a subset of the variance parameters for each trait for the genetic example expressed as a ratio to their asymptotic s e 343 Wald F statistics of the fixed effects for each trait for the genetic CXAMPlGs i k ka e bdo G44 REE bed nS a ar A EE 343 List of Tables xxi 16 16 Variance models fitted for each part of the ASReml job in the analysis of the genetic example oo a a a a 346 List of Figures 5 1 14 1 14 2 14 3 14 4 14 5 Variogram in 4 sectors for Cashmore data 92 Residual versus Fitted values 200 228 Variogram of residuals 2 aa a 237 Plot of residuals in field plan order 238 Plot of the marginal means of the residuals 239 Histogram of residuals 2 2 239 Residual plot for the rat data 2 2 0 2 0 00 0048 286 Residual plot for the voltage data 289 Trellis plot of the height for each of 14 plants 2 291 Residual plots for the EXP variance model for the plant data 294 Sample variogram of the residuals from the AR1xAR1 model for the Slate Hall data 2 2 2 ee 301 Sample variogram of the residuals from the AR1xAR1 model for the Tullibigeal data 2 2 ee 309 Sample variogram of the residuals from the AR1x AR1 pol column 1 model for the Tullibigeal data o o aaa 309 xxii List of Figures xxiii 16 8 16 10 16 11 16 12 16 13 16 14 16 15
202. ations New York Breslow N E 2003 Whither PQL Technical Report 192 UW Biostatistics Working Paper Series University of Washington Breslow N E and Clayton D G 1993 Approximate inference in generalized linear mixed models Journal of the American Statistical Association 88 9 25 Breslow N E and Lin X 1995 Bias correction in generalised linear mixed models with a single component of dispersion Biometrika 82 81 91 Browne W and Draper D 2004 A comparison of bayesian and likelihood based methods for fitting multilevel models Research Report 04 01 Not tingham Statistics Research Report 04 01 Callens M and Croux C 2005 Performance of likelihood based estimation methods for multilevel binary regression models Technical report Dept of Applied Economics Katholieke Universiteit Leuven Cox D R and Hinkley D V 1974 Theoretical Statistics London Chapman and Hall Cox D R and Snell E J 1981 Applied Statistics Principles and Examples London Chapman and Hall Cressie N A C 1991 Statistics for spatial data New York John Wiley and Sons Inc Cullis B R and Gleeson A C 1991 Spatial analysis of field experiments an extension to two dimensions Biometrics 47 1449 1460 Cullis B R Gleeson A C Lill W J Fisher J A and Read B J 1989 A new procedure for the analysis of early generation variety trials Applied Statistics 38 361 375 356
203. atistics see OUTLIER If a job is being run a large number of times signicicant gains in processing time can sometimes be made by reorganising the data so reading of irrelevant data is avoided use of CONTINUE to reduce the number of iterations and avoiding uncessessary output see SLNFORM YHTFORM and NOGRAPHICS Timing processes The elapsed time for the whole job can be calculated approximately by comparing the start time with the finish time Timings of particular processes can be ob tained by using the DEBUG LOGFILE qualifiers on the first line of the job This requests the asl file be created and hold some intermediate results especially from data setup and the first iteration Included in that information is timing information on each phase of the job 12 Command file Merging data files Introduction Merge Syntax Examples 210 12 Command file Merging data files 211 12 1 Introduction The MERGE directive described in this chapter is designed to combine information from two files into a third file with a range of qualifiers to accomodate various scenarios It was developed with assistance from Chandrapal Kailasanathan to replace the MERGE qualifier see page 66 which had very limited functionality The MERGE directive is placed BEFORE the data filename lines It is an inde pendent part of the ASReml job in the sense that none of the files are necessarily involved in the subsequent analyses performed
204. ay be placed on the datafile line and following lines They may also be defined using an environment variable called ASREML_QUAL The environment variable is processed immediately after the datafile line is processed All qualifier settings are reported in the asr file Use the Index to check for examples or further discussion of these qualifiers Important Many of these are only required in very special circumstances and new users should not attempt to understand all of them You do need to under stand that all general qualifiers are specified here Many of these qualifiers are referenced in other chapters where their purpose will be more evident Table 5 3 List of commonly used job control qualifiers qualifier action CONTINUE is used to restart resume iterations from the point reached in a previous run This qualifier can alternately be set from the command line using the option letters C continue or F fi nal see Section 11 3 on command line options After each iteration ASReml writes the current values of the variance pa rameters to a file with extension rsv re start values with information to identify individual variance parameters The CONTINUE qualifier causes ASReml to scan the rsv file for parameter values related to the current model replacing the values obtained from the as file before iteration resumes If the model has changed ASReml will pick up the values it recognises as being for the same terms Furtherm
205. basic theory which you may need to come back to New ASReml users are advised to read Chapter 3 before attempting to code their first job It presents an overview of basic ASReml coding demonstrated on a real data example Chapter 16 presents a range of examples to assist users further When coding you first job look for an example to use as a template Data file preparation is described in Chapter 4 and Chapter 5 describes how to input data into ASReml Chapters 6 and 7 are key chapters which present the syntax for specifying the linear model and the variance models for the random effects in the linear mixed model Variance modelling is a complex aspect of analysis We introduce variance modelling in ASReml by example in Chapter 7 Chapters 8 and 9 describe special commands for multivariate and genetic analyses respectively Chapter 10 deals with prediction of fixed and random effects from the linear mixed model and Chapter 13 presents the syntax for forming functions of variance components such as heritability Chapter 11 discusses the operating system level command for running an ASReml job Chapter 12 describes a new data merging facility Chapter 14 gives a detailed explanation of the output files Chapter 15 gives an overview of the error messages generated in ASReml and some guidance as to their probable cause 1 5 Getting assistance and the ASReml forum Audio Tutorials Support The ASReml help accessable through ASReml W can also
206. been spelt repl Portion of the output is displayed Since the model line is parsed before the data is read this run failed before reading the data Folder C data ex manex variety A QUALIFIERS SKIP 1 QUALIFIER DOPART Reading nin asd FREE FORMAT skipping 1 is active 1 lines Model term Repl is not valid recognised Fault Error reading model terms Last line read was Repl 15 Error messages 258 Currently defined structures COLS and LEVELS 1 variety id pid raw repl ann F WN nloc Finished 28 Jul 2005 10 06 49 173 il 2 e e re BP RB e A e FP be e BP e FP re N O O OOOO a fF W N e O Error reading model terms O o OOOO 6 Misspelt factor name and 7 Wrong levels declaration in the G struc ture definition lines The next fault ASReml detects is G structure header indicating that there is something wrong in Term not found nin alliance trial nin89 asd skip 1 yield mu variety the G structure definition lines In this case Repl the replicate term in the first G structure def at inition line has been spelt incorrectly To cor 2 0 IDV 0 1 rect this error replace Repl with repl Folder C data ex manex variety A QUALIFIERS SKIP 1 QUALIFIER DOPART 1 is active Reading nin asd FREE FORMAT skipping 1 lines Univariate analysis of yield Summary of 224 records retained of 242 read Model term Size miss zero MinNonO Mean 1 variety 56 0 0 1 28 5000
207. ble the path must also be given and the path is required when configuring ASReml W or Context In this guide we assume the command file has a filename extension as ASReml also recognises the filename extension asc as an ASReml command file When these are used the extension as or asc may be omitted from basename as in the command line if there is no file in the working directory with the name basename The options and arguments that can be supplied on the command line to modify a job at run time are described in Chapter 11 3 A guided tour 35 ASReml2 Forming a job template Notice that the data files nin89 asd and nin89aug asd commenced with a line of column headings Since these headings do not contain embedded blanks we can use ASReml to make a template for the as file by running ASReml with the datafile as the command argument see Chapter 11 For example running the command asreml nin89aug asd writes a file nin89aug as if it does not already exist which looks like Title nin89aug variety id pid raw rep nloc yield lat long row column LANCER 1 NA NA 1 4 NA 4 3 1 2 11 LANCER 1 NA NA 1 4 NA 4 3 2 4 2 1 LANCER 1 NA NA 1 4 NA 4 3 3 6 3 1 LANCER 1 NA NA 1 4 NA 4 3 4 841 variety A id pid raw rep nloc yield lat long row column Check Correct these field definitions nin89aug asd SKIP 1 column mu Specify fixed model Ir Specify random model 120 column column AR1 0 1
208. ble functions Searle 1971 page 408 e all variance parameters are held fixed at the current REML estimates from the maximal model In this example it is clear that the incremental Wald statistics may not produce the desired test for the main effect of A as in many cases we would like to produce a Wald statistic for A based on R A 1 B R 1 A B R 1 B 2 Some theory 22 The issue is further complicated when we invoke marginality considerations The issue of marginality between terms in a linear mixed model has been dis cussed in much detail by Nelder 1977 In this paper Nelder defines marginality for terms in a factorial linear model with qualitative factors but later Nelder 1994 extended this concept to functional marginality for terms involving quan titative covariates and for mixed terms which involve an interaction between quantitative covariates and qualitative factors Referring to our simple illustra tive example above with a full factorial linear model given symbolically by y 1 A B A B then A and B are said to be marginal to A B and 1 is marginal to A and B In a three way factorial model given by y 1 A B C A B A C B C A B C the terms A B C A B A C and B C are marginal to A B C Nelder 1977 1994 argues that meaningful and interesting tests for terms in such models can only be conducted for those tests which respect marginality relations This philos ophy underpins the following descriptio
209. by ASReml for the next part if the rsv is copied prior to running the next part That is we add the PATH 2 coding to the job copy mt1 rsv to mt2 rsv so that when we run PATH 2 it starts from where PATH 1 finished and run the job using asreml cnrw64 mt 2 The Loglikelihood from this run is 20000 1427 37 Finally we use the PATH 3 coding to obtain the final analysis copy mt2 rsv to mt3 rsv and run the final stage starting from the stage 2 results Note that we are using the automatic updating associated with CONTINUE A portion of the final output file is Notice LogL values are reported relative to a base of 20000 00 NOTICE 76 singularities detected in design matrix 1 LogL 1427 37 S2 1 0000 35006 df 2 components constrained 2 LogL 1424 58 S2 1 0000 35006 df 3 LogL 1421 07 52 1 0000 35006 df 1 components constrained 4 LogL 1420 11 52 1 0000 35006 df 5 LogL 1419 93 S2 1 0000 35006 df 6 LogL 1419 92 S2 1 0000 35006 df 7 LogL 1419 92 S2 1 0000 35006 df 8 LogL 1419 92 S2 1 0000 35006 df 9 LogL 1419 92 S2 1 0000 35006 df 10 LogL 1419 92 52 1 0000 35006 df 11 LogL 1419 92 52 1 0000 35006 df Source Model terms Gamma Component Comp SE C at Trait 1 age grp 49 49 0 135360E 02 0 135360E 02 2 03 OP at Trait 2 age grp 49 49 0 101561E 02 0 101561E 02 1 24 OP at Trait 4 age grp 49 49 0 176505E 02 0 176505E 02 1 13 OF 16 Examples 348 at Trait 5 at Trait 1 at Trait 2 at Tra
210. cate that variety is a character field Folder C asr ex manex QUALIFIERS SKIP 1 Reading nin89 asd FREE FORMAT skipping 1 lines Univariate analysis of yield Field 1 LANCER of record 1 line 1 is not valid Since this is the first data record you may need to skip some header lines see SKIP or append the A qualifier to the definition of factor variety Fault Missing faulty SKIP or A needed for variety Last line read was LANCER 1 NA NA 1 4 NA 4 31 21 1 15 Error messages 256 ninerr3 variety id pid raw rep nloc yield lat Model specification TERM LEVELS GAMMAS mu 0 0 000 variety 0 0 000 12 factors defined max 500 O variance parameters max 900 Last line read was 2 special structures LANCER 1 NA NA 1 4 NA 4 31 2 11 Finished 28 Jul 2005 09 51 12 817 Missing faulty SKIP or A needed for variety 4 A missing comma and 5 A misspelt factor name in linear model The model has been written over two lines but ASReml does not realise this be cause the first line does not end with a comma The missing comma causes the fault Error in variance header line as ASReml tries to interpret the second line of the model see Last line read as the vari ance header line The asr file is displayed IR Repl nin alliance trial variety A repl 4 nin89 asd skip 1 yield mu variety tr Repl below Note that the data has now been successfully read as indicated by the data summary You should
211. ch will appear in the table of Wald F statistics For example FOWN ABC mu FOWN A B B C A C mu ABC FOWN A B C mu ABC A B B C A C would request the Wald F statistics based on see page 21 R A mu B C sparse B mu A C sparse C mu A B sparse A B mu ABC B C A C sparse B C mu ABC A B A C sparse ra A C mu A B C A B B C sparse and B C mu ABC A B A C B C sparse Doy gt Warnings e For computational convenience ASReml calculates FOWN tests using a full rank parameterization of the fitted model with rank numerator degrees of freedom NumDF of terms generated by the incremental Wald F tests e Unfortunately if some terms in the implicit model defined by the requested FOWN test would have more or less NumDF than are present in the full rank parameterization because aliased effects are reordered it can not be calculated cor rectly from the full rank parameterization In this case AS Reml reverts to the conditional test but identifies the terms that need to be reordered in the fitted model to obtain the FOWN test s specified It is necessary to rerun ASReml after reordering these terms to obtain the FOWN test s specified Several reruns may be needed to perform all FOWN tests spec ified 5 Command file Reading the data 85 Table 5 5 List of rarely used job control qualifiers qualifier action e Any model terms in the FOWN lists which do not appear in the
212. cords which have v yield D lt 0 ID lt D lt v or missing value in the field subject yield D lt 1 D gt 100 ID gt D gt v to the logical operator o IDV DV lt gt v DV o v discards records subject to the yield DV lt 0 IDV lt DV lt v logical operator o which have v in the yield DV lt 1 DV gt 100 IDV gt DV gt v field but keeps records with missing value in the field if DV is used after 1A or I v should refer to the encoded factor level rather than the value in the data file see also Section 4 2 Use DV to discard just those records with a missing value in the field ID v is equivalent to DV DV v InitialWt DV 5 Command file Reading the data 57 Table 5 1 List of transformation qualifiers and their actions with examples qualifier argument action examples ASReml3 ASReml2 ASReml3 ASReml2 DO nlit to DOM f ENDDO EXP Jddm Jmmd Jyyd IM M lt gt Vv IM lt M lt IM gt M gt Vv e IMAX MIN v MOD 1MM S INA v causes ASReml to perform the follow ing transformations n times default is variables in current term increment ing the target by 7 default 1 and the argument if present by i default 0 Loops may not be nested A loop is terminated by ENDDO another DO or a new field definition copies and converts additive marker covariables 1 0 1 to dominance marker covariables see below
213. d mu variety r repl served words for example mv see Table 6 1 tase tates p for which Wald F statistics are not required 12 11 column AR1 424 22 row AR1 904 tions including special functions and re include large gt 100 levels terms 6 4 Random terms in the model The r random terms in the model formula NIN Alliance Trial 1989 variety e comprise random covariates factors and in teractions including special functions and ee reserved words see Table 6 1 column 11 i SENI nin89 asd skip 1 e involve an initial non zero variance compo yield mu variety ir rep1 nent or ratio relative to the residual vari If mv 1 2 11 column AR1 424 ance default 0 1 the initial value can be 22 row AR1 904 specified after the model term or if the vari ance structure is not scaled identity by syn tax described in detail in Chapter 7 an initial value of its variance ratio may be followed by a GP keep positive the default GU unrestricted or GF fixed qualifier see Table 7 4 use and to group model terms that may not be reordered Normally ASReml will reorder the model terms in the sparse equations putting smaller terms first to speed up calculations However the order must be preserved if the user defines a structure for a term which also covers the following term s a way of defining a covariance structure across model terms Grouping is specifically required if the model terms a
214. d not begin with a number see command line argu ments e Dollar substitution occurs before most other high level actions Consequently ASSIGN strings and commandline arguments may substitute into a CYCLE line e I J K and L are reserved as names refering to items in the CYCLE list and should therefore not be used as names of an ASSIGN string ICYCLE list is a mechanism whereby ASReml can loop through a series ASReml3 of jobs The CYCLE qualifier must appear on its own line starting in character 1 list is a series of values which are substituted into the job wherever the I string appears The list may spread over several lines if each incomplete line ends with a COMMA A series of sequential integer values can be given in the form 7 j no embedded spaces The output from the set of runs is concatenated into a single set of files For example ICYCLE 0 4 0 5 0 6 20 O mat2 1 9 I GPF would result in three runs and the results would be appended to a single file 11 Command file Running the job 206 High level qualifiers qualifier action ASReml3 The CYCLE mechanism now acts as an inner loop when used with RENAME ARG Previously both could not be used to gether As an example the RENAME ARG arguments might list a set of traits and the CYCLE arguments sequentially test a set of markers ASReml3 A cycle string may consist of up to 4 substrings separated by a semicolon and referenced as I J
215. d SED associated with the various models Choos ing a model on the basis of smallest SE or SED is not recommended because the model is not necessarily fitting the variability present in the data The predict statement included the qualifier TWOSTAGEWEIGHTS This generates an extra table in the pvs file which we now display for each model Predicted values with Effective Replication assuming Variance 38754 26 Heron Heron Heron Heron 1 2 3 4 1257 98 1501 45 1404 99 1412 57 22 1504 20 6831 22 5286 22 160293 16 Examples 305 Table 16 7 Summary of models for the Slate Hall data REML number of Wald model log likelihood parameters F statistic SED AR1xAR1 700 32 3 13 04 59 0 AR1xAR1 units 696 82 4 10 22 60 5 IB 707 79 4 8 84 62 0 Heron 5 1514 48 21 1830 Heron 25 1592 02 26 0990 Predicted values with Effective Replication assuming Variance 45796 58 Heron 1 1245 58 23 8842 Heron 2 1516 24 22 4423 Heron 3 1403 99 24 1931 Heron 4 1404 92 24 0811 Heron 5 1471 61 23 2995 Heron 25 1573 89 26 0505 Predicted values with Effective Replication assuming Variance 8061 808 Heron 1 1283 59 4 03145 Heron 2 1549 01 4 03145 Heron 3 1420 93 4 03145 Heron 4 1451 86 4 03145 Heron 5 1533 27 4 03145 Heron 25 1630 63 4 03145 The value of 4 for the IB analysis is clearly reasonable given there are 6 actual replicates but this analysis has used up 48 degrees of freedom for the rowblk
216. d a number i internally Some of these numbers are reported in the structure input section of the asr file These numbers are used to specify which parameters are to be constrained using this method e VCC c specifies that there are c constraint lines defining constraints to be applied e the constraint lines occur after the variance header line and any R and G structure lines that is there must be a variance header line each set of similar constraints is specified in a separate line in the form i kVa p Vp BLOCKSIZE n In this set i k p is the number of a variance model parameter and Vm m k p is an associated scale coefficient such that ym X Vm is equal in value to 7 x indicates the presence of the scale coefficient Vm for the parameter m if the coefficient is 1 you may omit the 1 if the coefficient is 1 you may write m instead of m x 1 Use the BLOCKSIZE n qualifier when constraints of the same form are re quired on blocks of n contiguous parameters See example below 7 Command file Specifying the variance structures 152 a variance parameter may only be included in constraint lists once To equate several components put them all in the one list e the i k L refer to positions in the full variance parameter vector This number may change if the model is changed and is often difficult to determine but the numbers are given in the ASReml file for variance structures If it ref
217. d as random and the treatment terms as fixed The choice of treatment terms as fixed or random depends largely on the aims of the experiment The aim of this example is to select the best varieties The definition of best is somewhat more com plex since it does not involve the single trait sqrt rootwt but rather two traits namely sqrt rootwt in the presence absence of bloodworms Thus to minimise selection bias the variety main effects and thence the tmt variety interactions are taken as random The main effect of treatment is fitted as fixed to allow for the likely scenario that rather than a single population of treatment by variety effects there are in fact two populations control and treated with a different mean for each There is evidence of this prior to analysis with the large differ ence in mean sqrt rootwt for the two groups 14 93 and 8 23 for control and treated respectively The inclusion of tmt as a fixed effect ensures that BLUPs of tmt variety effects are shrunk to the correct mean treatment means rather than an overall mean The model for the data is given by y XT LZ yu Zou Z3u3 Z4u4 Z5u5 e 16 7 16 Examples 314 where y is a vector of length n 264 containing the sqrt rootwt values T corresponds to a constant term and the fixed treatment contrast and u1 us correspond to random variety treatment by variety run treatment by run and variety by run effects The random effects and error are as
218. d is given by 2 2 2 2 2 op 0 04 o 06 recalling that 2 1 2 0 0 S 4 A 1 i E 02 In the half sib analysis we only use the estimate of additive genetic variance from the sire variance component The ASReml pin file is presented below along with the output from the following command asreml p mt3 F phenWYG 9 14 24 29 39 44 45 50 defines 55 60 16 Examples 350 F phenD 15 18 30 33 51 54 F phenF 19 23 34 38 F Direct 24 38 4 F Maternal 39 44 24 29 H WWTh2 70 55 H YWIh2 72 57 H GFWh2 75 60 H FDMh2 79 64 H FATh2 84 69 R GenCor 24 38 R MatCor 85 90 55 phenWYG 9 15 76 0 3130 56 phenWYG 10 11 76 0 3749 57 phenWYG 11 20 92 0 6313 70 Direct 24 2 376 0 6458 71 Direct 25 2 698 0 8487 72 Direct 26 6 174 1 585 73 Direct 27 0 1120 0 7330E 01 85 Maternal 39 1 567 0 3788 86 Maternal 40 1 521 0 4368 87 Maternal 41 0 6419 0 7797 WWTh2 Direct 2 70 phenWYG 55 YWTh2 Direct 2 72 phenWYG 57 GFWh2 Direct 2 75 phenWYG 60 FDMh2 Direct 3 79 phenD 18 64 FATh2 Direct 3 84 phenF 23 69 GenCor 2 1 Tr si 25 SQR Tr si 24 Tr si GenCor 3 1 Tr si 27 SQR Tr si 24 Tr si GenCor 3 2 Tr si 28 SQR Tr si 26 Tr si GenCor 4 1 Tr si 30 SQR Tr si 24 Tr si GenCor 4 2 Tr si 31 SQR Tr si 26 Tr si GenCor 4 3 Tr si 32 SQR Tr si 29 Tr si GenCor 5 1 Tr si 34 SQR Tr si 24 Tr si GenCor 5 2 Tr si 35 SQR Tr si 26 Tr si GenCor 5 3 Tr si 36 SQR Tr si 29 Tr si GenCor 5 4 Tr si 37 SQR Tr si 33 Tr
219. d oe ee ee A ae E a 223 The sin fil s sos aoc a ae a Re ee ee a 226 The yht fil casos id opat ee eda eh i iak es 228 14 4 Other ASReml output files a a a 229 Whe saot filens a 2 24 pene se Ga dae Peed ek eee a 229 The gash file 2 44 26 fe a eh ee ee Re 232 The dp file 2 gg we a ee ae a wed hoa di a wa a 232 The pve fil q sasos 4 ee 4a Dee eed ed ee 232 Thee xpvs file seor eb RO 4 Wel ee wa eG le be ae Ee Ge 233 The ares tile eg 6 eee eA a See eee eee ee a 233 Tihe lt svitile 3 34 26 foe a ee be ee ee Re 240 Wie Gab TG e g ge 6 2 a An ere ae ae ede dg i fg wk etl R 240 The vrbfile 2 2 2 ee 241 The vyp tile 2 2 i404 0 20 aos 4 we Ge ee a 242 14 5 ASReml output objects and where to find them 243 15 Error messages 246 15 1 Introduction 2 2 2 0 2 247 15 2 Common problems 2 2 0 0 00 ee 247 Contents xvi 15 3 Things to check inthe asrfile 0 250 15 4 An example 2 2465 2 en ans SRR eR ee a a aa 253 15 5 Information Warning and Error messages 263 16 Examples 278 16 1 Introduction 2 2 0 00000 2 ee 279 16 2 Split plot design Oats 2 0 0 0 0 00 0000 00004 279 16 3 Unbalanced nested design Rats 00 283 16 4 Source of variability in unbalanced data Volts 287 16 5 Balanced repeated measures Height 290 16 6 Spatial analysis of a field experiment Barley
220. data fields from the primary data file with data fields from a secondary file f This MERGE qualifier has been replaced by the much more powerful MERGE statement see Chapter 12 The effect is to open the named file skip n lines and then in sert the columns from the new file into field positions starting at position c If MATCH a b is specified ASReml checks that the field a 0 lt a lt c has the same value as field b If not it is assumed that the merged file has some missing records and missing values are inserted into the data record and the line from the MERGE file is kept for comparison with the next record It is assumed that the lines in the MERGE file are in the same order as the corresponding lines occur in the primary data file and that there are no extraneous lines in the MERGE file A much more powerful merging facility is provided by the MERGE directive described in chapter 12 For example assuming the field definitions define 10 fields PRIMARY DAT skip 1 IMERGE 6 SECOND DAT SKIP 1 MATCH 1 6 would obtain the first five fields from PRIMARY DAT and the next five from SECOND DAT checking that the first field in each file has the same value Thus each input record is obtained by combining information from each file before any transformations are performed formally instructs ASReml to read n data fields from the data file It is needed when there are extra columns in the data file that must be read but are
221. ded in binomial and Poisson models for Normal models just subtract the offset variable from the response variable for example count POIS OFFSET base DISP mu group The offset is included in the model as n X7 0 The offset will often be something like In n ITOTAL n is used especially with binomial and ordinal data where n is the field containing the total counts for each sample If omitted count is taken as 1 Residual qualifiers control the form of the residuals returned in the yht file The predicted values returned in the yht file will be on the linear predictor scale if the WORK or PVW qualifiers are used They will be on the observation scale if the DEVIANCE PEARSON RESPONSE or PVR qualifiers are used DEVIANCE produces deviance residuals the signed square root of d h from Table 6 4 where h is the dispersion parameter controlled by the DISP qualifier This is the default PEARSON writes Pearson residuals aa in the yht file PVR writes fitted values on the response scale in the yht file This is the default PVW writes fitted values on the linear predictor scale in the yht file RESPONSE produces simple residuals y WORK produces residuals on the linear predictor scale LTT Revised 08 A second dependent variable may be specified except with a multinomial re sponse MULTINOMIAL if a bivariate analysis is required but it will always be treated as a normal variate no syntax is pr
222. dels provide a rich and flexible tool for the analysis of many data sets commonly arising in the agricultural biological medical and en vironmental sciences Typical applications include the analysis of un balanced longitudinal data repeated measures analysis the analysis of un balanced de signed experiments the analysis of multi environment trials the analysis of both univariate and multivariate animal breeding and genetics data and the analysis of regular or irregular spatial data ASReml provides a stable platform for delivering well established procedures while also delivering current research in the application of linear mixed models The strength of ASReml is the use of the Average Information Al algorithm and sparse matrix methods for fitting the linear mixed model This enables it to analyse large and complex data sets quite efficiently One of the strengths of ASReml is the wide range of variance models for the ran dom effects in the linear mixed model that are available There is a potential cost for this wide choice Users should be aware of the dangers of either overfitting or attempting to fit inappropriate variance models to small or highly unbalanced data sets We stress the importance of using data driven diagnostics and encour age the user to read the examples chapter in which we have attempted to not only present the syntax of ASReml in the context of real analyses but also to Preface Revised 08 ASReml3 ind
223. dentified across REGION rather than within REGION Then the nested structure is hidden but ASReml will still detect the structure and produce a valid conditional Wald F statistic This situation will be flagged in the M code field by changing the letter to lower case Thus in the nested model the three M codes would be A and B because REGION SITE is obviously an interaction dependent 2 Some theory 24 ASReml3 on REGION In the second model REGION and SITE appear to be independent factors so the initial M codes are A and A However they are not independent because REGION removes additional degrees of freedom from SITE so the M codes are changed from A and Ato a and A When using the conditional Wald F statistic it is important to know what the maximal conditional model MCM is for that particular statistic It is given explicitly in the aov file The purpose of the conditional Wald F statistic is to facilitate inference for fixed effects It is not meant to be prescriptive of the appropriate test nor is the algorithm for determining the MCM foolproof The Wald statistics are collectively presented in a summary table in the asr file The basic table includes the numerator degrees of freedom 14 and the incremental Wald F statistic for each term To this is added the conditional Wald F statistic and the M code if FCON is specified A conditional Wald F statistic is not reported for mu in the asr but is in the aov fil
224. dentities are printed in the s1ln file identities should be whole numbers less than 200 000 000 unless ALPHA is specified pedigree lines for parents must precede their progeny unknown parents should be given the identity number 0 if an individual appearing as a parent does not appear in the first column it is assumed to have unknown parents that is parents with unknown parent age do not need their own line in the file identities may appear as both male and female parents for example in forestry We refer the reader to the sheep genetics example on page 341 1A white paper downloadable from http www vsni co uk resources doc contains de tails of these options 9 Command file Genetic analysis 168 9 5 Genetic groups Important If all individuals belong to one genetic group then use 0 as the identity of the parents of base individuals However if base individuals belong to various genetic groups this is indicated by the GROUPS qualifier and the pedigree file must begin by identifying these groups All base individuals should have group identifiers as parents In this case the identity 0 will only appear on the group identity lines as in the following example where three sire lines are fitted as genetic groups Genetic group example animal P sire 9 1A dam lines 2 damage adailygain harveyg ped ALPHA MAKE GROUP 3 harvey dat adailygain mu Ir animal 02 5 GU
225. diately moves the variance parameters back towards the previous values and restarts the iteration modifies the ability of ASReml to detect singularities in the mixed model equations This is intended for use on the rare occasions when ASReml detects singularities after the first iteration they are not expected Normally when no TOLERANCE qualifier is specified a singu larity is declared if the adjusted sum of squares of a covariable is less than a small constant 7 or less than the uncorrected sum of squares xn where 7 is 107 in the first iteration and 10 thereafter The qualifier scales n by 10 for the the first or subsequent iterations respectively so that it is more likely an equation will be declared singular Once a singular ity is detected the corresponding equation is dropped forced to be zero in subsequent iterations If neither argument is supplied 2 is assumed If the second argument is omitted it is given the value of the first If the problem of later singularities arises because of the low coefficient of variation of a covariable it would be better to centre and rescale the covariable If the degrees of freedom are correct in the first iteration the problem will be with the variance parameters and a different variance model or variance constraints is required requests writing of vrb file Previously the default was to write the file w GB w Fh w a a N this is a test of matern Vario
226. directive The intention is to simplify the model specification in MET Multi Environment Trials analyses where say Column ef fects are to be fitted to a subset of environments It may also be used on the intrinsic factor Trait in a multivariate analysis provided it correctly identifies the number of levels of Trait either by including the last trait number or appending sufficient zeros Thus if the analysis involves 5 traits SUBSET Trewe Trait 13400 sets hardcopy graphics file type to wmf 5 Command file Reading the data 79 Table 5 5 List of rarely used job control qualifiers qualifier action ASReml3 ASReml2 ATLOADINGS 7 ATSINGULARITIES BMP controls modification to AI updates of loadings in eXtended Factor Analytic models After ASReml calculates updates for variance parameters it checks whether the updates are reasonable and sometimes reduces them over and above any STEPSIZE shrinkage The extra shrinkage has two levels Loadings that change sign are restricted to doubling in mag nitude and if the average change in magnitude of loadings is greater than 10 fold they are all shrunk back When the user does not provide constraits ASReml rotates the loadings each iteration When AILOADINGS 7 is speci fied it also prevents AI updates of some loadings during the first i iterations For f gt 1 factors only the last factor is estimated conditional on the earlier ones in the first f
227. e controls form of the tab file TABFORM 1 is TAB separated tab becomes _tab txt TABFORM 2 is COMMA separated tab becomes _tab csv TABFORM 3 is Ampersand separated tab becomes _tab tex See TXTFORM for more detail sets the default argument for PVSFORM SLNFORM TABFORM and YHTFORM if these are not explicitly set TXTFORM or TXTFORM 1 replaces multiple spaces with TAB and changes the file extension to say _sln txt This makes it easier to load the solutions into Excel TXTFORM 2 replaces multiple spaces with COMMA and changes the file extension to say _sln csv However since factor labels sometimes contain COMMAS this form is not so convenient TXTFORM 3 replaces multiple spaces with Ampersand ap pends a double backslash to each line and changes the file extension to say _sln tex Latex style Additional significant digits are reported with these formats Omitting the qualifier means the standard fixed field format is used For yht and sln files setting n to 1 means the file is not formed modifies the appearance of the variogram calculated from the residuals obtained when the sampling coordinates of the spa tial process are defined on a lattice The default form is based on absolute distance in each direction This form dis tinguishes same sign and different sign distances and plots the variances separately as two layers in the same figure specifies that n constraints are to be applied to the
228. e YRK1i 8 3356 0 8190 E 69 4817 13 6534 sqrt yc YRK3 13 3057 0 9549 E 177 0428 25 4106 sqrt ye YRK3 8 1133 0 8190 E 65 8264 13 2894 SED Overall Standard Error of Difference 1 215 exposed BLUP control BLUP Figure 16 9 BLUPs for treated for each variety plotted against BLUPs for control 16 Examples 321 Interpretation of results Recall that the researcher is interested in varietal tolerance to bloodworms This could be defined in various ways One option is to consider the regression implicit in the variance structure for the trait by variety effects The variance structure can arise from a regression of treated variety effects on control effects namely Uv Buy F E where the slope 8 Ova o2 Tolerance can be defined in terms of the deviations from regression Varieties with large positive deviations have greatest tolerance to bloodworms Note that this is similar to the researcher s original intentions except that the regression has been conducted at the genotypic rather than the phenotypic level In Figure 16 9 the BLUPs for treated have been plotted against the BLUPs for control for each variety and the fitted regression line slope 0 61 has been drawn Varieties with large positive deviations from the regression line include YRK3 Calrose HR19 and WC1403 o o o fe 0 5 8 o o f o _ 88 o g o 2 DB 2 o Ss o 8 0 0 fe o a 5 o gt o 7 a a o
229. e adjusted for covariates The FOWN qualifier page 84 allows the user to replace any all of the conditional Wald F statistics with tests of the same terms but adjusted for other model terms as specified by the user the FOWN test is not performed if it implies a change in degrees of freedom from that obtained by the incremental model Kenward and Roger Adjustments In moderately sized analyses ASReml will also include the denominator degrees of freedom DenDF denoted by 12 Kenward and Roger 1997 and a probablity value if these can be computed They will be for the conditional Wald F statistic if it is reported The DDF i see page 69 qualifier can be used to suppress the DenDF calculation DDF 1 or request a particular algorithmic method DDF 1 for numerical derivatives DDF 2 for algebraic derivatives The value in the probability column either P_inc or P_con is computed from an F reference distribution An approximation is used for computational convenience when cal culating the DenDF for Conditional F statistics using numerical derivatives The DenDF reported then relates to a maximal conditional incremental model MCIM which depending on the model order may not always coincide with the max imal conditional model MCM under which the conditional F statistic is cal culated The MCIM model omits terms fitted after any terms ignored for the conditional test I after in marginality pattern In the example above M
230. e estimated a negative component by setting the GU option for this term The portion of the ASReml output for this analysis is 6 LogL 343 428 S2 1 1498 262 df 1 components constrained 7 LogL 343 234 S2 1 1531 262 df 8 LogL 343 228 S2 1 1572 262 df 9 LogL 343 228 S2 1 1563 262 df Source Model terms Gamma Component Comp SE C variety 44 44 2 01903 2 33451 3 01 OP run 66 66 0 276045 0 319178 059 OP pair 132 132 0 853941 0 987372 2 59 0P uni tmt 2 264 264 0 176158 0 203684 0 32 O P Variance 264 262 1 00000 1 15625 2 17 QP tmt variety DIAGonal 1 1 30142 1 50477 2 26 OU tmt variety DIAGonal 2 0 321901 0 872199 0 92 OY tmt run DIAGonal 1 1 20098 1 38864 2 19 0U tmt run DIAGonal 2 1 92457 2 22530 3 07 OU Wald F statistics Source of Variation NumDF DenDF F_ine Prob 7 mu 1 56 5 1276 73 lt 001 4 tmt 1 60 6 448 83 lt 001 The estimated variance components from this analysis are given in column b of table 16 8 There is no significant variance heterogeneity at the residual or tmt run level This indicates that the square root transformation of the data has successfully stabilised the error variance There is however significant variance heterogeneity for tmt variety interactions with the variance being much greater for the control group This reflects the fact that in the absence of bloodworms the potential maximum root area is greater Note that the tmt variety interaction variance for the treated group is negative The negative
231. e measure then the conclusions would have been inconsistent with the conclusions obtained from the REML log likelihood ratio see Table 16 3 Source Model terms Gamma Component Comp SE C setstat 10 10 0 233417 0 119370E 01 1 35 0 P setstat regulatr 80 64 0 601817 0 307 7715 01 3 64 OP teststat 4 4 0 642752E 01 0 328705E 02 0 93 OF 16 Examples 290 Variance 256 255 1 00000 0 511402E 01 72 OP Table 16 3 REML log likelihood ratio for the variance components in the voltage data REML 2x terms log likelihood difference P value setstat 200 31 5 864 0077 setstat regulatr 184 15 38 19 0000 teststat 199 71 7 064 0039 16 5 Balanced repeated measures Height The data for this example is taken from the GENSTAT manual It consists of a total of 5 measurements of height cm taken on 14 plants The 14 plants were either diseased or healthy and were arranged in a glasshouse in a completely random design The heights were measured 1 3 5 7 and 10 weeks after the plants were placed in the glasshouse There were 7 plants in each treatment The data are depicted in Figure 16 3 obtained by qualifier line IY y1 G tmt JOIN in the following multivariate ASReml job In the following we illustrate how various repeated measures analyses can be conducted in ASReml For these analyses it is convenient to arrange the data in a multivariate form with 7 fields representing the plant number treatment identification and
232. e with the model term that it is associated with an error occurred processing the pedigree The pedigree file must be ascii free format with ANIMAL SIRE and DAM as the first three fields ASReml failed to calculate the GLM working variables or weights Check the data 15 Error messages 271 Table 15 3 Alphabetical cause s remedies list of error messages and probable error message probable cause remedy Increase declared levels for factor Increase workspace Insufficient data read from file Insufficient points for Insufficient workspace invalid analysis trait number Invalid binary data Invalid Binomial Variable Invalid definition of factor Invalid error structure for Multivariate Analysis Invalid factor in model Invalid model factor Invalid SOURCE in R structure definition Invalid weight filter column number Iteration aborted because of singularities Either the field has alphanumeric values but has not been declared using the A qualifier or there is not enough space to hold the levels of the factor To increase the levels insert the expected number of levels after the A or I qualifier in the field definition Use WORKSPACE s to increase the workspace available to ASReml If the data set is not extremely big check the data summary Maybe the response variable is all missing there must be at least 3 distinct data values for a spline ter
233. e 16 16 Plot of the residuals from the nonlinear model of Pinheiro and Bates 16 10 Generalized Linear Mixed Models ASReml uses an approximate likelihood technique called penalized quasi likelihood PQL see section 6 8 to analyse data sampled from one of the common mem bers of the exponential family In this section we present a few examples to demonstrate the coding in ASReml Binomial analysis of Footrot score Mohommad Alwan pers comm for his Master thesis at Massey University scored the feet of 2513 lambs born in 1980 and 1981 The lambs were from 5 mating groups 7 Perendale rams over Perendale ewes in 1980 6 Booroola by Romney rams over Perendale ewes in 1980 3 Booroola rams over Romney ewes in 1980 6 Perendale rams over Perendale ewes in 1981 and 12 Booroola by Romney rams from froup 3 over Perendale ewes in 1981 This data was analysed by Gilmour 1984 and Gilmour et al 1987 16 Examples 332 The data file LAMB DAT contains grouped data for the 68 combinations of Sex and Sire for two footshape classes FS1 all four feet are normal FS2 one foot is deformed and two indicator variables for the presence of disease conditions Scald and Rot No scald or rot was present in group 4 lambs and these responses have been set to missing The genetic relationships among sires are ignored in this analysis although it would just require a sire relationship matrix to include them Our first analysis is of the incidence of foot
234. e Variance Correlation Matrix UnStructured Residual 1 000 0 3216E 03 0 1626E 03 0 2556 Covariance Variance Correlation Matrix UnStructured Trait SIRE 0 1661 0 1470E 01 0 3303E 02 0 3039 Wald F statistics Source of Variation NumDF DenDF_con F_inc F_con M P_con 11 Trait SEX 2 NA 393 15 76 10 A NA 12 Trait GRP 10 40 9 1993 52 1993 52 A lt 001 Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using numerical derivatives The YVar data was artificially created and the SIRE variance is too large to represent purely genetic variance Multinomial Ordinal GLM analysis of Cheese taste By way of introduction to ordinal analysis in ASReml consider the cheese data from page 175 of McCullagh and Nelder 1994 Four cheeses were scored on a nine point scale by 52 tasters giving Table 16 13 Response frequencies in a cheese tasting experiment Cheese I H IH IV V VI VI VII IX Total 1 7 8 8 19 8 1 52 12 11 7 6 1 0 0 52 6 8 23 7 5 1 0 52 0 1 3 7 L4 16 11 52 Jawe 0 6 1 0 O ooo There are several ways of supplying the data for multinomial analysis In this case totals in the 9 classes are supplied in a single grouped response It is analysed using a multiple 8 threshold model as in McCullagh and Nelder 1994 with the ASReml code McCullagh and Nelder Cheese example p 175 Cheese A Rating G 9 Total 16 Examples 339 Cheese txt Rating MULT 9 CUM Trait Cheese PREDICT Cheese
235. e are many other multivariate analysis techniques which are not covered by ASReml estimating the correlations between distinct traits for example fleece weight Multivariate analysis is used when we are interested in and fibre diameter in sheep and for repeated measures of a single trait Repeated measures on rats Wolfinger 1996 summarises a range of vari ance structures that can be fitted to repeated measures data and demonstrates the models using five weights taken weekly on 27 rats sub jected to 3 treatments This command file demonstrates a multivariate analysis of the five repeated measures Note that the two di mensional structure for common error meets the requirement of independent units and is correctly ordered traits with units Wether trial data Three key traits for the Australian wool in dustry are the weight of wool grown per year the cleanness and the diameter of that wool Much of the wool is produced from wethers and most major producers have traditionally used a particular strain or bloodline To as sess the importance of bloodline differences many wether trials were conducted One trial was conducted from 1984 to 1988 at Borenore near Orange It involved 35 teams The file wether dat shown below contains greasy of wethers representing 27 bloodlines fleece weight kg yield percentage of clean fleece weight to greasy fleece weight and fibre diameter microns The code wether as to the right p
236. e authors would appreciate feedback and suggestions for improvements to the program and this guide Proceeds from the licensing of ASReml are used to support continued develop ment to implement new developments in the application of linear mixed models The developmental version is available to supported licensees via a website upon request to VSN Most users will not need to access the developmental version unless they are actively involved in testing a new development Acknowledgements We gratefully acknowledge the Grains Research and Development Corporation of Australia for their financial support for our research since 1988 Brian Cullis and Arthur Gilmour wish to thank the NSW Department of Primary Industries for providing a stimulating and exciting environment for applied biometrical re search and consulting Rothamsted Research receives grant aided support from the Biotechnology and Biological Sciences Research Council of the United King dom We sincerely thank Ari Verbyla Sue Welham Dave Butler and Alison Smith the other members of the ASReml team Ari contributed the cubic smoothing splines technology information for the Marker map imputation on going test ing of the software and numerous helpful discussions and insight Sue Welham has overseen the incorporation of the core into Genstat and contributed to the predict functionality Dave Butler has developed the ASReml R class of func tions Alison contributed to the devel
237. e first step in an ASReml analysis is to prepare the data file Data file prepara tion is discussed in this chapter using the NIN example of Chapter 3 for demon stration The first 25 lines of the data file are as follows ARAPAHOE 5 1105 661 1 SCOUT66 10 1110 511 1 NE83498 12 1112 492 NE84557 13 1113 509 NE83432 14 1114 268 NE85556 15 1115 633 NE85623 16 1116 513 CENTURK78 17 1117 632 PRPRPRPPR Boop Bop NE86482 21 1121 560 1 HOMESTEAD 22 1122 566 LANCOTA 23 1123 514 1 NE86501 24 1124 635 1 NE86503 25 1125 840 1 variety id pid raw repl nloc yield lat long row column BRULE 2 1102 631 1 4 31 55 4 3 20 4 17 1 REDLAND 3 1103 701 1 4 35 05 4 3 21 6 18 1 CODY 4 1104 602 1 4 30 1 4 3 22 8 19 1 4 33 05 4 3 24 20 1 NE83404 6 1106 605 1 4 30 25 4 3 25 2 21 1 NE83406 7 1107 704 1 4 35 2 4 3 26 4 22 1 NE83407 8 1108 388 1 4 19 4 8 6 1 2 1 2 CENTURA 9 1109 487 1 4 24 35 8 6 2 4 2 2 4 25 55 8 6 3 6 3 2 COLT 11 1111 502 1 4 25 1 8 6 4 8 4 2 24 6 8 6 6 5 2 25 45 8 6 7 2 6 2 13 4 8 6 8 4 7 2 31 65 6 6 9 6 3 2 25 65 8 6 10 8 9 2 1 4 31 6 8 6 12 10 2 NORKAN 18 1118 446 1 4 22 3 8 6 13 2 11 2 KS8831374 19 1119 684 1 4 34 2 8 6 14 4 12 2 TAM200 20 1120 422 1 4 21 1 8 6 15 6 13 2 4 28 8 6 16 8 14 2 1 4 28 3 8 6 18 15 2 4 25 7 8 6 19 2 16 2 4 31 75 8 6 20 4 17 2 4 42 8 6 21 6 18 2 4 2 The data file The standard format of an ASReml data file is to have the data arranged in columns fields with a single line f
238. e given in a separate file if a filename in quotes is given as the argument to PRWTS Check the output to ensure that the values in the tables of weights are applied in the correct order ASReml may transpose the table of weights to match the order it needs for processing When weights are supplied in a separate file two layouts are allowed The default is to read all values in the file regardless of layout Otherwise the weights must appear a single column field one weight per line where the field is specified by appending c to the filename 10 Tabulation of the data and prediction from the model 192 Consider a rather complicated example from a rotation experiment conducted over several years One analysis was of the daily live weight gain per hectare of the sheep grazing the plots There were periods when no sheep grazed Different flocks grazed in the different years Daily liveweight gain was assessed between 5 and 8 times in the various years To obtain a measure of total productivity in terms of sheep liveweight we need to weight the daily gain by the number of sheep grazing days per month The production for each year is given by predict year 1 crop 1 pasture lime AVE month 56 55 56 53 57 63 6 0 predict year 2 crop 1 pasture lime AVE month 36 0 0 53 23 24 54 54 43 35 0 0 predict year 3 crop 1 pasture lime AVE month 70 0 21 17000 70 0 0 53 0 predict year 4 crop 1 pasture lime AVE month 53 56 22 92 19 44 0 0 36 0 O 49 predic
239. e gives the build date for the program and indicates whether it is a 32bit or 64bit version The third line gives the date and time that the job was run and reports the size of the workspace The general announcements box outlined in asterisks at the top of the file notifies the user of current release features The remaining lines report a data summary the iteration sequence the estimated variance parameters and a table of Wald F statistics The final line gives the date and time that the job was completed and a statement about convergence ASRem1 3 01d 01 Apr 2008 NIN alliance trial 1989 Build e 01 Apr 2008 32 bit 04 Apr 2008 17 00 47 453 32 Mbyte Windows nin89 Licensed to NSW Primary Industries permanent Fkk ak ak k ak ak ak ak 3K aK ak 3K ak ak 3K aK ak 3K ak 2 3K ak aK 3K ak 3K 3K a 3K K ak 3K ak ak 3K aK ICI I III A IK a A K 2 K K Contact support asreml co uk for licensing and support FECA OGRE ARG Folder C data asr3 ug3 manex variety A QUALIFIERS SKIP 1 QUALIFIER DOPART 1 is active Reading nin89 asd FREE FORMAT skipping 1 lines Univariate analysis of yield Summary of 224 records retained of 224 read 3 A guided tour 37 convergence sequence parameter estimates testing fixed effects Model term Size miss zero MinNonO Mean 1 variety 56 0 0 1 28 5000 2 id 0 O 1 000 28 50 3 pid 0 1101 2628 4 raw 0 21 00 510 5 5 repl 4 0 0 1 2 5000 6 nloc Q O 4 000 4 000 7 yield Variate 0 1
240. e half 0 5 with v It usually implies the variable zero 0 is not read see examples on page 53 5 Command file Reading the data 56 Table 5 1 List of transformation qualifiers and their actions with examples ASReml3 qualifier argument action examples 1 1 le v usual arithmetic meaning note that yield 10 0 0 gives 0 but v 0 gives a missing value where v is not 0 1 v raises the data which must be positive yield to the power v SQRyld yield 70 5 17 0 takes natural logarithms of the data yield which must be positive LNyield yield 70 17 1 takes reciprocal of data data must be yield positive INVyield yield 1 IS I lt gt v logical operators forming 1 if true 0 if yield lt false high yield gt 10 gt ABS takes absolute values no argument re yield quired ABSyield yield ABS ARCSIN v forms an ArcSin transformation using Germ Total the sample size specified in the argu ASG Germ ARCSIN Total ment a number or another field In the side example for two existing fields Germ and Total containing counts we form the ArcSin for their ratio ASG by copying the Germ field and applying the ArcSin transformation using the Total field as sample size COS SIN s takes cosine and sine of the data vari Day able with period s having default 2m CosDay Day COS 365 omit s if data is in radians set s to 360 if data is in degrees ID D lt gt v D o v discards re
241. e iteration during which predictions will be formed 5 Command file Reading the data 71 Table 5 3 List of commonly used job control qualifiers action ASReml2 qualifier SUM Xv lY vu IG vu JOIN On case sensitive operating systems eg Unix the filename ABORTASR NOW or FINALASR NOW must be upper case Note that the ABORTASR NOW file is deleted so nothing of importance should be in it If you perform a system level abort CTRL C or close the program window output files other than the rsv file will be incomplete The rsv file should still be functional for resuming iteration at the most recent parameter estimates see CONTINUE Use MAXIT 1 where you want estimates of fixed effects and predictions of random effects for the particular set of variance parameters supplied as initial values Otherwise the estimates and predictions will be for the updated variance parameters see the BLUP qualifier below If MAXIT 1 is used and an Unstructured Variance model is fit ted ASReml will perform a Score test of the US matrix Thus assume the variance structure is modelled with reduced pa rameters if that modelled structure is then processed as the initial values of a US structure ASReml tests the adequacy of the reduced parameterization causes ASReml to report a general description of the distribu tion of the data variables and factors and simple correlations among the variables for those records i
242. e lines of the pin file should follow on the next lines terminated by a blank line 13 Functions of variance components 216 13 3 Syntax Functions of the variance components are specified in the pin file in lines of the form letter label coefficients e letter either F H or R must occur in column 1 F is for linear combinations of variance components His for forming the ratio of two components Ris for forming the correlation based on three components e label names the result e coefficients is the list of coefficients for the linear function Linear combinations of components First ASReml extracts the variance compo phenvar 1 4 2 phone var nents from the asr file and their variance F genvar 1 4 geno var matrix from the vvp file Each linear func H berit 4 3 heritability tion formed by an F line is added to the list of components Thus the number of coefficients increases by one each line We seek to calculate k c v cov c v v and var c v where v is the vector of existing variance components c is the vector of coefficients for the linear function and k is an optional offset which is usually omitted but would be 1 to represent the residual variance in a probit analysis and 3 289 to represent the residual variance in a logit analysis The general form of the directive is F lablla b tc tdtmx k where a b c and d are subscripts to existing components Va Up Ve and vg
243. e models are listed in Table 7 3 As indicated in the discussion of 2b care must be taken with respect to scale parameters when combining variance models see also Section 7 7 R structure definition For each of the s sections there must be c R structure definitions Each definition may take several lines Each R structure definition specifies a variance model and has the form order field model initial_values qualifiers additional_initial_values e order is either the number of levels in the corresponding term or the name of a factor that has the same number of levels as the term for example 11 column AR1 0 5 is equivalent to column column AR1 0 5 when column is a factor with 11 levels NIN Alliance Trial 1989 variety A row 22 column 11 nin89aug asd skip 1 yield mu variety r repl f mv 121 11 column AR1 0 3 22 row AR1 0 3 repl 1 repl 0 IDV 0 1 term and therefore indexes the levels of the term ASReml uses this field to sort the units so they match the R structure in the example the data will be sorted internally rows within columns for the analysis but the residuals will be printed in the yht file in the original order which is actually rows within columns in this case field is the name of the data field variate or factor that corresponds to the Important It is assumed that the joint indexing of the components uniquely defines the experimental units if field i
244. e nominate the data file e specify qualifiers to modify the reading of the data the output produced the operation of ASReml Data line syntax NIN Alliance Trial 1989 variety A row 22 column 11 nin89aug asd skip 1 yield mu variety The datafile line appears in the ASReml command file in the form datafile qualifiers e datafile is the path name of the file that contains the variates factors covari ates traits response variates and weight variables represented as data fields see Chapter 4 enclose the path name in quotes if it contains embedded blanks the qualifiers tell ASReml to modify either the reading of the data and or the output produced see Table 5 2 below for a list of data file related qualifiers the operation of ASReml see Tables 5 3 to 5 6 for a list of job control qual ifiers e the data file related qualifiers must appear on the data file line e the job control qualifiers may appear on the data file line or on following lines e the arguments to qualifiers are represented by the following symbols f a filename n an integer number typically a count p a vector of real numbers typically in increasing order r areal number s a character string t a model term label v the number or label of a data variable vlist a list of variable labels 5 Command file Reading the data 64 5 7 Data file qualifiers Table
245. e options D E 199 Graphics command line options G H 1 N Q 199 Job control command line options C F O R 201 Workspace command line options S W 202 Examples 2 424646 6 0 4 4 4 04 49 4o 4 be eo 203 11 4 Advanced processing arguments 0 4 203 Standard use of arguments 00004 203 Prompting for input 2 00000002 pe eee 204 Paths and Loops 0 0000 eee eee eee 204 Contents xiv Order of Substitution 11 5 Performance issues aooaa a aa Multiple processors ooa a Slow processes ooo ooo a a Timing processes o oo a 12 Command file Merging data files 12 1 Introduction 220 12 2 Merge Syntax oaoa aa 12 3 Examples or s s aha Ye we ae A eee eS 13 Functions of variance components 13 1 Introduction 0 0 2 000 13 2 VPREDICT PIN file processing 1I Synta an ee eee DE AETR E E a Linear combinations of components Heritability oo a a Correlation ooa aaa a A more detailed example 14 Description of output files 14 1 Introduction oaa a 208 208 208 208 209 210 211 211 213 214 215 215 216 216 217 217 218 220 Contents XV 14 2 An example 22 0 8 e 452 98 e204 bee Behe BOS a ee os 222 14 3 Key output files 02000000202 eee 223 The asr file soo a
246. e trend in their means Field PL GE NSi DA Jul 205 12 41 18 ange E a pe ee fists tpg tneant Saint caren e en er ae ee eS st ag Ta Da et Elegie A EE a EE aea a E ee ee oe Figure 14 3 Plot of residuals in field plan order N W Ho O Bw Residuals V HB ana CF inh hasit Range 8 Figure 14 4 Plot of the marginal means of the residuals Hist A oa eect ta 2005 1 18 Peak Count 17 Range 24 87 15 91 Figure 14 5 Histogram of residuals 14 Description of output files 240 Finally we present a small example of the display produced when an XFA struc ture is fitted The output from a small example with 9 environments and 2 factors is DISPLAY of variance partitioning for XFA structure in xfa Env 2 Geno LW sst ssstasestessstesestensstessotss 4 TotalVar Zexpl PsaiVar Loadings il 1 0 3339 79 7 0 0679 0 5147 0 0335 2 12 0 1666 100 0 0 0000 0 4003 0 0797 3 1 2 0 2475 67 8 0 0798 0 3805 0 1514 4 a 2 0 1475 100 0 0 0000 0 3625 0 1269 5 1 2 0 4496 100 0 0 0000 0 6104 0 278 6 1 2 0 1210 100 0 0 0000 0 2287 0 2622 z 1 2 0 4106 54 4 0 1872 0 4152 0 226 8 1 2 0 0901 100 0 0 0000 0 0922 0 2857 9 1 2 0 1422 100 0 0 0000 0 2819 0 2506 Q ssssteses esaatesaafeaast osste t s t gt Average 0 2343 89 1 0 0372 0 3651 0 0763 In
247. easonable to specify the AISINGULARITIES qualifier sets hardcopy graphics file type to bmp 5 Command file Reading the data 80 Table 5 5 List of rarely used job control qualifiers action qualifier IBRIEF n ASReml2 IBLUP n ASReml3 suppresses some of the information written to the asr file The data summary and regression coefficient estimates are suppressed This qualifier should not be used for initial runs of a job until the user has confirmed from the data summary that the data is correctly interpreted by ASReml Use BRIEF 2 to cause the predicted values to be written to the asr file instead of the pvs file Use BRIEF 1 to get BLUE fixed effect estimates reported in asr file The BRIEF qualifier may be set with the B command line option is used to calculate the effects reported in the sln file with out calculating any derived quantities such as predicted val ues or updated variance parameters For argument values 1 3 ASReml solves for the effects directly while for values 4 19 it solves the mixed model equations by iteration al lowing larger models to be fitted With direct solution the estimation REML iteration routine is aborted after n 1 forming the estimates of the vector of fixed and ran dom effects by matrix inversion n 2 forming the estimates of the vector of fixed and ran dom effects REML log likelihood and residuals this is the default n 3 forming the estimate
248. ed in the variance header line these lines are always placed after any R structure definition lines variance parameter constraints are included if parameter constraints are to be imposed see the VCC c qualifier in Table 5 5 and Section 7 9 on constraints between and within variance structures A schematic outline of the variance model specification lines variance header line and R and G structure definition lines is presented in Table 7 2 using the variance model of 4 for demonstration Table 7 2 Schematic outline of variance model specification in ASReml general syntax model 4 variance header line s e g 12 2 R structure definition lines Si C 1 11 column AR1 0 3 C_2 22 row AR1 0 3 C_c S2 C1 C_c S_s C 1 7 Command file Specifying the variance structures 128 Table 7 2 Schematic outline of variance model specification in ASReml general syntax model 4 G structure definition lines G1 repl 1 4 0 IDV 0 1 G_2 G_g Variance header line The variance header line is of the form NIN Alliance Trial 1989 s e g variety A id e sand c relate to the R structures g is the number of G structures PR e the variance header line may be omitted column 11 if the default IID R structure is required BENE GSS FORA o yield mu variety r repl no G structures are being explicitly defined 1f my and there are no parameter constraints see 1 2 1 VCC and examples 1 and 2a
249. ed matrices one for each term Additionally we assume the residuals for each trait may be correlated Thus for this example we would like to fit a total of 4 unstructured variance models For such a situation it is sensible to commence the modelling process with a series of univariate analyses These give starting values for the diagonals of the variance matrices but also indicate what variance components are estimable The ASReml job for the univariate analyses is Multivariate Sire amp Dam model tag sire 92 II dam 3561 I grp 49 sex brr 4 litter 4871 age wwt IMO ywt MO MO recodes zeros as missing values gfw MO fdm IMO fat MO coop fmt wwt mu age brr sex age sex r sire dam lit age grp sex grp f grp Tables 16 14 and 16 15 present the summary of these analyses Fibre diameter was measured on only 2 female lambs and so interactions with sex were not fitted The dam variance component was quite small for both fibre diameter and fat The REML estimate of the variance component associated with litters was effectively zero for fat Table 16 14 REML estimates of a subset of the variance parameters for each trait for the genetic example expressed as a ratio to their asymptotic s e term wwt ywt gfw fdm fat sire dam litter age grp sex grp 3 68 6 25 8 79 2 29 2 90 3 57 4 93 0 99 1 39 3 43 3 95 2 78 2 23 0 31 3 70 1 92 0 37 1 91 1 15 1 92 0 05 0 00 1 74 1 83 Tab
250. ee lines there are actually only 5 genetic groups and two constraints so that the fixed effects for A B and C sum to zero and for D and E sum to zero leaving only 3 fixed degrees of freedom fitted Therefore if the A inverse for this pedigree was saved it will contain GROUPSDF 3 in the GIV file The example continued Below is an extension of harvey as to use harvey giv which is partly shown to the right This G inverse matrix is an identity matrix of order 74 scaled by 0 5 that is 0 5Z This model is simply an example which is easy to verify Note that harvey giv is specified on the line immediately preceding harvey dat command file giv file GIV file example 01 01 5 animal P 02 02 5 sire P 03 03 5 dam 04 04 5 lines 2 05 05 5 damage adailygain harvey ped ALPHA harvey giv giv structure file te t2 lt 8 harvey dat to Tor 2B adailygain mu line r giv sire 1 25 74 74 5 9 Command file Genetic analysis 174 Model term specification associating the harvey giv structure to the coding of sire takes precedence over the relationship matrix structure implied by the P qualifier for sire In this case the P is being used to amalgamate animals and sires into a single list and the giv matrix must agree with the list order 10 Tabulation of the data and prediction from the model Introduction Tabulation Prediction Underlying principles Syntax Examples 175 10 Tabulation of
251. efine the index of vigour as the residual from this regression This approach is clearly inefficient since there is error in both variables We seek to determine an index of tolerance from the joint analysis of treated and control root area this is for the paired data Y sye X S5yc Y axis 1 8957 14 8835 X axis 8 2675 23 5051 Figure 16 8 Rice bloodworm data Plot of square root of root weight for treated versus control Standard analysis 16 Examples 313 The allocation of bloodworm treatments within varieties and varieties within runs defines a nested block structure of the form run variety tmt run run variety run variety tmt run pair pair tmt run run variety units There is an additional blocking term however due to the fact that the blood worms within a run are derived from the same batch of larvae whereas between runs the bloodworms come from different sources This defines a block structure of the form run tmt variety C run run tmt run tmt variety run run tmt pair tmt Combining the two provides the full block structure for the design namely run run variety run tmt run tmt variety run run variety run tmt units run pair run tmt pair tmt In line with the aims of the experiment the treatment structure comprises va riety and treatment main effects and treatment by variety interactions In the traditional approach the terms in the block structure are regarde
252. efix letter Therefore the title MUST NOT include an exclamation mark 5 4 Specifying and reading the data Important Typically a data record consists of all the information pertaining to an experi mental unit plot animal assessment Data field definitions manage the process of converting the fields as they appear in the data file to the internal form needed by ASReml This involves mapping coding factors general transformations skipping fields and discarding unnecessary records If the necessary information is not in a single file the MERGE facility See chapter 12 may help The data fields to be saved for analysis are defined immediately after the job title The definitions indicate how each field in the data file is handled as it is read into ASReml ASReml deduces how many of them are read from the data file from the associated transformation information override with the READ qualifier described in Table 5 5 No more than 10 000 variables may be read or formed Data field definitions NIN Alliance Trial 1989 variety A should be given for all fields in the data file id fields can be skipped and fields on the end pid of a data line without a field definition are ra ignored if there are not enough data fields es a on a data line the remainder are taken from yield the next line s lat x A long e must be presented in the order in which vow 22 they appear in the data file column 11 nin89aug asd sk
253. elated residuals are in different orders data file order and field order respectively the residuals are printed in the yht file but the statistics in the res file are calculated from the combined residual the Covariance Variance Correlation C V C matrix calculated directly from the residuals it contains the covariance below the diagonals the vari ances on the diagonal and the correlations above the diagonal The FITTED matrix is the same as is reported in the asr file and if the Logl has converged is the one you would report the BLUPS matrix is clculated from the BLUPS and is provided so it can be used as starting values when a simple initial model has been used and you are wanting to attempt to fit a full unstructured matrix the rescaled has the variance from the FITTED and the covariance from the BLUPS and might we more suitable as an initial matrix if the variances have been estimated The FITTED and RESCALEd matrices should not be reported relevant portions of the estimated variance matrix for each term for which an R structure or a G structure has been associated a variogram and spatial correlations for spatial analysis the spatial correlations are based on distance between data points see Gilmour et al 1997 the slope of the log absolute residual on log predicted value for assessing pos sible mean variance relationships and the location of large residuals For ex ample SLOPES FOR LOG ABS RES O
254. eml command file to running an ASReml job and inter preting the output files You are encouraged to read this chapter before moving to the later chapters e areal data example is used in this chapter for demonstration see below e the same data are also used in later chapters e links to the formal discussion of topics are clearly signposted by margin notes This example is of a randomised block analysis of a field trial and is only one of many forms of analysis that ASReml can perform It is chosen because it allows an introduction to the main ideas involved in running ASReml However some aspects of ASReml in particular pedigree files see Chapter 9 and multivariate analysis see Chapter 8 are only covered in later chapters ASReml is essentially a batch program with some optional interactive features The typical sequence of operations when using ASReml is e Prepare the data typically using a spreadsheet or data base program e Export that data as an ASCII file for example export it as a csv comma separated values file from Excel e Prepare a job file with filename extension as e Run the job file with ASReml Review the various output files revise the job and re run it or extract pertinent results for your report You will need a file editor to create the command file and to view the various output files On unix systems vi and emacs are commonly used Under Win dows there are several suitable program editors av
255. eml is running and deleted when it finishes It will normally be invisible to the user unless the job crashes It is used by ASReml W to tell when the job finishes An ASReml run generates many files and the sln and yht files in particular are often quite large and could fill up your disk space You should therefore regularly tidy your working directories maybe just keeping the as asr and pvs files 14 2 An example In this chapter the ASReml output files are NIN Alliance Trial 1989 discussed with reference to a two dimensional variety A i id separable autoregressive spatial analysis of the oe NIN field trial data see model 3b on page 123 repl 4 of Chapter 7 for details The ASReml com nloc mand file for this analysis is presented to the isla right Recall that this model specifies a sep n arable autoregressive correlation structure for row 22 residual or plot errors that is the direct prod column 11 i I i I uct of an autoregressive correlation matrix of 7892 as skip 1 DISPLAY 15 order 22 for rows and an autoregressive corre yield mu variety f mv lation matrix of order 11 for columns In this predict variety case 0 5 is the starting correlation for both 1 2 row row AR1 0 5 columns and rows column column AR1 0 5 14 Description of output files 223 14 3 Key output files Revised 08 The key ASReml output files are the asr sln and yht files The asr
256. ent of a cubic spline for variable v vA J ae S S S lt L So Ke Se US o amp S 6 Command file Specifying the terms in the mixed model 97 Table 6 1 Summary of reserved words operators and functions model term brief description common usage fixed random other functions t n and t r c f cos v r ge f giv f n gt f h f ide f inv v 7r le f leg v n 1t f log vL r mai f mai fits variable n from the G set of variables t This is a special case of the SUBGROUP qualifier function applied to G variables Note that the square parentheses are permit ted alternative syntax adds r times the design matrix for model term to the previous design matrix r has a default value of 1 If t is complex if may be necessary to predefine it by saying t and t r factor f is fitted with sum to zero constraints forms cosine from v with period r condition on factor variable f gt r associates the nth giv G inverse with the factor f condition on factor variable f gt r factor fis fitted Helmert constraints fits pedigree factor f without rela tionship matrix forms reciprocal of v r condition on factor variable f lt r forms n 1 Legendre polynomials of order 0 intercept 1 linear n from the values in v the intercept polynomial is omitted if v is pre ceded by the negative sign condition on factor variable f l
257. envar 9 0 2875 0 1430 phencorr phenvar SQR phenvar phenvar 0 4495 0 0483 gencor 2 i Tr si 5 SQR Tr si 4 Tr si 6 0 7722 0 1537 14 Description of output files Introduction An example Key output files The The The asr file sln file yht file Other ASReml output files The The The The The The The The The aov file res file vrb file vvp file rsv file dpr file pvc file pvs file tab file ASReml output objects and where to find them 220 14 Description of output files 221 14 1 Introduction With each ASReml run a number of output files are produced ASReml generates the output files by appending various filename extensions to basename A brief description of the filename extensions is presented in Table 14 1 Table 14 1 Summary of ASReml output files file description Key output files asr contains a summary of the data and analysis results pvc contains the report produced with the P option pvs contains predictions formed by the predict directive res contains information from using the pol spl and fac functions the iteration sequence for the variance components and some statistics derived from the residuals rsv contains the final parameter values for reading back if the CONTINUE qualifier is invoked see Table 5 4 sln contains the estimates of the fixed and random effects and their corresponding standard errors tab contains tables for
258. equested workspace the request will be diminished until it can be satisfied On multi user systems do not unnecessarily request the maximum or other users may complain Having started with an initial allocation if ASReml realises more space is required as it is running it will attempt to restart the job with increased workspace If the system has already allocated all available memory the job will stop 11 Command file Running the job 203 Examples ASReml code action asreml LW64 rat as increase workspace to 64 Mbyte send screen output to rat asl and suppress interactive graphics asreml IL rat as send screen output to rat asl but display interactive graphics asreml N rat as allow screen output but suppress interactive graphics asreml ILW512 rat as increase workspace to 512 Mbyte send screen output to rat asl but display interactive graphics asreml rs3 coop wwt ywt runs coop as twice writing results to coopwwt as and coopywt as using 64Mb workspace and substituting wwt and ywt for 1 in the two runs 11 4 Advanced processing arguments Standard use of arguments Command line arguments are intended to facilitate the running of a sequence of jobs that require small changes to the command file between runs The output file name is modified by the use of this feature if the R option is specified This use is demonstrated in the Coopworth example of Section 16 11 see page 346 Command line arguments are strings
259. equired Debug command line options D E D and E DEBUG DEBUG 2 invoke debug mode and increase the information written to the screen or asl file This information is not useful to most users On Unix systems if ASReml is crashing use the system script command to capture the screen output rather than using the L option as the as1 file is not properly closed after a crash Graphics command line options G H 1 N Q Graphics are produced in the PC Linux and SUN 32bit versions of ASReml using the Winteracter graphics library The I INTERACTIVE option permits the variogram and residual graphics to be displayed This is the default unless the L option is specified The N NOGRAPHICS option prevents any graphics from being displayed This is the default when the L option is specified The Gg GRAPHICS g option sets the file type for hard copy versions of the 11 Command file Running the job 200 ASReml2 ASReml2 graphics Hard copy is formed for all the graphics that are displayed H g HARDCOPY g replaces the G option when graphics are to be written to file but not displayed on the screen The H may be followed by a format code e g H22 for eps Q QUIET is used when running under the control of ASReml W to suppress any POPUPs PAUSES from ASReml ASReml writes the graphics to files whose names are built up as lt basename gt lt args gt lt type gt lt pass gt lt section gt lt ext gt where
260. er is not used Tree 5 age 118 484 664 1004 1231 1372 1582 circ season L Spring Autumn orange asd skip 1 filter 2 select 1 SPLINE spl age 7 118 484 664 1004 1231 1372 1582 PVAL age 150 200 1500 circ mu age r spl age 7 predict age 16 Examples 325 Note that the data for tree 1 has been selected by use of the filter and select qualifiers Also note the use of PVAL so that the spline curve is properly predicted at the additional nominated points These additional data points are required for ASReml to form the design matrix to properly interpolate the cubic smoothing spline between knot points in the prediction process Since the spline knot points are specifically nominated in the SPLINE line these extra points have no effect on the analysis run time The SPLINE line does not modify the analysis in this example since it simply nominates the 7 ages in the data file The same analysis would result if the SPLINE line was omitted and spl age 7 in the model was replaced with spl age An extract of the output file is 1 LogL 20 9043 S2 48 470 5 df 0 1000 1 000 2 LogL 20 9017 S2 49 022 5 df 0 9266E 01 1 000 3 LogL 20 8999 S2 49 774 5 df 0 8356E 01 1 000 4 LogL 20 8996 S2 50 148 5 df 0 7937E 01 1 000 5 LogL 20 8996 S2 50 213 5 df 0 7866E 01 1 000 Final parameter values 0 78798E 01 1 0000 Degrees of Freedom and Stratum Variances 1 49 97 4813 12 0 1 0 3 51 50 1888 0 0 1 0 Source Model terms Gamma Component Comp
261. er may be used anywhere in the job and the line is modified from that point Unfortunately the prompt may not appear on the top screen under some windows operating systems in which case it may not be obvious that ASReml is waiting for a keyboard response Paths and Loops ASReml is designed to analyse just one model per run However the analysis of a data set typically requires many runs fitting different models to different traits It is often convenient to have all these runs coded into a single as file and control the details from the command line or top job control line using arguments The highlevel qualifiers CYCLE and DOPATH enable multiple analyses to be defined and run in one execution of ASReml 11 Command file Running the job 205 Table 11 3 High level qualifiers qualifier action ASSIGN list An ASSIGN string qualifier has been added to extend ASReml3 coding options It is a high level qualifier command which may appear anywhere in the job on a line by itself The syntax is beginning in position 1 ASSIGN name string and the defined string is substituted into the job where name appears string is the rest of the line and may include blanks For example ASSIGN TRT xfa Treat 1 TRT geno TRT geno 2 TRT O XFA1 geno Restrictions e A maximum of 20 assign strings may be defined e The combined length of all strings is 1000 charac ters e name may consist of 1 4 characters but shoul
262. erforms a basic bivariate analysis of this data Wolfinger rat data treat A wtO wti wt2 wt3 wt4 rat dat wtO wti wt2 wt3 wt4 Trait treat Trait treat 120 27 O ID error variance Trait 0 US 15 0 Orange Wether Trial 1984 8 SheepID IL TRIAL BloodLine I TEAM YEAR GFW YLD FDIAM wether dat skip 1 GFW FDIAM Trait Trait YEAR lr Trait TEAM Trait SheepID 12 2 1485 0O ID Trait 0 US GP 42 24 Trait TEAM 2 Trait 0 US 0 4 0 3 1 3 TEAM O ID Trait SheepID 2 Trait O US GP O 2 0522 SheepID 0 ID predict YEAR Trait 8 Command file Multivariate analysis 159 SheepID Site Bloodline Team Year GFW Yield FD 0101 3 21 1 1 5 6 74 3 18 5 0101 3 21 1 2 6 0 71 2 19 6 0101 3 21 13 8 0 75 7 21 5 0102 3 21 f 1 5 3 70 9 20 8 0102 3 21 1 2 6 7 66 1 20 9 0102 3 21 1 3 6 8 70 3 22 1 0103 3 21 1 1 5 0 80 7 18 9 0103 3 21 1 2 5 5 75 5 19 9 0103 3 21 1 3 7 0 76 6 21 9 4013 3 43 35 1 7 9 75 9 22 6 4013 3 43 35 2 7 8 70 3 23 9 4013 3 43 35 3 9 0 76 2 25 4 4014 3 43 35 1 8 3 66 5 22 2 4014 3 43 35 2 7 8 63 9 23 3 4014 3 43 35 3 9 9 69 8 25 5 4015 3 43 35 1 6 9 75 1 20 0 4015 3 43 35 2 7 6 71 2 20 3 4015 3 43 35 3 8 5 78 1 21 7 8 2 Model specification The syntax for specifying a multivariate linear model in ASReml is Y variates fixed r random f sparse_fixed e Y variates is a list of up to 20 traits there may be more than 20 actual variates if the list includes s
263. ers to a parameter which is a single traditional variance component associated with a random term the name of the random term may be given instead of the parameter number The full parameter vector includes a term for each factor in the model and then a term for each parameter defined in the R and G structures The list of parameter numbers and their initial values is returned in the res file to help you to check the numbers Alternatively examine the asr file from an initial run with VCC included but no arguments supplied The job will terminate but ASReml will provide the parameter numbers and values associated with each variance component The following are examples ASReml code action 5 7 ii parameter 7 is a tenth of parameter 5 5 parameter 7 is the negative of parameter 5 32 34 35 37 38 39 for a 4 x 4 US matrix given by parameters 31 40 the covariances are forced to be equal units uni check parameter associated with model term uni check has the same magnitude but opposite sign to the pa rameter associated with model term units 21 29 BLOCKSIZE 8 equates parameters 29 with 21 30 with 22 36 with 28 Equating variance structures ASReml3 In some plant breeding applications it is sometimes convenient to define a vari ance structure as the sum of two simpler terms Then it is necessary to give the same variance model to each term and use parameter constraints to equate the parameters If there
264. es Key fields have different names IMERGE filel Key keyla key1b WITH file2 KEY key2a key2b to newfile Key fields have common name and other fields are also duplicated IMERGE filel Key keya keyb WITH file2 to newfile CHECK IMERGE filel Key key KEEP WITH file2 to newfile will discard records from file2 that do not match records in filel but all records in filel are retained Omitting fields from the merged file IMERGE filel Key key skip sla sib WITH file2 skip s2as2b to newfile Single insertion merging IMERGE adult txt Key ewe KEEP WITH birth txt KEEP TO newfile NODUP bwt 13 Functions of variance components Introduction VPREDICT directive PIN file syntax Linear combinations of components Heritability Correlation A more detailed example 214 13 Functions of variance components 215 13 1 Introduction ASReml includes a post analysis procedure to F phenvar 1 2 pheno var calculate functions of variance components F genvar 1 4 geno var Its intended use is when the variance compo H herit 4 3 heritability nents are either simple variances or are vari ances and covariances in an unstructured matrix The functions covered are linear combinations of the variance components for example phenotypic variance a ratio of two components for example heritabilities and the correlation based on three components for example genetic correlation The user must prepare a
265. es of three wplots yield oats asd skip 2 and four subplots which received 4 rates of CONTRAST linNitr nitro i nitrogen A CONTRAST qualifier defines the 0 4 0 2 0 0 model term linNitr as the linear covariate FCON yield mu variety linNitr nitrogen variety linNitr variety nitrogen Ir blocks blocks wplots whole plots to which variety was randomised representing ntrogen applied Fitting this be fore the model term nitrogen means that this 14 Description of output files 230 latter term represents lack of fit from a linear response The FCON qualifier requests conditional Wald F statistics As this is a small example denominator degrees of freedom are reported by default An extract from the asr file is followed by the contents of the aov file Results from analysis of yield Approximate stratum variance decomposition Stratum Degrees Freedom Variance Component Coefficients blocks 5 00 3175 06 12 0 4 0 1 0 blocks wplots 10 00 601 331 0 0 4 0 1 0 Residual Variance 45 00 177 083 0 0 0 0 1 0 Source Model terms Gamma Component Comp SE C blocks 6 6 1 21116 214 477 1 27 OP blocks wplots 18 18 0 598937 106 062 1 56 0P Variance 72 60 1 00000 177 083 4 74 OP Wald F statistics Source of Variation NumDF DenDF_con F_inc F_con M P_con 8 mu 1 6 0 245 14 138 14 lt 001 4 variety 2 10 0 1 49 1 49 A 0 272 7 linNitr 1 45 0 110 32 110 32 a lt 001 2 nitrogen 2 45 0 1 37 1 37 A 0 265 9 variet
266. escribed on page 18 variety LANCER 0 000 0 000 variety BRULE 2 987 2 842 variety REDLAND 4 707 2 978 variety CODY 0 3131 2 961 variety ARAPAHOE 2 954 PPA variety NE87615 1 035 2 934 variety NE87619 5 939 2 850 variety NE87627 4 376 2 998 mu 1 24 09 2 465 mv_estimates 1 21 91 6 729 mv_estimates 2 203 08 Delal mv_estimates 3 22 52 6 708 mv_estimates 4 23 49 6 676 mv_estimates 5 22 26 6 698 mv_estimates 6 24 47 6 707 mv_estimates z 20 14 6 697 mv_estimates 8 25 01 6 691 mv_estimates 9 24 29 6 676 mv_estimates 10 26 30 6 658 14 Description of output files 228 The yht file The yht file contains the predicted values of the data in the original order this is not changed by supplying row column order in spatial analyses the residuals and the diagonal elements of the hat matrix Figure 14 1 shows the residuals plotted against the fitted values Yhat and a line printer version of this figure is written to the res file Where an observation is missing the residual missing values predicted value and Hat value are also declared missing The missing value estimates with standard errors are reported in the s1n file NIN alliance trial 1989 Residuals vs Fitted values Residuals Y 24 87 15 91 Fitted values X 16 77 35 94 o o o o o o o i o go o y O o o 8 o o 8 0320 can a 3s M20 of oo 5 e g Be g aon o 6 y 7 op 28 r 8 o o o 3 a mi TE E ae s Pas o 8 e8 o o Ki 8 o0 Figure 14 1 Res
267. ess specified with the AVERAGE ASSOCIATE or PRESENT qualifiers Explicit weights may be supplied directly or from a file The default is equal weights weights can be expressed like 3 1 0 2 1 5 to represent the sequence 0 2 0 2 0 2 0 0 2 0 2 The string inside the curly brace is expanded first and the expression n c means n occur rences of c When there are a large number of weights it may be convenient to prepare them in a file and retrieve them All values in the file are taken unless n is specified in which case they are taken from field column n ASAVERAGE f weights is used to control averaging over associated factors The default ASAVERAGE f is to simply average at the base level Hierarchal averaging is gt file n achieved by listing the associated factors to average in f Explicit weights may be supplied directly or from a file as for AVERAGE PARALLEL v without arguments means all classify variables are expanded in parallel Otherwise list the variables from the classify set whose levels are to be taken in parallel 10 Tabulation of the data and prediction from the model 184 Table 10 1 List of prediction qualifiers qualifier action ASReml2 ASReml2 ASReml2 PRESENT v is used when averaging is to be based only on cells with data v is a list of variables and may include variables in the classify set v may not include variables with an explicit AVERAGE qualifier The variable
268. eters in model i and v n p is the residual degrees of freedom AIC and BIC are calculated for each model and the model with the smallest value is chosen as the preferred model Diagnostics In this section we will briefly review some of the diagnostics that have been im plemented in ASReml for examining the adequacy of the assumed variance matrix for either R or G structures or for examining the distributional assumptions re garding e or u Firstly we note that the BLUP of the residual vector is given by e y WB RPy 2 16 It follows that E 0 var R WC W The matrix WC W is the so called extended hat matrix It is the linear mixed effects model analogue of o X X X 1X for ordinary linear models The diagonal elements are returned in the fourth field of the yht file The OUTLIER qualifier invokes a partial implementation of research by Alison Smith Ari Verbyla and Brian Cullis With this qualifier ASReml writes e G tu and G u diagV G G C74G to the s1n file e R e and R e diagy Rt R WC W R to the yht file 2 Some theory 19 Variogram ASReml2 e and copies lines where the last ratio exceeds 3 in magnitude to the res file e and reports the number of such lines to the asr file e It is not debugged for multivariate models or XFA models with zero Ws The variogram has been suggested as a useful diagnostic for assisting with the identification of app
269. ethod for constructing orthogonal polynomials when the independent variable is unequally spaced Biometrics 15 187 191 Rodriguez G and Goldman N 2001 Improved estimation procedures for multilevel models with binary response A case study Journal of the Royal Statistical Society A General 164 2 339 355 Sargolzaei Iwaisaki and Colleau 2005 A fast algorithm for computing in breeding coefficients in large populations Genetics Selection and Evolution 122 325 331 Schall R 1991 Estimation in generalized linear models with random effects Biometrika 78 4 719 27 Searle S R 1971 Linear Models New York John Wiley and Sons Inc Searle S R 1982 Matrix algebra useful for statistics New York John Wiley and Sons Inc Searle S R Casella G and McCulloch C E 1992 Variance Components New York John Wiley and Sons Inc Bibliography 361 Self S C and Liang K Y 1987 Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under non standard conditions Journal of the American Statistical Society 82 605 610 Smith A B Cullis B R and Gilmour A R 2001a The analysis of crop variety evaluation data in Australia Australian and New Zealand Journal of Statistics 43 129 145 Smith A B Cullis B R Gilmour A R and Thompson R 1998 Multi plicative models for interaction in spatial mixed model analyses of multi environment trial data
270. ets of variates defined with G on page 50 e fixed random and sparse_fized are as in the univariate case see Chapter 6 but involve the special term Trait and interactions with Trait The design matrix for Trait has a level column for each trait Trait by itself fits the mean for each variate In an interaction Trait Fac fits the factor Fac for each variate and Trait Cov fits the covariate Cov for each variate ASReml internally rearranges the data so that n data records containing t traits each becomes n sets of t analysis records indexed by the internal factor Trait i e nt analysis records ordered Trait within data record If the data is already in this long form use the ASMV t qualifier to indicate that a multivariate analysis is required 8 Command file Multivariate analysis 160 8 3 Variance structures Using the notation of Chapter 7 consider a multivariate analysis with t traits and n units in which the data are ordered traits within units An algebraic expression for the variance matrix in this case is I9 X where is an unstructured variance matrix This is the general form of variance structures required for multivariate analysis Specifying multivariate variance structures in ASReml For a standard multivariate analysis the error structure for the residual must be specified as two dimensional with indepen dent records and an unstructured variance matrix across traits records may have
271. etween model terms Sometimes it is appropriate to include a covariance Then it is essential that the model terms be listed together and that the variance structure defined for the first term be the structure required for both terms When the terms are of different size the terms must be linked together with the and qualifiers Table 6 1 While ASReml 7 Command file Specifying the variance structures 149 will check the overall size it does not check that the order of effects matches the structure definition so the user must be careful to get this right Check that the Check the order terms are conformable by considering the order of the fitted effects and ensuring the first term of the direct product corresponds to the outer factor in the nesting of the effects Two examples are e random regressions where we want a covariance between intercept and slope Ir animal animal time animal 2 20 Ue 2 5 2 animal is equivalent though not identical because of the scaling differences to Ir pol time 1 animal pol time 1 animal 2 pol time i 0 US 1 1 2 animal maternal direct genetic covariance lambid P sireid P damid P wwt ywt Trait Trait sex r Trait lambid at Trait 2 damid Trait lambid 2 3 0 US 1 3 Var wwt_D 1 0 252 Cov wwt_D ywt_D Var ywt_D ni sa O08 Cov wwt_D wwt_M Cov ywt_D wwt_M Var wwt M lambid O AINV AINV explicitly requests to use A inverse 7 Command file Specifyi
272. ex r dam PATH 3 weight mu littersize dose sex r dam PATH 4 weight mu littersize dose sex The input file contains an example of the use of the DOPATH qualifier Its ar gument specifies which part to execute We will discuss the models in the two parts It also includes the FCON qualifier to request conditional Wald F statistics Abbreviated output from part 1 is presented below 1 LogL 74 2174 52 0 19670 315 df 0 1000 1 000 2 LogL 79 1579 S2 0 18751 315 df 0 1488 1 000 3 LogL 83 9408 S2 0 17755 315 df 0 2446 1 000 4 LogL 86 8093 S2 0 16903 315 df 0 4254 1 000 5 LogL 87 2249 S2 0 16594 315 df 0 5521 1 000 6 LogL 87 2398 S2 0 16532 315 df 0 5854 1 000 7 LogL 87 2398 S2 0 16530 315 df 0 5867 1 000 8 LogL 87 2398 S2 0 16530 315 df 0 5867 1 000 Final parameter values 0 58667 1 0000 Results from analysis of weight Approximate stratum variance decomposition Stratum Degrees Freedom Variance Component Coefficients dam 22 56 1 27762 11 5 1 0 Residual Variance 292 44 0 165300 0 0 1 0 Source Model terms Gamma Component Comp SE C dam 27 27 0 586674 0 969770E 01 2 92 OP Variance 322 315 1 00000 0 165300 12 09 OF Wald F statistics Source of Variation NumDF DenDF_con F_inc F_con M P_con 7 mu 1 32 0 9049 48 1099 20 b lt 001 3 littersize 1 31 5 27 99 46 25 B lt 001 1 dose 2 23 9 12 15 11 51 lt 001 2 sex 1 299 8 57 96 57 96 A lt 001 8 dose sex 2 302 1 0 40 0 40 B 0 673 Notice The DenDF values are calc
273. except for simple variance component terms where ASReml inserts an initial value of 0 1 if the user supplies none In some common cases ASReml will provide plausible initial values if the supplied value is zero Initial values may be in the wrong order or on the wrong scale Is the parameter a correlation a variance ratio independent of the scale of the data or a variance Strategies include letting ASReml supply an inital value and fitting a simpler model to gain an idea of the scale required It may be that the model is too sophisticated to be estimated from the data Satisfactory convergence is unlikely if the fitted model is not appropriate One user could not get an AR1 model to converge It turned out the data was sim ulated under an equal correlation model not an AR model and sometimes the correlation was greatest between the two most distant points when the AR model expected it to be smallest Another user had problems getting a model to con verge when using a GIV variance structure The GIV matrix had 3 large negative eigen values and 5 negative diagonal elements which for certain parameter values resulted in negative roots to the mixed model equations In animal models the residual variance can be negative if appropriate fixed effects are not fitted and end up appearing as inflated genetic variance Alternatively the variance model may contain highly related terms which the data cannot effectively separate into 7 Command file Specif
274. f occasionally used job control qualifiers qualifier action ASReml3 IMBF mbf v n f FACTOR FIELD s IKEY k NOKEY IRENAME IRFIELD r ISKIP k ISPARSE specified on a separate line after the datafile line predefines the model term mbf v n as a set of n covariates indexed by the data values in variable v MBF stands for My Basis Function and uses the same mechanism as the leg polQ and spl model functions but with covariates supplied by the user It is used for reading in specialized design matri ces indexed by a factor in the data including genetic marker covariables By default the file f should contain 1 n fields where the first field the key field contains the values which are in the data variable or at which prediction is required and the remaining n fields define the corresponding covari ate values If n is omitted all fields after the key field are taken unless FACTOR is specified for which n is 1 and the covariate values are treated as coding for a multilevel factor IRENAME t changes the name of the the term from mbf to the new name t This is necessary when several mbf terms are being defined which would otherwise have the same name label For example IMBF mbf entry mlib m35 csv rename Marker35 If the key values are the ordered sequence 1 N the key field may be omitted if NOKEY is specified If the key is not in the first field its location can be specified with KEY k
275. file This file contains a general announcements box outlined in asterisks containing current mes sages a summary of the data to for the user to confirm the data file has been inter preted correctly and to review the basic structure of the data and validate the specification of the model the iteration sequence of REML loglikelihood values to check convergence a summary of the variance parameters The Gamma column reports the actual parameter fitted the Component column reports the gamma converted to a variance scale if appropriate Comp SE is the ratio of the component relative to the square root of the diagonal element of the inverse of the average information matrix Warning Comp SE should not be used for formal testing The shows the percentage change in the parameter at the last iteration use the pin file described Chapter 13 to calculate meaningful functions of the variance components an table of Wald F statistics for testing fixed effects Section 6 11 The ta ble contains the numerator degrees of freedom for the terms and incremental F statistics for approximate testing of effects It may also contain denomi nator degrees of freedon a conditional Wald F statistic and a significance probability estimated effects their standard errors and t values for equations in the DENSE portion of the SSP matrix are reported if BRIEF 1 is invoked the T prev column tests difference between successive c
276. fined for at Tr 1 dam which is of size 2 x d and so also covers at Tr 2 dam ASReml uses the relationship matrix for the dam dimen since dam is defined with P In this case it makes no difference since there sion is no pedigree information on dams It is preferable to be explicit specify dam O AINV when the relationship matrix is required and otherwise use ide dam in the model specification and ide dam O ID in the G structure definition A portion of the output file is A inverse retrieved from ainverse bin PEDIGREE pcoop fmt has 10696 identities 29474 Non zero elements QUALIFIERS CONTINUE MAXIT 20 STEP 0 01 QUALIFIERS EXTRA 4 QUALIFIER DOPATH 3 is active Reading pcoop fmt FREE FORMAT skipping 0 lines Multivariate analysis of wwt ywt gfw fdm Multivariate analysis of fat Using 7043 records of 7043 read Model term Size miss zero MinNonO Mean MaxNonO reported in the asr file 16 Examples 354 I 2 3 tag sire IP 10696 oO IP 10696 0 Forming 95033 equations 40 dense Initial updates will be shrunk by factor Restarting iteration from previous solution Notice LogL values are reported relative to a base of detected in design matrix 35006 NOTICE 1 COANOO AK WD po 16 76 LogL 1437 LogL 1436 LogL 1434 LogL 1430 LogL 1424 LogL 1417 LogL 1417 LogL 1417 Source at Trait 1 at Trait 2 at Trait 4 at Trait 5 at Trait
277. gen is simply the order those treatment labels were discovered in the data file Split plot analysis oat Variety Nitrogen 14 Apr 2008 16 15 49 oats Ecode is E for Estimable for Not Estimable The predictions are obtained by averaging across the hypertable calculated from model terms constructed solely from factors in the averaging and classify sets Use AVERAGE to move ignored factors into the averaging set SS ee a Se a ee 1 Bas nn ee Predicted values of yield The averaging set variety The ignored set blocks wplots nitrogen Predicted_Value Standard_Error Ecode 0 6 cyt 123 3889 7 1747 E 0 4_cwt 114 2222 7 1747 E 0 2_cwt 98 8889 7 1747 E O_cwt 79 3889 7 1747 E SED Overall Standard Error of Difference 4 436 SS es Se a es S 2 a ya cs ee a a ce Predicted values of yield The averaging set nitrogen The ignored set blocks wplots variety Predicted_Value Standard_Error Ecode Marvellous 109 7917 T T9TS E Victory 97 6250 7 7976 E Golden_rain 104 5000 fares E SED Overall Standard Error of Difference T079 16 Examples 283 a L G 3 enn tn N Mn mmm am a lt i Predicted values of yield The ignored set blocks wplots nitrogen variety Predicted_Value Standard_Error Ecode 0 6_cwt Marvellous 126 8333 9 1070 E 0 6_cwt Victory 118 5000 9 1070 E 0 6_cwt Golden_rain 124 8333 9 1070 E 0 4_cwt Marvellous 117 1667 9 1070 E 0 4_cwt Victory 110 8333 9 1070 E 0 4_cwt Golden_rain 114 6667 9 1070 E O 2_ewt Marvellous
278. gging See the discussion on AISINGULARITIES the field order coding in the spatial error model does not generate a complete grid with one observation in each cell missing values may be deleted they should be fitted Also may be due to incorrect specification of num ber of rows or columns ASReml attempts to hold the data on a scratch file Check that the disk partition where the scratch files might be written is not too full use the NOSCRATCH qualifier to avoid these scratch files 15 Error messages 276 Table 15 3 Alphabetical cause s remedies list of error messages and probable error message probable cause remedy Structure Factor mismatch Too many alphanumeric factor level labels Too many factors with A or I max 100 Too many max 20 dependent variables Unable to invert R or G US 7 matrix Unable to invert R or G CORR matrix Variance structure is not positive definite the declared size of a variance structure does not match the size of the model term that it is associated with if the factor level labels are actually all inte gers use the I option instead Otherwise you will have to convert a factor with alphanu meric labels to numeric sequential codes ex ternal to ASReml so that an A option can be avoided The data file may need to be rewritten with some factors recoded as sequential integers This is an internal limit Reduce the number of response
279. giv is name grm SKIP n DENSEGRM o GROUPDF n ND PSD NSD or name giv SKIP n DENSEGIV o GROUPDF n SAVEGIV f e the named file must have a giv or grm extension e the G inverse files must be specified on the line s immediately prior to the data file line after any pedigree file up to 98 G inverse matrices may be defined e the file must be in SPARSE format unless the DENSE qualifier is specified e adense format file has the whole matrix presented lower triangle rowwise with each row beginning on a new line e a sparse format file must be free format 11 1 with three numbers per line namely i row column value 4414 5 5 1 0666667 defining the lower triangle row wise of the 6 5 0 2666667 matrix 6 6 1 0666667 eee 7 7 1 0666667 e the file must be sorted column within row 8 7 0 2666667 e every diagonal element must be repre 8 8 1 0666667 d missi Edi Lel 9 9 1 0666667 sented missing off diagonal elements are as 45 9 0 2666667 sumed to be zero cells 10 10 1 0666667 Sit ai 11 11 1 0666667 e the file is used by associating it with a fac 45 4 0 2666667 tor in the model The number and order of 12 12 1 0666667 the rows must agree with the size and order of the associated factor the SKIP n qualifier tells ASReml to skip n header lines in the file 9 Command file Genetic analysis 172 ASReml3 The giv file presented in the code box I 0
280. gives the G inverse matrix on the right 0 Lg 1 067 0 267 0 267 1 067 If the file has a grm file extension ASReml will invert it If it is not Positive Def inite the job will abort unless an appropriate qualifier ND PSD or NSD is sup plied ND NSD allows the matrix to be Negative Semi Definite PSD allows the matrix to be Positive SemiDefinite If the matrix is Negative Semi Definite the iteration sequence may fail as some parameter values will generate Negative Residual Sum of Squares If SemiDefinite is permitted and the matrix is singular ASReml forms an expanded Singular representation of the inverse which allows the REML algorithm to proceeds The effects for the extra equations have no natural interpretation If the specified giv file does not exist but there is a grm file of the same name ASReml will read and invert the grm file and write the inverse to the giv file if SAVEGIV f is specified Its is written in DENSE format unless f 1 The giv file can be associated with a factor in two ways e the first is to declare a G structure for the model term and to refer to the giv file with the corresponding identifier GIV1 GIV2 GIV3 for example animal 1 for a one dimensional structure put the scale pa animal O GIV1 0 12 rameter 0 12 in this case after the GIVg identifier site variety 2 for a two dimensional structure site 0 CORUH 0 5 8 1 5 variety 0 GIV1 e the second is f
281. gram of fac xsca ysca predictors 2 80 Distance Figure 5 1 Variogram in 4 sectors for Cashmore data 6 Command file Specifying the terms in the mixed model Introduction Specifying model formulae in ASReml General rules Examples Fixed terms in the model Primary fixed terms Sparse fixed terms Random terms in the model Interactions expansions and conditional factors Interactions Model Expansions Conditional factors Alphabetic list of model functions Weights Missing values Missing values in the response Missing values in the explanatory variables Some technical details about model fitting in ASReml Sparse versus dense Ordering of terms in ASReml Aliassing and singularities Examples of aliassing m Wald F Statistics 6 Command file Specifying the terms in the mixed model 94 6 1 Introduction The linear mixed model is specified in ASReml as a series of model terms and qualifiers In this chapter the model formula syntax is described 6 2 Specifying model formulae in ASReml The linear mixed model is specified in AS NIN Alliance Trial 1989 Reml as a series of model terms and qualifiers variety Model terms include factor and variate labels Section 5 4 functions of labels special terms column 11 and interactions of these The model is speci nin89 asd skip 1 yield mu variety r repl fied immediately after the datafile and any job bE mv control qualifier and or tabul
282. gularities 4243 4503 4506 4506 4506 S52 S2 S52 S52 S2 Deviance from GLM fit Variance heterogeneity factor Deviance DF 0000 0000 0000 0000 0000 21 21 adf Dev DF 21 df Dev DF 21 dt Dev DF 21 df Dev DF 21 df Dev DF 20 31 0 97 Results from analysis of Rating Notice While convergence of the LogL value indicates that the model 0 3356 0 3376 0 3376 0 3376 0 3376 2 872 4 359 5 500 4 193 8 770 0 8165 9 2241 7 411 5 354 0 000 has stabilized its value CANNOT be used to formally test differences between Generalized Linear Mixed Models 16 Examples 340 Source Model terms Gamma Component Comp SE C Wald F statistics Source of Variation NumDF F inc 4 Trait 8 17 45 1 Cheese 3 38 38 Warning These Wald F statistics are based on the working variable and are not equivalent to an Analysis of Deviance Standard errors are scaled by the variance of the working variable not the residual deviance Finished 17 Jun 2008 13 19 51 484 LogL Converged Multinomial Ordinal GLMM analysis of Footrot score Reverting to the collapsed lamb data the two response variables FS1 and FS2 contain counts of the lambs with all feet sound and with one foot deformed respectively The count for those with two or more deformed is given by difference from Total A threshold model analysis of this data is given by the model line FS1 FS2 mult 3 TOTAL Total Trait SEX GRP r SIRE wi
283. he code in V2 variety changes whether this creates a variable or overwrites an input vari able depends on whether any subsequent variables are input variables assuming Var is coded 1 3 and Nit is coded 1 4 this syntax could be used to create a new factor VxN with the 12 levels of the composite Var by Nit factor will discard records where both YA and YB have miss ing values assuming neither have zero as valid data The first line sets the focus to variable 98 copies YA into V98 and changes any missing values in V98 to zero The second line sets the focus to variable 99 copies YB into V99 and changes any missing values in V99 to zero It then adds V98 and discards the whole record if the result is zero i e both YA and YB have missing values for that record Variables 98 and 99 are not labelled and so are not retained for subsequent use in analysis Special note on covariates Covariates are variates that appear as independent variables in the model It is recommended that covariates be centred and scaled to have a mean of zero and a variance of approximately one to avoid failure to detect singularities This can be achieved either e externally to ASReml in data file preparation e using RESCALE mean scale where mean and scale are user supplied values for example age rescale 140 142857 in weeks 5 Command file Reading the data 63 5 6 Datafile line The purpose of the datafile line is to
284. he estimated variety effects intercept and random replicate effects in this order column 3 with stan dard errors column 4 Note that the variety effects are returned in the order of their first appearance in the data file see replicate 1 in Table 3 1 variety LANCER 0 000 0 000 variety BRULE 2 487 4 979 variety REDLAND 1 938 4 979 variety CODY 7 350 4 979 variety ARAPAHOE 0 8750 4 979 variety NE83404 f 176 4 979 variety NE83406 4 287 4 979 variety NE83407 6 575 4 979 variety CENTURA 6 912 4 979 variety SCOUT66 L057 4 979 variety COLT 1 562 4 979 variety NE83498 1 563 4 979 variety NE84557 8 037 4 979 variety NE83432 S Bo0 4 979 variety NE87615 2 875 4 979 variety NE87619 2 700 4 979 variety NE87627 BesT 4 979 mu 1 29 56 3 856 repl 1 1 880 1 765 repl 2 2 843 1 755 repl 3 0 9713 1 755 repl 4 3 852 1 755 The yht file The following is an extract from nin89 yht containing the predicted values of the observations column 2 the residuals column 3 and the diagonal elements of the hat matrix This final column can be used in tests involving the residuals see Section 2 5 under Diagnostics 3 A guided tour 39 Record Yhat Residual Hat 1 30 442 1 192 13 01 2 27 955 3 595 13 01 3 32 380 2 670 13 01 4 23 092 7 008 13 01 5 31 317 1 733 13 01 6 29 267 0 9829 13 01 T 26 155 9 045 13 01 8 24 567 5 167 13 01 9 23 530 0 8204 13 01 222 16 673 9 877 13 01 223 24 548 1 052 13 01 224 23 786 3 114 13 01
285. he file did not exist or was of the wrong file type binary unformatted sequential There are several messages of this form where something is what ASReml is attempting to read Either there is an error telling ASReml to read something when it does not need to or there is an error in the way something is specified the data file could not be interpreted al phanumeric fields need the A qualifier data file name may be wrong the model specification line is in error a vari able is probably misnamed The VCC constraints are specified last of all and require knowing the position of each pa rameter in the parameter vector the specified dependent variable name is not recognised It is likely that the covariate values do not match the values supplied in the file The val ues in the file should be in sorted order the declared size of the error structures does not match the actual number of data records There is some problem on the SPLINE line It could be a wrong variable name or the wrong number of knot points Knot points should be in increasing order Try increasing workspace The problem may be due to the use of the SORT qualifier in the data definition section 15 Error messages 270 Table 15 3 Alphabetical list cause s remedies of error messages and probable error message probable cause remedy Failed to parse R G structure line Failed to read R G structure line Failed to
286. he model NIN Alliance Trial 1989 variety A id pid raw repl 4 row 22 column 11 nin89 asd skip 1 yield mu variety r repl For this reason the only change to the former command file is the insertion of r before repl Important All random terms other than error which is implicit must be written after r in the model specification line s 7 Command file Specifying the variance structures 121 See Section 7 4 See page 131 See Sections 2 1 and 7 5 2b Random effects RCB analysis with a G structure specified This model is equivalent to 2a but we explic itly specify the G structure for repl that is ur N 0 yro2I to introduce the syntax The 0 O 1 line is called the variance header line In general the first two elements of this line refer to the R structures and the third el ement is the number of G structures In this case 0 0 tells ASReml that there are no ex plicit R structures but there is one G structure 1 The next two lines define the G structure The first line a G structure header line links the structure that follows to a term in the lin ear model rep1 and indicates that it involves NIN Alliance Trial 1989 variety A id pid raw repl 4 row 22 column 11 nin89 asd skip 1 yield mu variety r repl oO 7 repl i 40 IDV 0 1 one variance model 1 a 2 would mean that the structure was the direct product of two variance models The second line
287. he sources of variation rather than assess the significance of imposed treatments The data are taken from Cox and Snell 1981 and involve an experiment to examine the variability in the production of car voltage regulators Standard production of regulators involves two steps Regulators are taken from the production line to a setting station and adjusted to operate within a specified voltage range From the setting station the regulator is then passed to a testing station where it is tested and returned if outside the required range The voltage of 64 regulators was set at 10 setting stations setstat between 4 and 8 regulators were set at each station The regulators were each tested at four testing stations teststat The ASReml input file is presented below Voltage data 16 Examples 288 teststat 4 4 testing stations tested each regulator setstat A 10 setting stations each set 4 8 regulators regulatr 8 regulators numbered within setting stations voltage voltage asd skip 1 voltage mu r setstat setstat regulatr teststat setstat teststat 000 The factor regulatr numbers the regulators within each setting station Thus the term setstat regulatr allows for differential effects of each regulator while the other terms examine the effects of the setting and testing stations and possible interaction The abbreviated output is given below LogL 188 604 S2 0 67074E 01 255 df LogL 199 530 52 0 59303E 01 255 df LogL 203
288. iance model Equality of parameters in a variance model can be specified using the s qualifier where s is a string of letters and or zeros see Table 7 4 Positions in the string correspond to the parameters of the variance model e all parameters with the same letter in the structure are treated as the same parameter e 1 9 are different from a z which are different from A Z so that 61 equalities 7 Command file Specifying the variance structures 151 difficult can be specified 0 and mean unconstrained A colon generates a sequence viz a e is the same as abcde Putting as the first character in s makes the interpretation of codes absolute so that they apply across structures e Putting as the first character in s indicates that numbers are repeat counts A Z are equality codes only represents unconstrained and a z is not dis tinquised from A Z giving only 26 equalities Thus 3A2 is equivalent to 0AAA00 or 0aaa00 This syntax is limited in that it cannot apply constraints to simple variance components random terms which do not have an explicit variance structure or to residual variance parameters The VCC syntax is required for these cases Examples are presented in Table 7 5 Constraints between and within variance models More general relationships between variance parameters can be defined using the VCC c qualifier placed on the data file definition line Each variance parameter qi is allocate
289. iassing The sequence of models in Table 6 5 are presented to facilitate an understanding of over parameterised models It is assumed that var is a factor with 4 levels trt with 3 levels and rep with 3 levels and that all var trt combinations are present in the data Table 6 5 Examples of aliassing in ASReml model number of order of fitting singularities yield var r rep 0 rep var yield mu var r rep 1 rep mu var first level of var is aliassed and set to Zero yield var trt r rep 1 rep var trt var fully fitted first level of trt is aliassed and set to zero yield mu var trt 8 rep mu var trt var trt var trt r rep first levels of both var and trt are aliassed and set to zero together with subsequent interactions yield mu var trt r rep 8 var trt rep mu var trt If var trt var trt fitted before mu var and trt var trt fully fitted mu var and trt are completely singular and set to zero The order within var trt rep is de termined internally 6 Command file Specifying the terms in the mixed model 116 6 11 Wald F Statistics The so called ANOVA table of Wald F statistics has 4 forms Source NumDF F inc Source NumDF F inc F con M Source NumDF DDF_inc F inc P inc Source NumDF DDF_con F inc F con M P con depending on whether conditional Wald F statistics are reported requested by the FCON qualifier and whether the denominator degrees of freedom are re ported ASReml always repo
290. iate form Multivariate Analysis is used in the narrow sense where an unstructured error variance matrix is fitted across traits records are independent and observations may be missing for particular traits see Chapter 8 for a complete discussion The data is presumed arranged in lots of n records where n is the number of traits It may be necessary to expand the data file to achieve this structure inserting a missing value NA on the additional records This option is sometimes relevant for some forms of repeated measures analysis There will need to be a factor in the data to code for trait as the intrinsic Trait factor is undefined when the data is presented in a univariate manner 5 Command file Reading the data 73 Table 5 4 List of occasionally used job control qualifiers qualifier action ASUV ICOLFAC v DISPLAY n EPS indicates that a univariate analysis is required although the data is presented in a multivariate form Specifically it allows you to have an error variance other than J amp where amp is the unstructured US see Table 7 3 variance structure If there are missing values in the data include f mv on the end of the linear model It is often also necessary to specify the S2 1 qualifier on the R structure lines The intrinsic factor Trait is defined and may be used in the model See Chapter 8 for more information This option is used for repeated measures analysis when the
291. ic conventions 5 unbalanced data 287 nested design 283 UNIX 195 Unix crashes 199 Unix debugging 232 Index 372 unreplicated trial 305 variance parameter 7 variance components functions of 214 variance header line 127 128 variance model combining 16 147 description 132 forming from correlation models 137 qualifiers 146 specification 118 specifying 119 variance parameters 11 constraining 127 150 between structures 151 within a model 150 variance structures 33 126 multivariate 160 Wald F statistics 20 weight 94 108 weights 43 Working Folder 64 workspace options 202 XFA extension 143
292. icate some of the modelling approaches we have found useful There are several interfaces to the core functionality of ASReml The program name ASReml relates to the primary program ASReml W_ refers to the user interface program developed by VSN and distributed with ASReml ASReml R refers to the S language interface to a DLL of the core ASReml routines Genstat uses the same core routines for its REML directive Both of these have good data manipulation and graphical facilities The focus in developing ASReml has been on the core engine and it is freely acknowledged that its user interface is not to the level of these other packages Nevertheless as the developers interface it is functional it gives access to every thing that the core can do and is especially suited to batch processing and running of large models without the overheads of other systems Feedback from users is welcome and attempts will be made to rectify identified problems in ASReml The guide has 15 chapters Chapter 1 introduces ASReml and describes the con ventions used in this guide Chapter 2 outlines some basic theory while Chapter 3 presents an overview of the syntax of ASReml through a simple example Data file preparation is described in Chapter 4 and Chapter 5 describes how to input data into ASReml Chapters 6 and 7 are key chapters which present the syntax for specifying the linear model and the variance models for the random effects in the linear mixed model Chapte
293. icitly specifies the model terms to use ignoring all others The qualifier EXCEPT explicitly specifies the model terms not to use including all others These qualifiers will not override the definition of the averaging set The fourth step is to choose the weights to use when averaging over dimensions in the hyper table The default is to simply average over the specified levels but the qualifier AVERAGE factor weights allows other weights to be specified PRESENT and ASSOCIATE ASAVERAGE generate more complicated averaging processes The basic prediction process is described in the following example yield site variety r site variety at site block predict variety puts variety in the classify set site in the averaging set and block in the ig nore set Consequently ASReml implicitly forms the sitexvariety hyper table from model terms site variety and site variety but ignoring all terms in at site block and then averages across the sites to produce variety predic tions This prediction will work even if some varieties were not grown at some sites because the site variety term was fitted as random If site variety was fitted as fixed variety predictions would be non estimable for those vari eties which were not grown at every site 10 Tabulation of the data and prediction from the model 182 prediction problems Predict failure It is not uncommon for users to get the message Warning non estimable aliased cel
294. idual versus Fitted values This is the first 20 lines of nin89a yht Note that the values corresponding to the missing data first 15 records are all 0 1000E 36 which is the internal value used for missing values Record Yhat Residual Hat 1 0 10000E 36 0 1000E 36 0 1000E 36 2 0 10000E 36 0 1000E 36 0 1000E 36 14 9 10000E 36 0 1000E 36 0 1000E 36 15 0 10000E 36 0 1000E 36 0 1000E 36 16 24 088 5 162 6 074 17 27 074 4 476 6 222 18 23 795 6 255 6 282 19 23115 6 325 6 235 20 27 042 6 008 5 962 14 Description of output files 229 240 24 695 1 855 6 114 241 25 452 0 1475 6 158 242 22 465 4 435 6 604 14 4 Other ASReml output files The aov file This file reports details of the calculation of Wald F statistics particularly as re lating to the conditional Wald F statistics not computed in this demonstration In the following table relating to the incremental Wald F statistic the columns are e model term e columns in design matrix e numerator degrees of freedom e simple Wald F statistic e Wald F statistic scaled by A e as defined in Kenward amp Roger e denominater degrees of freedom mu 1 1 331 8483 331 8483 1 0000 25 0082 variety 56 55 2 2259 2 2259 0 9995 110 8419 A more useful example is obtained by adding Split plot analysis oat a linear nitrogen contrast to the oats example blocks nitrogen A Section 16 2 sibpdets variety A The basic design is six replicat
295. ier has been redefined Warning The X Y G qualifiers are ignored There is no data to plot Warning Warning The default action with missing values in multivariate data Warning The estimation was ABORTED The computed LogL value is occasionally very large in magnitude but our interest is in rel ative changes Reporting relative to an offset ensures that differences at the units level are apparent missing cells are normally not reported consider setting levels correctly the limit is 100 PREDICT statements because it contains errors if you really want to fit this term twice create a copy with another name gives details so you can check ASReml is doing what you intend that is these standard errors are approximate use the correct syntax the A fields will be treated as factors but are coded as they appear in the binary file use correct syntax revise the qualifier arguments The issue is to match the declared R structure to the physical data Dropping observations which are missing will often usually destroy the pattern Estimating missing values allows the pattern to be retained Do not accept the estimates printed 15 Error messages 267 Table 15 2 List of warning messages and likely meaning s warning message likely meaning Warning The FOWN test of is not calculated Warning The labels for predictions are erroneous Warning This US structure is not posit
296. ier will exclude its effects from the prediction but not ignore the structural information implied by the association Normally it is not necessary for any model term to involve more than 1 of the as sociated factors One exception is if an interaction is required so that the variance can differ between sections For example fitting the terms at region trial as random effects would allow the trials in region 1 to have a different variance component to those in region 2 Prediction in these cases is more complicated and has only been implemented for this specific case and the analagous region trial case The associated factors must occur together in this order for the prediction to give correct answers The ASSOCIATE effect with base averaging can usually be achieved with the PRESENT qualifier except when the factors have many levels so that the product of levels exceeds 2147 000 000 it fails in this case because the KEY for identifying the cells present is a simple combination of the levels and is stored as a normal 10 Tabulation of the data and prediction from the model 191 ASReml2 Caution 32bit integer However ASSOCIATE is preferred because it formally checks the association structure as well as allowing sequential averaging Two ASSOCIATE clauses may be specified for example PRED entry ASSOC family entry ASSOC reg loc trial ASAVE reg loc Only one member of an ASSOCIATE list may also appear in a PRESENT list
297. ifiers qualifier action EMFLAG n ASReml2 PXEM n Caution requests ASReml use Expectation Maximization EM rather than Average Information AI updates when the AI updates would make a US structure non positive definite This only applies to US structures and is still under development When IGP is associated with a US structure ASReml checks whether the updated matrix is positive definite PD If not it re places the AI update with an EM update If the non PD characteristic is transitory then the EM update is only used as necessary If the converged solution would be non PD there will be a EM update each iteration even though EM is omitted EM is notoriously slow at finding the solution and ASReml includes several modified schemes discussed by Cullis et al 2004 particularly relevant when the AI update is consis tently outside the parameter space These include optionally performing extra local EM or PXEM Parameter Expanded EM iterates These can dramatically reduce the number of iterates required to find a solution near the boundary of the parameter space but do not always work well when there are several matrices on the boundary The options are EMFLAG 1 Standard EM plus 10 local EM steps EMFLAG 2 Standard EM plus 10 local PXEM steps PXEM 2 Standard EM plus 10 local PXEM steps EMFLAG 3 Standard EM plus 10 local EM steps EMFLAG 4 Standard EM plus 10 local EM steps EMFLAG 5 Standard EM only EMFLAG 6
298. ile The dpr file contains the data and residuals from the analysis in double pre cision binary form The file is produced when the RES qualifier Table 4 3 is invoked The file could be renamed with filename extension dbl and used for input to another run of ASReml Alternatively it could be used by another For tran program or package Factors will have level codes if they were coded using A or I All the data from the run plus an extra column of residuals is in the file Records omitted from the analysis are omitted from the file The pvc file The pvc file contains functions of the variance components produced by running a pin file on the results of an ASReml run as described in Chapter 13 The pin and pvc files for a half sib analysis of the Coopworth data are presented in Section 16 11 14 Description of output files 233 title line predicted variety means SED summary The pvs file The pvs file contains the predicted values formed when a predict statement is included in the job Below is an edited version of nin89a pvs See Section 3 6 for the pvs file for the simple RCB analysis of the NIN data considered in that chapter nin alliance trial 14 Jul 2005 12 41 18 nin89a Ecode is E for Estimable for Not Estimable Warning mv_estimates is ignored for prediction Predicted values of yield variety Predicted_Value Standard_Error Ecode LANCER 24 0894 2 4645 E BRULE 27 0728 2 4944 E REDLAND 28 7954 2
299. inNonO Mean MaxNonO 1 variety 56 0 0 1 28 5000 56 11 column 11 0 0 1 6 3304 11 12 mu 1 11 AR AutoReg 0 1000 22 AR AutoReg 0 1000 Maybe you need to include mv in the model Fault R structures imply O 242 records only 224 e Last line read was 22 column AR1 0 100000 ninerr9 variety id pid raw rep nloc yield lat Model specification TERM LEVELS GAMMAS variety 56 mu 1 SECTIONS 242 3 a STRUCT if 1 1 4 1 i 10 22 1 1 5 1 i 11 12 factors defined max 500 5 variance parameters max1i500 2 special structures Final parameter values 0 0000 10000E 360 10000 0 10000 Last line read was 22 column AR1 0 100000 Finished 11 Apr 2008 20 07 11 046 R structures imply 0 242 records only 224 exist 10 Field layout error in a spatial analysis The final common error we highlight is the misspecification of the field layout In this case we have accidently switched the levels in rows and columns However ASReml can detect this error because we have also asked it to sort the data into field order Had sorting not been requested ASReml would not have been able to detect that the lines of the data file were not sorted into the appropriate field order and spatial analysis would be wrong 10 row 22 0 0 1 11 5000 22 11 column a 0 0 1 6 0000 1 12 mu 1 13 mv_estimates 18 11 AR AutoReg 0 1000 22 AR AutoReg 0 1000 15 Error messages 262 Warning Spatial mapping information for side 1 of order 11 ranges from 1 0 to 22 0
300. ing the corresponding variance parameters to the list of parameters This convention holds for most models However no V or H should be appended to the base identifiers for the heterogeneous variance models at the end of the table from DIAG on In summary to specify e acorrelation model provide the base identifier given in Table 7 3 for example EXP 1 is an exponential correlation model e an homogeneous variance model append a V to the base identifier and provide an additional initial value for the variance for example EXPY lt i 33 is an exponential variance model a heterogeneous variance model append an H to the base identifier and provide additional initial values for the diagonal variances for example CORUH 1 3 4 2 is a 3 x 3 matrix with uniform correlations of 0 1 and heterogeneous variances 0 3 0 4 and 0 2 Important See Section 7 7 for rules on combining variance models and important notes regarding initial values The algebraic forms of the homogeneous and heterogeneous variance models are determined as follows Let C Ci denote the correlation matrix for a particular correlation model If is the corresponding homogeneous variance matrix then 5 C It has just one more parameter than the correlation model For example the homogeneous variance model corresponding to the ID correlation model has vari ance matrix o7I specified IDV in the ASReml command file see below and
301. ing values defined If the file contains unwanted fields put the pseudo variate label skip in the appropriate position in vlist to ignore them The file should only have numeric values predict_points cannot be specified for design factors is used with SECTION v and COLFAC v to instruct ASReml to setup the R structures for multi environment spatial analysis v is the name of a factor or variate containing row numbers 1 m where n is the number of rows on which the data is to be sorted See SECTION for more detail 5 Command file Reading the data 7 Table 5 4 List of occasionally used job control qualifiers qualifier action SECTION v SPLINE spl v n p specifies the factor in the data that defines the data sections This qualifier enables ASReml to check that sections have been correctly dimensioned but does not cause ASReml to sort the data unless ROWFAC and COLFAC are also specified Data is assumed to be presorted by section but will be sorted on row and column within section The following is a basic example assuming 5 sites sections When ROWFAC v and COLFAC v are both specified ASReml generates the R structures for a standard AR amp AR spatial analysis The R structure lines that a user would normally be required to work out and type into the as file see the example of Section 16 6 are written to the res file The user may then cut and paste them into the as file for a later run if the s
302. ion models Additional notes of variance models Variance structure qualifiers Rules for combining variance models G structures involving more than one random term Constraining variance parameters Parameter constraint within a variance model Constraints between and within variance models Model building using the CONTINUE qualifier 117 7 Command file Specifying the variance structures 118 7 1 Introduction The subject of this chapter is variance model specification in ASReml ASReml allows a wide range of models to be fitted The key concepts you need to under stand are e the mixed linear model y XT Zu e has a residual term e N 0 R and random effects u N 0 G e we use the terms R structure and G structure to refer to the independent blocks of R and G respectively e R and G structures are typically formed as a direct product of particular variance models e the order of terms in a direct product must agree with the order of effects in the corresponding model term e variance models may be correlation matrices or variance matrices with equal or unequal variances on the diagonal A model for a correlation matrix eg AR1 can be converted to an equal variance form eg AR1V and to a heterogeneous variance form eg AR1H e variances are sometimes estimated as variance ratios relative to the residual variance These issues are fully discussed in Chapter 2 In this chapter we begin by con sidering an
303. ip 1 e must be indented one or more spaces yield wy variety e can appear with other definitions on the same line data fields can be transformed see below 5 Command file Reading the data 49 Revised 08 transformation qualifiers should be listed after the data field labels for the fields being modified created additional data fields can be created by transformation qualifiers Data field definition syntax Data field definitions appear in the ASReml command file in the form SPACE label field_type transformations SPACE is a required space label is an alphanumeric string to identify the field has a maximum of 31 characters although only 20 are ever printed displayed must begin with a letter must not contain the special characters or reserved words Table 6 1 and Table 7 3 must not be used field_type defines how a variable is interpreted as it is read and whether it is regarded as a factor or variable if specified in the linear model for a variate leave field_type blank or specify 1 for a model factor various qualifiers are required depending on the form of the factor coding where n is the number of levels of the factor and s is a list of labels to be assigned to the levels or n is used when the data field has values 1 directly coding for the factor unless the levels are to be labelled see L Row 1 12 for example
304. irregularity or models fitted The data we consider is taken from Gilmour et al 1995 and involves a field experiment designed to compare the performance of 25 varieties of barley The experiment was conducted at Slate Hall Farm UK in 1976 and was designed as a balanced lattice square with replicates laid out as shown in Table 16 6 The data fields were Rep RowBlk ColBlk row column and yield Lattice row and column numbering is typically within replicates and so the terms specified in the linear model to account for the lattice row and lattice column effects would be Rep latticerow Rep latticecolumn However in this example lattice rows and columns are both numbered from 1 to 30 across replicates see Table 16 6 The terms in the linear model are therefore simply RowB1k ColBlk Additional fields row and column indicate the spatial layout of the plots 16 Examples 299 The ASReml input file is presented below Three models have been fitted to these data The lattice analysis is included for comparison in PATH 3 In PATH 1 we use the separable first order autoregressive model to model the variance structure of the plot errors Gilmour et al 1997 suggest this is often a useful model to commence the spatial modelling process The form of the variance matrix for the plot errors R structure is given by os 6 7 S 8 X 16 5 where Xe and X are 15 x 15 and 10 x 10 matrix functions of the column e and row autoregressive pa
305. is 0 instructing ASReml to put the record number into the target field operator is one of the symbols defined in Table 5 1 value is the argument a real number required by the transformation V is the literal character and is followed by the number target or field of a data field the data field is used or modified depending on the context Vfield may be replaced by the label of the field if it already has a label in the first three forms the operation is performed on the current field this will be the field associated with the label unless the focus has been reset by specifying a new target in a preceding transformation the last four forms change the focus for subsequent transformations to the target in the last two forms a value is assigned to the target field For example V22 V11 copies existing field 11 into field 22 Such a statement would typically be followed by more transformations If there are fewer than 22 variables labelled then V22 is used in the transformation stage but not kept for analysis only the DOM and RESCALE transformations automatically process a set of variables defined with the G field definition All other transformations always operate on only a single field Use the DO ENDDO transformations to perform them on a set of variables Table 5 1 List of transformation qualifiers and their actions with examples qualifier argument action examples I v used to overwrite create a variabl
306. is used when the data field is numeric with values 1 and labels are to be assigned to the n levels for example Sex L Male Female IL can also be used in conjunction with A to set the order of the levels For example SNP A L C C C T T T defines the levels over riding the default data dependent order If there are many labels they may be written over several lines by using a trailing comma to indicate continuation of the list is required if the data field is alphanumeric for example Location A names for example 5 Command file Reading the data 50 ASReml2 ASReml2 ASReml2 ASReml2 II n is required if the data is numeric defining a factor but not 1 n I must be followed by n if more than 1000 codes are present Year I 1995 1996 for example AS p is required if the data field has level names in common with a previous A or I factor p and is to be coded identically for example in a plant diallel experiment Male A 22 Female AS Male integrated coding IP indicates the special case of a pedigree factor ASReml will determine whether the identifiers are integer or alphanumeric from the pedigree file qualifiers and set the levels after reading the pedigree file see Section 9 3 Animal P coded according to pedigree file A warning is printed if the nominated value for n does not agree with the actual number of levels found in the data and if the nominated value is too small the correct value is used f
307. it 3 at Trait 5 Residual age sex sex sex sex grp grp grp grp grp UnStru 1 i 49 49 0 209279E 03 0 209279E 03 49 49 0 919610 0 919610 49 49 15 3912 15 3912 49 49 0 279496 0 279496 49 49 1 44032 1 44032 9 46220 9 46220 Covariance Variance Correlation Matrix UnStructured Residual 9 462 0 5691 0 2356 0 1640 0 2163 7 332 17 54 0 4241 0 2494 0 4639 0 2728 0 6686 0 1417 0 3994 0 1679 0 9625 1 994 0 2870 3 642 0 4875E 01 0 8336 2 412 0 7846E 01 0 1155 1 541 Covariance Variance Correlation Matrix UnStructured Tr sire 0 5941 0 7044 0 2966 0 2032 0 2703 0 6745 1 544 0 1364E 01 0 1224 0 5726 0 2800E 01 0 2076E 02 0 1500E 01 0 1121 0 4818E 02 0 6238E 01 0 6056E 01 0 5469E 02 0 1586 0 6331 0 3789E 01 0 1294 2 161 1 010 0 7663 2 196 2 186 0 8301 0 1577 0 1718 0 1959E 01 Covariance Variance Correlation Matrix UnStructured at Tr 1 1lit 3 547 0 5065 0 1099 0 4096E 01 1 555 2 657 0 1740 0 5150 0 1073E 03 0 4586E 01 0 3308E 01 Covariance Variance Correlation Matrix UnStructured at Tr 1 dam 0 2787E 01 0 3821E 01 0 1815E 01 0 3282 0 7312E 01 0 7957 0 4191E 01 0 8984 Wald F sta Source of Variation NumDF 15 Tr age 5 16 TA Bre 15 17 Tr sex 5 19 Tr age sex 4 tistics F ime 98 95 116272 59 78 4 90 68 89 50 ok 80 30 oo o 6 Oo is i Oe gt ibe In the res file is reported an eigen analysis of these four variance structures Eigen Analysis of UnStructured
308. its mean value can be formally introduced as part of the classify or averaging set c Determine which terms from the linear mixed model are to be used when pre dicting the cells in the multiway hyper table in order to obtain either conditional or marginal predictions That is you may choose to ignore some random terms in addition to those ignored because they involve variables in the ignored set All terms involving associated factors are by default included d Choose the weights to be used when averaging cells in the hyper table to pro duce the multiway table to be reported The multiway table may require partial and or sequential averaging over associated factors Operationally ASReml does the averaging in the prediction design matrix rather than actually predicting the cells of the hyper table and then averaging them The main difference in this prediction process compared to that described by Lane and Nelder 1982 is the choice of whether to include or exclude model terms when forming predictions In linear models since all terms are fixed factors not in the classify set must be in the averaging set and all terms must contribute to the predictions Predict syntax The first step is to specify the classify set of NIN Alliance trial 1989 explanatory variables after the predict direc variety A tive The predict statement s may appear immediately after the model line before or af column 11 nin89 asd skip 1 yield
309. ive definite Warning Unrecognised qualifier at character Warning US matrix was not positive definite MODIFIED Warning User specified spline points Warning Variance parameters were modified by BENDing Warning Likelihood decreased Check gammas and singularities The FOWN test requested is not calculated because it results in different numbers of de grees of freedom to that obtained for the in cremental tests for the terms in the model as fitted the FOWN calculations are based on the reduced design matrix formed for the in cremental model ASReml performs the stan dard conditional test instead The user must reorder swap the terms in the model spec ification and rerun the job to perform the re quested FOWN test the labels for predicted terms are probably out of kilter Try a simpler predict statement If the problem persists send for help check the initial values the qualifier either is misspelt or is in the wrong place the initial values were modified by a bending process the points have been rescaled to suit the data values ASReml may not have converged to the best estimate a common reason is that some constraints have restricted the gammas Add the GU qualifier to any factor definition whose gamma value is approaching zero or the correlation is ap proaching 1 Alternatively more singular ities may have been detected You should identify where the singularities are expected
310. ively the residuals might relate to a multivariate analysis with n traits and n units and be ordered traits within units In this case an appropriate variance structure might be I9 X where xm is a general or unstructured variance matrix Direct products in G structures Likewise the random terms in u in the model may have a direct product variance structure For example for a field trial with s sites g varieties and the effects ordered varieties within sites the model term site variety may have the variance structure UI where amp is the variance matrix for sites This would imply that the varieties are independent random effects within each site have different variances at each site and are correlated across sites Important Whenever a random term is formed as the interaction of two factors you should consider whether the IID assumption is sufficient or if a direct product structure might be more appropriate 2 Some theory 9 Variance structures for the errors R structures The vector e will in some situations be a series of vectors indexed by a fac tor or factors The convention we adopt is to refer to these as sections Thus e e e3 e4 and the ej represent the errors of sections of the data For ex ample these sections may represent different experiments in a multi environment trial MET or different trials in a meta analysis It is assumed that R is the direct sum of s matrices R j 1 s that is
311. ized Linear Mixed Models Table 6 3 Link qualifiers and functions Qualifier Link Inverse Link Available with IDENTITY n p N All SQRT n yH p Poisson Normal Poisson LOGARITHM n In p u exp 7 Negative Binomial Gamma Normal Gamma ee ate p Negative Binomial _ _ 1 Binomial Multi ee a H TeEPEM nomial Threshold 1 PROBIT n t u p a n Binomial Multi nomial Threshold en Binomial Multi COMPLOGLOG ln ln 1 e OMPLOGLO 7 In In M H e nomial Threshold where u is the mean on the data scale and n XT is the linear predictor on the underlying scale ASReml includes facilities for fitting the family of Generalized Linear Models GLMs McCullagh and Nelder 1994 A GLM is defined by a mean variance function and a link function In this context y is the observation n is the count for grouped data specified by the TOTAL qualifier 6 Command file Specifying the terms in the mixed model 109 is a parameter set with the PHI qualifier u is the mean on the data scale calculated using the inverse link function from the predicted value 7 on the underlying scale where 7 XT v is the variance under some distributional assumption calculated as a function of u and n and d is the deviance twice the log likelihood for that distribution GLMs are specified by qualifiers after the name of the dependent variable but before the character Table 6 3 lists the link function q
312. l data values These values are successive observations namely observation 210 and 211 being 16 Examples 289 testing stations 2 and 3 for setting station 9 J regulator 2 These observa tions will not be dropped from the following analyses for consistency with other analyses conducted by Cox and Snell 1981 and in the GENSTAT manual ltage example 5 3 6 from the GENSTAT REML manual Residuals vs Fitted valu Residuals Y 1 08 1 45 Fitted values X 15 56 16 81 o Figure 16 2 Residual plot for the voltage data The REML log likelihood from the model without the setstat teststat term was 203 242 the same as the REML log likelihood for the previous model Ta ble 16 3 presents a summary of the REML log likelihood ratio for the remaining terms in the model The summary of the ASReml output for the current model is given below The column labelled Comp SE is printed by ASReml to give a guide as to the significance of the variance component for each term in the model The statistic is simply the REML estimate of the variance component divided by the square root of the diagonal element for each component of the inverse of the average information matrix The diagonal elements of the expected not the av erage information matrix are the asymptotic variances of the REML estimates of the variance parameters These Comp SE statistics cannot be used to test the null hypothesis that the variance component is zero If we had used this crud
313. l has a certain number of parameters If insufficient non zero values are found on the model line ASReml expects to find them on the following line s initial values of 0 0 will be ignored if they are on the model line but are accepted on subsequent lines the notation n v for example 5 0 1 is permitted on subsequent lines but not the model line when there are n repeats of a particular initial value V only in a few specified cases is O permitted as an initial value of a non zero parameter 7 Command file Specifying the variance structures 131 G structure header and definition lines There are g sets of G structure definition lines and each set is of the form model_term d order key model initial_values qualifier additional_initial_values NIN Alliance Trial 1989 order key model initial_values qualifier oo A additional_initial_values row 22 order key model initial_values qualifier column 11 additional_initial_values nin89aug asd skip 1 yield mu variety r repl If mv model_term is the term from the linear 121 model to which the variance structure ap 22 row AR1 0 3 plies the variance structure may cover ad 1 AEL DS rep ditional terms in the linear model see Sec repl 0 IDV 0 1 tion 7 8 dis the number of variance models and hence direct product matrices involved in the G structure the following lines define the d variance models order is either the
314. l s may be omitted because ASReml checks that predictions are of estimable functions in the sense defined by Searle 1971 p160 and are invariant to any constraint method used Immediate things to check include whether every level of every fixed factor in the averaging set is present and whether all cells in every fixed interaction is filled For example in the previous example no variety predictions would be obtained if site was declared as having 4 levels but only three were present in the data The message is also likely if any fixed model terms are IGNOREd The TABULATE command may be used to see which treatment combinations occur and in what order More formally there are often situations in which the fixed effects design matrix X is not of full column rank This aliasing has three main causes e linear dependencies among the model terms due to over parameterisation of the model e no data present for some factor combinations so that the corresponding effects cannot be estimated e linear dependencies due to other usually unexpected structure in the data The first type of aliasing is imposed by the parameterisation chosen and can be determined from the model The second type of aliasing can be detected when setting up the design matrix for parameter estimation which may require revision of imposed constraints All types are detected in ASReml during the absorption process used to obtain the predicted values ASReml doesn
315. l will read until the end of the predict ta ble The keyword Ecode which occurs once at the beginning and then immediately before each block of data in the pvs file is used to count the sections Combining rows from separate files ASReml can read data from multiple files provided the files have the same layout The file specified as the primary data file in the command file can contain lines of the form INCLUDE lt filename gt SKIP n where lt filename gt is the path name of the data subfile and SKIP n is an optional qualifier indicating that the first n lines of the subfile are to be skipped After reading each subfile input reverts to the primary data file Typically the primary data file will just contain INCLUDE statements identifying the subfiles to include For example you may have data from a series of related experiments in separate data files for individual analysis The primary data file for the subsequent combined analysis would then just contain a set of INCLUDE statements to specify which experiments were being combined 5 Command file Reading the data 68 If the subfiles have CSV format they should all have it and the CSV file should be declared on the primary datafile line This option is not available in combination with MERGE 5 8 Job control qualifiers The following tables list the job control qualifiers These change or control various aspects of the analysis Job control qualifiers m
316. late lines may appear after the model 01 j model 2b below for details predict and line and before the first variance structure repl 1 line These are described in Chapter 10 repl 0 IDV 0 1 Table 7 3 presents the full range of variance models available in ASReml The identifiers for specifying the individual variance models in the command file are described in Section 7 5 under Specifying the variance models in ASReml Many of the models are correlation models However these are generalized to homoge neous variance models by appending V to the base identifier They are generalized to heterogeneous variance models by appending H to the base identifier 7 3 A sequence of structures for the NIN data See Section 2 1 Eight variance structures of increasing complexity are now considered for the NIN field trial data see Chapter 3 for an introduction to these data This is to give a feel for variance modelling in ASReml and some of the models that are possible Before proceeding it is useful to link this section to the algebra of Chapter 2 In this case the mixed linear model is y XT Zut e where y is the vector of yield data 7 is a vector of fixed variety effects but would also include fixed replicate effects in a simple RCB analysis and might also include fixed missing value effects when spatial models are considered u N 0 G is a vector of random effects for example random replicate effects and the errors are
317. ld mu variety nitrogen variety nitrogen r blocks blocks wplots predict nitrogen Print table of predicted nitrogen means predict variety predict variety nitrogen SED The data fields were blocks wplots subplots variety nitrogen and yield The first five variables are factors that describe the stratification or experi ment design and treatments The standard split plot analysis is achieved by fitting the model terms blocks and blocks wplots as random effects The blocks wplots subplots term is not listed in the model because this interac tion corresponds to the experimental units and is automatically included as the residual term The fixed effects include the main effects of both variety and nitrogen and their interaction The tables of predicted means and associated standard errors of differences SEDs have been requested These are reported in the pvs file Abbreviated output is shown below Results from analysis of yield Approximate stratum variance decomposition Stratum Degrees Freedom Variance Component Coefficients blocks 5 00 3175 06 12 0 4 0 LG blocks wplots 10 00 601 331 0 0 4 0 1 0 Residual Variance 45 00 177 083 0 0 0 0 Lake Source Model terms Gamma Component Comp SE C blocks 6 6 1 21116 214 477 1 27 0P blocks wplots 18 18 0 598937 106 062 1 56 0P Variance T2 60 1 00000 177 083 4 74 OP 16 Examples 281 Wald F statistics Source of Variation NumDF DenDF Fine Prob 7 mu 1 5 0 245 14 lt 001 4 v
318. ld be joined by lines by default they are only joined if the x axis variable is numeric Predictions involving two or more factors If these arguments are used all prediction factors except for those specified with only one prediction level must be listed once and only once otherwise these arguments are ignored 10 Tabulation of the data and prediction from the model 187 Table 10 2 List of predict plot options option action xaxis factor superimpose factors condition factors Layout goto n saveplot filename layout rows cols pycols plankpanels n extrablanks n extraspan p and specifies the prediction factor to be plotted on the x axis specifies the prediction factors to be superimposed on the one panel specifies the conditioning factors which define the panels These should be listed in the order that they will be used specifies the page to start at for multi page predictions specifies the name of the file to save the plot to specifies the panel layout on each page specifies that the panels be arranged by columns default is by rows specifies that each page contains n blank panels This sub option can only be used in combination with the layout sub option specifies that an additional n blank panels be used every p pages These can only be used with the layout sub option Improving the graphical appearance and readability labcharsize n
319. lds ITO newfile CHECK SORT Check output Warning Fields in the merged file will be arranged with key fields followed by field order other fields from the primary file and then fields from the secondary file Table 12 1 List of MERGE qualifiers qualifier action CHECK requests ASReml confirm that fields having a common name have the same contents Discrepancies are reported to the asr file If there are fields with common names which are not key fields and CHECK is omitted the fields will be assumed different and both versions will be copied IKEY keyfields names the fields which are to be used for matching records in the files If the fields have the same name in both file headers they need only be named in association with the primary input file If the key fields are the only fields with common names the KEY qualifier may be omitted altogether If key fields are not nominated and there are no common field names the files are interleaved KEEP instructs ASReml to include in the merged file records from the input file which are not matched in the other input file Missing values are inserted as the values from the other file Otherwise unmatched records are discarded KEEP may be specified with either or both input files NODUP fields Typically when a match occurs the field contents from the second file are combined with the field contents of the first file to produce the merged file The NODUP qualifier
320. le 16 15 Wald F statistics of the fixed effects for each trait for the genetic example term wwt ywt gfw fdm fat age 331 3 67 1 52 4 26 7 5 brr 554 6 734 149 0 3 13 9 sex 196 1 123 3 0 2 2 9 0 6 age sex 10 3 1 7 19 5 0 16 Examples 344 Thus in the multivariate analysis we consider fitting the following models to the sire dam and litter effects var us Ys Io2 var ug La 3561 var w DY Lagoi where 2 53 and 5 are positive definite symmetric matrices correspond ing to the between traits variance matrices for sires dams and litters respectively The variance matrix for dams does not involve fibre diameter and fat depth while the variance matrix for litters does not involve fat depth The effects in each of the above vectors are ordered levels within traits Lastly we assume that the residual variance matrix is given by Me Q I7043 Table 16 16 presents the sequence variance models fitted to each of the four random terms sire dam litter and error in the ASReml job Multivariate Sire amp Dam model tag sire 92 II dam 3561 I grp 49 sex brr 4 litter 4871 age wwt mO ywt mO MO identifies missing values giw mO fdm mO fat mO coop fmt DOPATH 1 CONTINUE MAXIT 20 PATH 3 EXTRA 4 PATH wwt ywt gfw fdm fat Trait Tr age Tr brr Tr sex Tr age sex ly Tr sire t at Tr 1 dam at Tr 2 dam at Tr 3 dam lf at Te i lit aetir 2 1it at Tr 3 lat at Tr 4 lit
321. lem to VSN indicates ASReml has failed deep in its core It is likely to be an interaction between the data and the variance model being fitted Try increasing the memory simplifying the model and changing starting values for the gammas If this fails send the problem to the VSN mailto support asreml co uk for investiga tion Check the argument POWER structures are the spatial variance models which require a list of distances Dis tances should be in increasing order If the distances are not obtained from variables the SORT field is zero and the distances are pre sented after all the R and G structures are defined something is wrong in the terms definitions It could also be that the data file is misnamed Check the argument There is probably a problem with the output from MYOWNGDG Check the files including the time stamps to check the gdg file is being formed properly if you read less data than you expect there are two likely explanations First the data file has less fields than implied by the data structure definitions you will probably read half the expected number Second there is an alphanumeric field where a numeric field is expected check the STEP qualifier argument either all data is deleted or the model fully fits the data 15 Error messages 275 Table 15 3 Alphabetical list cause s remedies of error messages and probable error message probable cause remedy
322. level simple covariates are predicted at their overall mean and covariates used as a basis for splines or orthogonal polynomials are predicted at their design points Covariates grouped into a single term using G qualifier page 50 are treated as covariates Model terms mv and units are always ignored Model terms which are functions such as at and pol sin spl including those defined using CONTRAST GROUP SUBGROUP SUBSET and MBF are implicitly defined through their base variables and can not be directly referenced in the classify and average sets For example GROUP Year YearLoc 1 112233344 forms a new factor Year with 4 levels from the existing factor YearLoc with 10 levels The prediction must be in terms of YearLoc not Year even if YearLoc does not formally appear in the model For default averaging in prediction the weights for the levels of the grouped factor Year will be in this example 0 3 0 2 0 3 0 2 derived from the weights for the base factor YearLoc Use AVE YearLoc 2223322 23 3 24 to produce equal weighting of Year effects If G sets of variables are included in the classify set only the first variable is reported in labelling the predict values except that for G MM sets the marker position is reported Prediction at particular values of a covariate or particular levels of a factor is achieved by listing the levels values after the variate factor name Where there is a sequence of values
323. lia no part of the publication may be reproduced by any process electronic or otherwise without specific written permission of the copyright owner Nei ther may information be stored electronically in any form whatever without such permission Published by VSN International Ltd 5 The Waterhouse Waterhouse Street Hemel Hempstead HP1 1ES UK E mail info asreml co uk Website http www vsni co uk The correct bibliographical reference for this document is Gilmour A R Gogel B J Cullis B R and Thompson R 2009 ASReml User Guide Release 3 0 VSN International Ltd Hemel Hempstead HP1 1ES UK www vsni co uk Preface ASReml3 ASReml2 Revised 08 ASReml is a statistical package that fits linear mixed models using Residual Max imum Likelihood REML It has been under development since 1993 and is a joint venture between the Biometrics Program of NSW Department of Primary Industries and the Biomathematics and Bioinformatics Division previously the Statistics Department of Rothamsted Research Release 2 of ASReml was dis tributed in 2006 This guide relates to Release 3 first distributed in 2008 Changes in this version are indicated by the word ASReml3 in the margin Features added in Release 2 have ASReml2 in the margin Other significant changes to the text are indicated by Revised in the margin A separate document ASReml 3 Update is available to highlight the changes from Release 2 00 Linear mixed effects mo
324. listed on the command line after basename the command file name or specified on the top job control line after the ARGS qualifier These strings are inserted into the command file at run time When the input routine finds a n in the command file it substitutes the nth argument string n may take the values 1 9 to indicate up to 9 strings after the command file name If the argument has 1 character a trailing blank is attached to the character and inserted into the command file If no argument exists a zero is inserted For example asreml rat as alpha beta tells ASReml to process the job in rat as as if it read alpha wherever 1 appears in the command file beta wherever 2 appears and 0 wherever 3 appears 11 Command file Running the job 204 Warning Table 11 2 The use of arguments in ASReml in command file on command line becomes in ASReml run abc 1def no argument abcO def abc 1def with argument X abcX def abc 1def with argument XY abcXYdef abc 1def with argument XYZ abcXYZdef abc 1 def with argument XX abcXX def abc 1 def with argument XXX abcXXX def abc 1 def with argument XXX abcXXX def multiple spaces Prompting for input Another way to gain some interactive control of a job in the PC environment is to insert tezxt in the as file where you want to specify the rest of the line at run time ASReml prompts with tert and waits for a response which is used to compete the line The qualifi
325. lists for fac X Y model terms For kriging prediction in 2 dimensions X Y the user will typically want to predict at a grid of values not necessarily just at data combinations The values at which the prediction is required can be specified separately for X and Y using two PVAL statements Normally predict points will be defined for all combinations of X and Y values This qualifier is required with optional argument 1 to specify the lists are to be taken in parallel The lists must be the same length if to be taken in parallel Be aware that adding two dimensional prediction points is likely to substantially slow iterations because the variance structure is dense and becomes larger For this reason AS Reml will ignore the extra PVAL points unless either FINAL or GKRIGE are set to save processing time The GROUPFACTOR qualifier like SUBSET must appear on a line by itself after the data line and before the model line Its purpose is to define a factor t by merging levels of an existing factor v The syntax is GROUPFACTOR lt Group _factor gt lt Exist_factor gt lt new codes gt for example GROUPFACTOR Year YearLoc 1112233344 forms a new factor Year with 4 levels from the existing factor YearLoc with 10 levels Alternatively Year could be formed data transformation YearLoc set 111223334 4 L 2001 2002 2003 2004 is used to join lines in plots see X 5 Command file Reading the data 75 Table 5 4 List o
326. lly be a variance ratio Revised 08 see page 126 This depends on how the R structure is defined It is important to recognise whether it is a variance or a variance ratio when setting initial values Table 7 3 Details of the variance models available in ASReml base description algebraic number of parameters identifier form corr homo s variance hetero s variance Correlation models One dimensional equally spaced ID identity Ca 1 C 0 i j 0 1 AR 1 E order Ca 1 Cosa 1 2 autoregressive Cy Os i gt j 1 lpi lt 1 AR2 2 order G1 2 3 autoregressive Orne 1 Q Ci OORE 039 55 i gt j 1 1d lt 1 65 a lt 1 AR3 3 order Ca 1 2 1 4 te 3 4 ASReml2 autoregressive Craig 4505 0 Cina 4 Qz T 2 1 B b2 Q Cy Cia F P2Ci 2 3 gg O3Ci_3 55 i gt j 2 1d lt 1 2 l 2 lt 1 5 lt 1 l w 2 w 3 w 7 Command file Specifying the variance structures 133 Table 7 3 Details of the variance models available in ASReml ASReml2 base description algebraic number of parameters identifier form corr homo s hetero s variance variance SAR symmetric CG L 1 2 1l w autoregressive Cure O A 2 4 Cis OA Cias g g 4 Cisza i gt g 1 Id lt 1 SAR2 constrained as for AR3 using 2 3 2 w autoregressive 3 bd 7 2 used for _ ig 72 competition 2 oo Va Ya s s VNV MA 1 1 order C 1
327. lly found that the closer the plot centroids the higher the spatial correlation This is not always the case and if the highest between plot correlation relates to the larger spatial distance then this may suggest the presence of extraneous variation see Gilmour et al 1997 for example Figure 16 5 presents a plot of the sample variogram of the residuals from this model The plot appears in reasonable agreement with the model The next model includes a measurement error or nugget effect component That is the variance model for the plot errors is now given by 07S 07 E 8 Er YIis0 16 6 where 7 is the ratio of nugget variance to error variance a7 The abbreviated output for this model is given below There is a significant improvement in the REML log likelihood with the inclusion of the nugget effect see Table 16 7 Vauiogrer ot Pei Rale 96 aug Btw 17 08 51 Outer displacement Inner displacement Figure 16 5 Sample variogram of the residuals from the AR1xAR1 model for the Slate Hall data AR1 x AR1 16 Examples 302 1 LogL 739 681 S2 36034 125 df 1 000 0 1000 0 1000 2 LogL 714 340 S2 28109 125 df 1 000 0 4049 0 1870 3 LogL 703 338 S2 29914 125 df 1 000 0 5737 0 3122 4 LogL 700 371 S2 37464 125 df 1 000 0 6789 0 4320 5 LogL 700 324 S2 38602 125 df 1 000 0 6838 0 4542 6 LogL 700 322 S2 38735 125 df 1 000 0 6838 0 4579 7 LogL 700 322 S2 38754 125 df 1 000 0 6838 0 4585 8 LogL 700 322 S2
328. lsewhere in the variance model via the USE f qualifier see page 152 7 Command file Specifying the variance structures 147 Table 7 4 List of R and G variance structure definition line qualifiers The variance model see Section 2 2 is O 0 Ri di ZG y Z e For multivariate models and g are 1 and the variances are built qualifier action 1S2 r 52 1S2 r into Ri ASReml3 SUBSECTION f e For multiple section univariate analyses is 1 and S2 r can be used to initialize o or S2 r to fix it commonly R is a correlation model e For univariate single section analyses including ASUV the default action is to estimate possibly initialized using S2 r with o 1 and R being a correlation matrix Alternatively using S2 r fixes 1 and r a variance parameter may then be incorporated in Ri allows many independent blocks of correlated observations to be ASReml3 modelled with common variance and correlation parameters The observations need to be sorted on a variable which defines the blocks The blocks can be of different sizes Any homogeneous variance correlation model defined in Table 7 3 may be used for the variance structure This extends the R structure definition R 6j_ Ri where Ri 8 15 i such that i1 may have direct sum structure with common parameters So for generic times 1 10 data sorted bids within auctions O O AR1 0 5 SUBSECTION auction and
329. ly one or more factors can be superimposed on the one panel The data can be added to the plot to assist informal examination of the model fit With no plot options ASReml chooses an arrangement for plotting the predictions by recognising any covariates and noting the size of factors However the user is able to customize how the predictions are plotted by either using options to the PLOT qualifier or by using the graphical interface The graphical interface is accessed by typing Esc when the figure is displayed The PLOT qualifier has the following options Table 10 2 List of predict plot options option action Lines and data addData superimposes the raw data addlabels factors superimposes the raw data with the data points labelled using the given factors which must not be prediction factors This option may be useful to identify individual data points on the graph for instance potential outliers or alternatively to identify groups of data points e g all data points in the same stratum addlines factors superimposes the raw data with the data points joined using the given factors which must not be prediction factors This option may be useful for repeated measures data noSEs specifies that no error bars should be plotted by default they are plotted semult r specifies the multiplier of the SE used for creating error bars default 1 0 joinmeans specifies that the predicted values shou
330. m If ASReml has not obtained the maximum available workspace then use WORKSPACE to increase it The problem could be with the way the model is specified Try fitting a sim pler model or using a reduced data set to dis cover where the workspace is being used The response variable nominated by the YVAR command line qualifier is not in the data The data values are out of the expected range for binary binomial data there is a problem with forming one of the generated factors The most probable cause is that an interaction cannot be formed You must either use the US error structure or use the ASUV qualifier and maybe include mv in the model a term in the model specification is not among the terms that have been defined Check the spelling there is a problem with the named variable The second field in the R structure line does not refer to a variate in the data the weight and filter columns must be data fields Check the data summary See the discussion of AISINGULARITIES 15 Error messages 272 Table 15 3 Alphabetical list of error messages and probable cause s remedies error message probable cause remedy Iteration failed Matern Maximum number of special structures exceeded Maximum number of variance parameters exceeded Missing faulty SKIP or A needed for Missing values in design variables factors Missing Value Miscount forming design Missing values not allo
331. m to the current model defined by the model which includes those terms appearing above the current term given the variance parameters For example the test of nitrogen is calculated from the change in sums of squares for the two models mu variety nitrogen and mu variety No refitting occurs that is the variance parameters are held constant at the REML estimates obtained from the currently specified fixed model The incremental Wald statistics have an asymptotic x distribution with degrees of freedom df given by the number of estimable effects the number in the DF column In this example the incremental Wald F statistics are numerically the 16 Examples 282 same as the ANOVA Wald F statistics and ASReml has calculated the appropriate denominator df for testing fixed effects This is a simple problem for balanced designs such as the split plot design but it is not straightforward to determine the relevant denominator df in unbalanced designs such as the rat data set described in the next section Tables of predicted means are presented for the nitrogen variety and variety by nitrogen tables in the pvs file The qualifier SED has been used on the third predict statement and so the matrix of SEDs for the variety by nitrogen table is printed For the first two predictions the average SED is calculated from the average variance of differences Note also that the order of the predictions e g 0 6_cwt 0 4_cwt 0 2_cwt O_cwt for nitro
332. ma 6 979 ie 0 0 0 0 0 0 0 0 ie 0 0 0 0 0 74 64 90 9i 86 65 141 72 29 62 20 61 11 132 26 0 63 15 99 9 37 84 48 110 228 49 131 20 9 87 1 32 14 26 30 3 37 6 4 23 32 44 46 109 97 83 67 68 141 69 40 44 11 0 3 6 0 21 41 15 51 25 32 120 33 10 58 117 113 109 63 57 25 18 18 2 84 19 pk 45 18 30 56 9 12 53 41 ig 99 123 47 119 181 101 104 40 29 87 103 81 61 81 130 94 10 55 53 55 106 15 109 153 23 0 50 66 111 29 75 43 24 90 37 23 64 130 84 122 129 126 90 38 91 133 126 16 57 30 70 99 114 219 332 174 77 19 30 29 58 63 88 4 124 49 101 129 113 45 92 70 198 257 333 3652 319 253 166 152 52 28 997 135 67T 16 9 36 86 24 62 46 7 29 227 167 356 335 183 179 189 118 124 14 52 19 7 56 8i 33 63 40 57 15 24 73 183 277 352 323 288 151 56 130 188 29 78 7 12 30 39 67 89 3 116 27 2 64 14 Description of output files 237 Residual section 1 Residual section 1 Residual section 1 Residual section 1 Residual section 1 Residual section 1 6 possible ee a9 3393 3 9 E TE a gt 29 gt gt Ei gt eK if gt 4 ii i i S gut t re ls ae se column 8 11 row 4 22 is 3 column 9 11 row 2 22 is 3 column 9 11 row 3 22 is 3 columm 10 11 row 3 22 is 3 column 10 11 row 4 22 ie 3 column 11 11 row 3 22 is 3 outliers in section 1 test value
333. marginality see Section 2 6 The detail of exactly which terms are conditioned on is reported in the aov file The marginality principle used in determining this conditional test is that a term cannot be adjusted for another term which encompasses it explicitly e g term A C cannot be adjusted for A B C or implicitly e g term REGION cannot be adjusted for LOCATION when lo cations are actually nested in regions although they are coded independently FOWN on page 84 provides a way of replac ing the conditional Wald F statistic by specifying what terms are to be adjusted for provided its degrees of freedom are unchanged from the incremental test sets the maximum number of iterations the default is 10 ASReml iterates for n iterations unless convergence is achieved first Convergence is presumed when the REML log likelihood changes less than 0 002 current iteration number and the individual variance parameter estimates change less than 1 If the job has not converged in n iterations use the CONTINUE qualifier to resume iterating from the current point To abort the job at the end of the current iteration create a file named ABORTASR NOW in the directory in which the job is running At the end of each iteration ASRemlchecks for this file and if present stops the job producing the usual output but not producing predicted values since these are calculated in the last iteration Creating FINALASR NOW will stop ASReml after one mor
334. matrix for Residual 22 458 69 474 Eigen values Percentage 1 op WN 0 8509 0335 1168 List a o 5 amp Eigen Analysis of Eigen values 4970 5 210 3 395 16 118 10 502 0 8663 0 0141 0 4765 0 1316 0 0230 0 0585 0 0871 0 9843 0 1196 0 1010 1 160 3 588 0 0470 0 1746 0 0048 0 0769 0 9805 UnStructured matrix for Tr sire 1 904 0 304 0 114 0 013 0 103 0 318 0 0027 0 0327 0 9974 0 0633 0 0039 0 010 16 Examples 349 Percentage 31 199 12 963 4 859 0 535 0 444 1 0 4578 0 7476 0 4695 0 1052 0 0087 2 0 8860 0 3646 0 2766 0 0248 0 0700 3 0 0077 0 0798 0 0826 0 9438 0 3098 4 0 0163 0 5260 0 8015 0 1116 0 2612 5 0 0710 0 1587 0 2320 0 2918 0 9115 Eigen Analysis of UnStructured matrix for at Tr 1 dam Eigen values 4 382 0 010 0 025 Percentage 100 352 0 225 0 577 1 0 7041 0 2321 0 6711 2 0 7081 0 1585 0 6881 3 0 0533 0 9597 0 2760 Eigen Analysis of UnStructured matrix for at Tr 1 1lit Eigen values 4 795 1827 0 482 0 016 Percentage 67 345 25 664 6 769 0 221 1 0 7762 0 5928 0 2178 0 0133 2 0 6159 0 6328 0 4691 0 0106 3 0 0016 0 0340 0 0255 0 9991 4 0 1403 0 4969 0 8555 0 0390 The REML estimates of all the variance matrices except for the dam components are positive definite Heritabilities for each trait can be calculated using the pin file facility of ASReml The heritability is given by 7284 2 vp where 0 is the phenotypic variance an
335. med by the tabulate directive yht contains the predicted values residuals and diagonal elements of the hat matrix for each data point Other output files asl contains a progress log and error messages if the L command line option is specified aov contains details of the ANOVA calculations apj is an ASReml project file created by ASReml W ask holds the RENAME ARG argument from the most recent run so that ASReml can retrieve restart values from the most recent run when CONTINUE is specified but there is no particular rsv file for the current ARG argument asp contains transformed data see PRINT in Table 5 2 ass contains the data summary created by the SUM qualifier see page 71 dbr dpr spr contains the data and residuals in a binary form for further analysis see RESIDUALS Table 5 5 veo holds the equation order to speed up re running big jobs when the model is unchanged This binary file is of no use to the user 14 Description of output files 222 Table 14 1 Summary of ASReml output files file description vll holds factor level names when data residuals are saved in binary form See SAVE on page 87 vrb contains the estimates of the fixed effects and their variance VVP contains the approximate variances of the variance parameters It is designed to be read back with the P option for calculating functions of the variance parameters was basename was is open while ASR
336. mmended Models 4 6 have too few variance pa rameters and are likely to cause serious estimation problems For model 3 where the scale parameter 0 has been fitted univariate single site analysis it becomes the scale for G This parameterisation is bizarre and is not recommended Mod els 7 9 have too many variance parameters and ASReml will arbitrarily fix one of the variance parameters leading to possible confusion for the user If you fix the variance parameter to a particular value then it does not count for the purposes of applying the principle that there be only one scaling variance parameter That is models 7 9 can be made identifiable by fixing all but one of the nonidentifiable scaling parameters in each of G and R to a particular value Table 2 1 Combination of models for G and R structures model G Go Ry Ro 0 comment 1 VC C C y valid 2 V C V C n valid 3 C C V y valid but not recommended 4 n inappropriate as R is a correlation model 5 C C C C y inappropriate same scale for R and G 6 C C V C n inappropriate no scaling parameter for G 7 V V nonidentifiable 2 scaling parameters for G 8 V C V y nonidentifiable scale for R and overall scale 9 V V nonidentifiable 2 scaling parameters for R indicates the entry is not relevant in this case Note that G1 and G are interchangeable in this table as are R and R 2 Some theory 17 2 5 Inference Random effects Revised 08 Tests
337. n Oats Unbalanced nested design Rats Source of variability in unbalanced data Volts Balanced repeated measures Height Spatial analysis of a field experiment Barley Unreplicated early generation variety trial Wheat Paired Case Control study Rice Balanced longitudinal data Oranges Initial analyses Random coefficients and cubic smoothing splines Multivariate animal genetics data Sheep Half sib analysis Animal model 278 16 Examples 279 16 1 Introduction In this chapter we present the analysis of a variety of examples The primary aim is to illustrate the capabilities of ASReml in the context of analysing real data sets We also discuss the output produced by ASReml and indicate when problems may occur Statistical concepts and issues are discussed as necessary but we stress that the analyses are illustrative not prescriptive 16 2 Split plot design Oats The first example involves the analysis of a split plot design originally presented by Yates 1935 The experiment was conducted to assess the effects on yield of three oat varieties Golden Rain Marvellous and Victory with four levels of nitrogen application 0 0 2 0 4 and 0 6 cwt acre The field layout consisted of six blocks labelled I II II IV V and VI with three whole plots per block each split into four sub plots The three varieties were randomly allocated to the three whole plots while the four levels of nitrogen application were rand
338. n 2513 records of the lamb data from the previous example augmented with an extra simulated variable YVar It was created from the summarized data without knowing which actual individuals had which combinations of trait values The binary variable Score1 indicates whether all four feet are sound The following code produces a bivariate analysis of Score1 on the underlying logistic scale and YVar on the Normal scale Lamb data from ARG thesis page 177 8 Year GRP 5 v99 V2 4 IM 1 SEX SIRE II Scoret Score2 Scald V99 Rot V99 YVar binnor txt skip 1 ASUV MAXIT 40 Score1 YVar bin Trait SEX Trait GRP r Trait SIRE 121 16 Examples 337 2513 20 US IJGFPP 1 01 0 25 Trait SIRE 2 Trait 0 US 0 015 0 01 1 05 SIRE There are several issues addressed in this code e ASUV is required and if there had been any missing values in the data the fixed model term mv would also be required e ASReml constructs the R matrix by scaling the reported matrix by the binomial variance calculated from the fitted value of the binomial variate Consequently to avoid over under dispersion being also fitted the residual variance for the binomial trait is fixed at 1 0 by giving its initial value as 1 0 and using the qualifier GFPP e The response variables must be listed before the qualifiers If written as Score BIN YVar YVar would be parsed as an argument to BIN rather than as a response variable e Only one categorical resp
339. n asso ciation with the OWN variance model page 144 PRINT n causes ASReml to print the transformed data file to base name asp If n lt 0 data fields 1 mod n are written to the file n 0 nothing is written n 1 all data fields are written to the file if it does not exist n 2 all data fields are written to the file overwriting any previous contents n gt 2 data fields n t are written to the file where tis the last defined column PNG sets hardcopy graphics file type to png IPS sets hardcopy graphics file type to ps PVSFORM n modifies the format of the tables in the pvs file and changes ASReml2 the file extension of the file to reflect the format PVSFORM 1 is TAB separated pvs pvs txt PVSFORM 2 is COMMA separated pvs _pvs csv PVSFORM 3 is Ampersand separated pvs _pvs tex See TXTFORM for more detail RESIDUALS 2 instructs ASReml to write the transformed data and the resid uals to a binary file The residual is the last field The file basename srs is written in single precision unless the argu ment is 2 in which case basename drs is written in double precision Factor names are held in a v11 file see SAVE below 5 Command file Reading the data 87 Table 5 5 List of rarely used job control qualifiers qualifier action ASReml2 ISAVE n ISCREEN n SMX m The file will not be written from a spatial analysis two dimensional error when the d
340. n lead to inconsistent comparisons between check varieties and test lines Given the large amount of replication afforded to check varieties there will be very little shrinkage irrespective of the realised heritability We consider an initial analysis with spatial correlation in one direction and fitting the variety effects check replicated and unreplicated lines as random We present three further spatial models for comparison The ASReml input file is Tullibigeal trial linenum yield weed column 10 row 67 variety 532 testlines 1 525 check lines 526 532 wheat asd skip 1 DOPATH 1 PATH 1 ARI x I y mu weed mv r variety 12 67 row AR1 0 1 10 column I 0 PATH 2 ARI x AR1 y mu weed mv r variety i 2 67 row AR1 0 1 10 column AR1 0 1 PATH 3 AR1 x ARI column trend y mu weed pol column 1 mv r variety 12 67 row AR1 0 1 16 Examples 307 10 column AR1i 0 1 PATH 4 1 2 67 row AR1 0 1 10 column AR1 0 1 predict var AR1 x AR1 Nugget column trend y mu weed pol column 1 mv r variety units The data fields represent the factors variety row and column a covariate weed and the plot yield yield There are three paths in the ASReml file We begin with the one dimensional spatial model which assumes the variance model for the plot effects within columns is described by a first order autoregressive process The abbreviated output file is LogL 4280 LogL 4268 LogL 4255 LogL 4
341. n of the second Wald statistic available in ASReml the so called conditional Wald statistic This method is invoked by placing FCON on the datafile line ASReml attempts to construct conditional Wald statistics for each term in the fixed dense linear model so that marginality relations are respected As a simple example for the three way factorial model the conditional Wald statistics would be computed as Term Sums of Squares M code 1 R 1 A R A 1 B C B C R 1 A B C B C R 1 B C B C A B R B 1 A C A C R 1 A B C A C R 1 A C A C A C R C 1 A B A B R 1 A B C A B R 1 A B A B A A B R A B 1 A B C A C B C R 1 A B C A B A C B C R 1 A B C A C B C B A C R A C 1 A B C A B B C R 1 A B C A B A C B C R 1 A B C A B B C B B C R B C 1 A B C A B A C R 1 A B C A B A C B C R 1 A B C A B A C B A B C R A B C 1 A B C A B A C B C R 1 A B C A B A C B C A B C R 1 A B C A B A C B C c Of these the conditional Wald statistic for the 1 B C and A B C terms would be the same as the incremental Wald statistics produced using the linear model y 14 A4 B4 C AB A C4 B C4 A B C The preceeding table includes a so called M marginality code reported by ASRem when conditional Wald statistics are presented All terms with the highest M code letter are tested conditionally on all other terms in the model i e by dropping the term from the maximum model All terms with the preceeding M code letter 2 Some
342. n reported to perform adequately e g Breslow 2003 McCulloch and Searle 2001 also discuss the use of PQL for GLMMs The performance of PQL in other respects such as for hypothesis testing has received much less attention and most studies into PQL have examined only relatively simple GLMMs Anecdotal evidence suggests that this technique may give misleading results in certain situations Therefore we cannot recommend the use of this technique for general use and it is included in the current version of ASReml for advanced users If this technique is used we recommend the use of cross validatory assessment such as applying PQL to simulated data from the same design Millar and Willis 1999 The standard GLM Analysis of Deviance A0D should not be used when there are random terms in the model as the variance components are reestimated for each submodel 6 9 Missing values Missing values in the response 6 Command file Specifying the terms in the mixed model 113 Revised 08 It is sometimes computationally convenient to NIN Alliance Trial 1989 estimate missing values for example in spa variety tial analysis of regular arrays see example 3a in Section 7 3 Missing values are estimated if row 22 _ lumn 11 the model term mv is included in the model a nin89 asd skip 1 Formally mv creates a factor with a covari yield mu variety r repl ate for each missing value The covariates are If mv 12 11 column
343. names copied across 11 3 Command line options ASReml2 Command line options and arguments may be specified on the command line or on the top job control line This is an optional first line of the as file which sets command line options and arguments from within the job If the first line of the as file contains a qualifier other than DOPATH it is interpreted as setting command line options and the Title is taken as the next line The option string actually used by ASReml is the combination of what is on the command line and what is on the job control line with options set in both places taking arguments from the command line Arguments on the top job control line are ignored if there are arguments on the command line This section defines the options Arguments are discussed in detail in a following section Command line options are not case sensitive and are combined in a single string preceded by a minus sign for example LNW128 The options can be set on the command line or on the first line of the job either as a concatenated string in the same format as for the command line or as a list of qualifiers For example the command line ASReml h22r jobname 1 2 3 could be replaced with ASReml jobname if the first line of jobname as was either l h2gr 1 2 3 or HARDCOPY EPS RENAME ARGS 1 2 3 Table 11 1 presents the command line options available in ASReml with brief descriptions It also specifies the equivalent qualifier
344. nary files binary files can only be used in conjunction with a pedigree file if the pedigree fields are coded in the binary file so that they correspond with the pedigree file this can be done using the SAVE option in ASReml to form the binary file see Table 5 5 or the identifiers are whole numbers less than 9 999 999 and the RECODE qualifier is specified see Table 5 5 Command file Reading the data Introduction Important rules Title line Specifying and reading the data Data field definition syntax Transforming the data Transformation syntax Other rules and examples Special note on covariates Other examples Datafile line Datafile line syntax Datafile qualifiers Job control qualifiers 46 5 Command file Reading the data 47 5 1 5 2 ASReml2 Introduction In the code box to the right is the ASReml command file nin89a as for a spatial analysis of the Nebraska Intrastate Nursery NIN field experiment introduced Chapter 3 The lines that are highlighted in bold blue type relate to reading in the data In this chapter we use this example to discuss reading in the data in detail Notice in line comment introduced by the character and joining of lines indicated by Important rules In the ASReml command file e all blank lines are ignored NIN Alliance Trial 1989 variety A Alphanumeric id pid raw repl 4 nloc yield lat long row 22 column 11 nin89a
345. ncated when used in the model line but care must be taken that the truncated form is not ambiguous If the truncated form matches more than one label the term associated with the first match is assumed For example dens is an abbeviation for density but spl dens 7 is a different model term to spl density 7 because it does not represent a simple truncation model terms may only appear once in the model line repeated occurrences are ignored model terms other than the original data fields are defined the first time they appear on the model line They may be abbreviated truncated if they are referred to again provided no ambiguity is introduced Important It is often clearer if labels are not abbreviated If abbreviations are used then they need to be chosen to avoid confusion e if the model is written over several lines all but the final line must end with a comma to indicate that the list is continued In Tables 6 1 and 6 2 the arguments in model term functions are represented by the following symbols f the label of a data variable defined as a model factor k n an integer number r a real number t a model term label includes data variables v y the label of a data variable Parsing of model terms in ASReml is not very sophisticated Where a model term takes another model term as an argument the argument must be predefined If necessary include the argument in the model line with a leading
346. nce and spline type mod els e un balanced designed experiments e multi environment trials and meta analysis univariate and multivariate animal breeding and genetics data involving a relationship matrix for correlated effects e regular or irregular spatial data The engine of ASReml underpins the REML procedure in GENSTAT An interface for R called ASReml R is available and runs under the same license as the ASReml program While these interfaces will be adequate for many analyses some large problems will need to use ASReml The ASReml user interface is terse Most effort has been directed towards efficiency of the engine It normally operates in a batch mode Problem size depends on the sparsity of the mixed model equations and the size of your computer However models with 500 000 effects have been fitted suc cessfully The computational efficiency of ASReml arises from using the Average Information REML procedure giving quadratic convergence and sparse matrix operations ASReml has been operational since March 1996 and is updated peri odically Installation Installation instructions are distributed with the program If you require help with installation or licensing please email support asreml co uk 1 Introduction 3 1 3 User Interface ASReml2 ASReml is essentially a batch program with some optional interactive features The typical sequence of operations when using ASReml is e Prepare the data typically u
347. nce structures 122 See Chapter 15 See page 129 or on the next line 0 1 directly after IDV in this case 0 is ignored as an initial value on the model line if there is no initial value after the identifier ASReml will look on the next line if ASReml does not find an initial value it will stop and give an error message in the asr file e in this case V o2 Z Z 02I which is fitted as o2 yr Zr Z I where yr is a variance ratio yp 02 02 and o is the scale parameter Thus 0 1 is a reasonable initial value for y regardless of the scale of the data 3a Two dimensional spatial model with spatial correlation in one direc tion This code specifies a two dimensional spatial structure for error but with spatial correla tion in the row direction only that is e N 0 o2I p The variance header line tells ASReml that there is one R struc ture 1 which is a direct product of two vari ance models 2 there are no G structures 0 The next two lines define the components of A structure definition line must be specified for each component For V 021 p the first matrix is an iden tity matrix of order 11 for columns ID the the R structure second matrix is a first order autoregressive NIN Alliance Trial 1989 variety A id pid raw repl 4 row 22 column 11 nin89aug asd skip 1 yield mu variety f mv 120 11 column ID 22 row AR1 0 3
348. ncluded in the anal ysis This summary will ignore data records for which the variable being analysed is missing unless a multivariate anal ysis is requested or missing values are being estimated The information is written to the ass file is used to plot the transformed data Use X to specify the x variable Y to specify the y variable and G to specify a grouping variable JOIN joins the points when the x value increases between consecutive records The grouping variable may be omitted for a simple scatter plot Omit Y y produce a histogram of the x variable For example X age Y height G sex Note that the graphs are only produced in the graphics ver sions of ASReml Section 11 3 5 Command file Reading the data 72 Table 5 3 List of commonly used job control qualifiers qualifier action For multivariate repeated measures data ASReml can plot the response profiles if the first response is nominated with the Y qualifier and the following analysis is of the multi variate data ASReml assumes the response variables are in contiguous fields and are equally spaced For example Response profiles Treatment A Yi Y2 Y3 Y4 Y5 rat asd Y Yi G Treatment JOIN Yi Y2 Y3 Y4 Y5 Trait Treatment Trait Treatment Table 5 4 List of occasionally used job control qualifiers qualifier action ASMV n indicates a multivariate analysis is required although the data is presented in a univar
349. nd file Running the job 208 PhenData txt ICYCLE 1 1000 IMBF mbf Genotype MLIB Marker I csv rename Marker I IMBF mbf Genotype MLIB Marker35 csv rename MKRO35 yld mu r MKRO35 Marker I We have given Marker35 a new name because it is still also generated by the CYCLE unless it is modified to read ICYCLE 1 34 36 1000 Order of Substitution The substitution order is ASSIGN CYCLE TP command line arguments and finally the interactive prompt 11 5 Performance issues The following subsections raise several issues which affect the performance of ASReml Multiple processors ASReml has not been configured for parallel processing Performance is down graded if it tries to use two processors simultaneously as it wastes time swapping between processors Slow processes The processing time is related to the size of the model the complexity of the variance mmodel in particular the number of parameters the sparsity of the mixed model equations the amount of data being processed Typically the first iteration take longer than other iterations The extra work in the first iteration is to determine an optimum equation order for processing the model see EQORDER The extra processes in the last iteration are optional They include e calculation of predicted values see PREDICT statement e calculation of denominator degrees of freedom see DDF 11 Command file Running the job 209 e calculation of outlier st
350. nd of incomplete lines so that ASReml will to continue read ing values from the next line of input If the explicit points do not adequately cover the range a message is printed and the values are rescaled unless NOCHECK is also specified Inade quate coverage is when the explicit range does not cover the midpoint of the actual range See KNOTS PVAL and SCALE reduces the update step sizes of the variance parameters The default value is the reciprocal of the square root of MAXIT It may be set between 0 01 and 1 0 The step size is increased towards 1 each iteration Starting at 0 1 the sequence would be 0 1 0 32 0 56 1 This option is useful when you do not have good starting values especially in multivariate analyses forms a new group factor t derived from an existing group factor v by selecting a subset p of its variables A subgroup factor may not be used in a PREDICT or TABULATE directive forms a new factor t derived from an existing factor v by selecting a subset p of its levels Missing values are transmitted as missing and records whose level is zero are transmitted as zero The qualifier occupies its own line after the datafile line but before the linear model e g I SUBSET EnvC Env 3 5 8 9 15 21 33 defines a reduced form of the factor Env just selecting the environments listed It might then be used in the model in an interaction A subset factor can be used in a TABULATE directive but not in a PREDICT
351. ng the variance structures 150 Table 7 5 Examples of constraining variance parameters in ASReml ASReml code action ABACBAOCBA site gen 2 G header line site 0 US 3 OAOAAO GPUPUUP ed of cl od d gen site 0 FA2 G4PZ3P4P Q0000000VVVV 4 9 initial values for 1st factor 0 3 1 initial values for 2nd factor first fixed at 0 AP 2 init values for site variances xfa site 2 O XFA2 VVVVO 4P4PZ3P ara initial specific variances 4 1 2 initial loadings for 1st factor 0 3 3 initial loadings for 2nd factor constrain all parameters corresponding to A to be equal similarly for B and C The 7th parameter would be left uncon strained This sequence applied to an unstructured 4 x 4 matrix would make it banded that is A BA CBA OCBA this example defines a structure for the genotype by site interaction effects in a MET in which the genotypes are inde pendent random effects within sites but are correlated across sites with equal co variance a 2 factor Factor Analytic model for 4 sites with equal variance is specified us ing this syntax The first loading in the second factor is constrained equal to 0 for identifiability P places restrictions on the magnitude of the loadings and the variances to be positive a 2 factor Factor analytic model in which the specific variances are all equal 7 9 Constraining variance parameters difficult Parameter constraints within a var
352. ng treatment level will generate a singularity but in the first coefficient rather than in the coefficient corre sponding to the missing treatment In this case the coefficients will not be readily interpretable When interacting constrained factors all cells in the cross tabulation should have data fac v forms a factor with a level for each value of x and any addi tional points inserted as discussed with the qualifiers PPOINTS and PVAL fac v y forms a factor with a level for each combination of values from vand y The values are reported in the res file associates the nth giv G inverse with the factor This is used when there is a known except for scale G structure other than the additive inverse genetic relationship matrix The G inverse is supplied in a file whose name has the file extension giv described in Section 9 6 h f requests ASReml to fit the model term for factor f using Helmert constraints Neither Sum to zero nor Helmert constraints gen erate interpretable effects if singularities occur ASReml runs more efficiently if no constraints are applied Following is an example of Helmert and sum to zero covariables for a factor with 5 levels H1 H2 H3 H4 C1 C2 C3 C4 Fl 1 1 1 1 1 0 0 0 F2 1 1 1 1 0 1 0 0 F3 0 2 1 1 0 0 1 0 F4 0 0 3 1 0 0 0 1 F5 0 0 0 4 1 1 1 1 is used to take a copy of a pedigree factor f and fit it without the ge netic relationship covariance This facilitates fitting a second animal
353. nits model is smaller than the Wald F statistic for the AR1xAR1 Predicted values of yield AR1 x AR1 variety 1 0000 2 0000 3 0000 4 0000 5 0000 Predicted_Value Standard_Error Ecode 64 6146 E 1257 9763 1501 4483 1404 9874 1412 5674 1514 4764 64 9783 64 6260 64 9027 65 5889 Mmmm 16 Examples 304 23 24 25 SED Overall Standard Error of Difference 0000 0000 0000 AR1 x AR1 units varie ty 1 2 0000 3 0000 4 5 0000 23 24 25 0000 0000 0000 0000 0000 SED Overall IB Rep RowBlk ColB1lk varie ty 1 2 0000 3 0000 4 5 0000 23 24 25s SED Overall Standard Error of 0000 0000 0000 0000 0000 Standar 1311 4888 1586 7840 1592 0204 64 64 63 0767 7043 5939 59 05 Predicted_Value Standard_Error 1245 5843 1516 2331 1403 9863 1404 9202 1471 6197 1316 8726 1557 5278 1573 8920 d Error of Difference OF of 98 ots OS oS 98 9T 8591 8473 2398 9875 3607 0402 1272 9803 60 51 is ignored in the prediction is ignored in the prediction is ignored in the prediction Predicted_Value Standard_Error 1283 5870 1549 0133 1420 9307 1451 8554 1533 2749 1329 1088 1546 4699 1630 6285 Difference 60 60 60 60 60 60 60 60 1994 1994 1994 1994 1994 1994 1994 1994 62 02 Ecode Mm mm Pl tH Ecode Mmm mw mi m Notice the differences in SE an
354. nlike the case with G structures ASReml automatically includes and esti mates a scale parameter for R structures o2 for V 02 I p in this case This is why the variance models specified for row AR1 and column ID are correlation models The user could specify a non correlation model diagonal elements 1 in the R structure definition for example ID could be replaced by IDV to represent V 02 02J amp p However IDV would then need to be followed by S2 1 to fix o at 1 and prevent ASReml trying unsuccessfully to estimate both parameters as they are confounded the scale parameter associated with IDV and the implicit error variance parameter see Section 2 1 under Combining variance models Specifically the code 11 column IDV 48 S2 would be required in this case where 48 is the starting value for the variances This complexity allows for heterogeneous error variance 3b Two dimensional separable autoregressive spatial model This model extends 3a by specifying a first order autoregressive correlation model of or der 11 for columns AR1 The R structure in this case is therefore the direct product of two autoregressive correlation matrices that is V 02 pc Er pr giving a two dimensional first order separable autoregres sive spatial structure for error The starting column correlation in this case is also 0 3 Again note that o is implicit NIN Alliance Trial 1989 variety A id
355. nterpolated points see PPOINTS and PVAL in Table 5 4 It includes the intercept if n is positive omits it if n is negative For example pol time 2 forms a design matrix with three columns of the orthogonal polynomial of degree 2 from the variable time Alternatively pol time 2 is a term with two columns having centred and scaled linear coefficients in the first column and centred and scaled quadratic coefficients in the second column The actual values Robson 1959 Steep and Torrie 1960 of the coeffi cients are written to the res file This factor could be interacted with a design factor to fit random regression models The leg function differs from the pol function in the way the quadratic and higher polynomials are calculated pow z p o defines the covariable 0 for use in the model where z is a variable in the data p is a power and o is an offset pow z 0 5 0 is equivalent to sqr x 0 pow x 0 o is equivalent to log x o pow z 1 0 is equivalent to inv x o qtl f r calculates an expected marker state from flanking marker information ASReml2 at position r of the linkage group f see MM to define marker locations r may be specified as TPn where TPn has been previously internally defined with a predict statement see page 185 r should be given in Morgans sin v r forms sine from v with period r Omit r if v is radians If v is degrees r is 360 spl v k In order to fit spline models associa
356. nverse relationship matrix is not the appropriate required matrix the user can provide a particular general inverse variance GIV matrix explicitly in a giv file In this chapter we consider data presented in Harvey 1977 using the command file harvey as 9 2 The command file In ASReml the P data field qualifier indicates Pedigree file example that the corresponding data field has an asso animal P i I ciated pedigree The file containing the pedi e A gree harvey ped in the example for animal Vises S is specified after all field definitions and before damage the datafile definition See below for the first ogar Meen 20 lines of harvey ped together with the cor a l responding lines of the data file harvey dat adailygain mu lines r All individuals appearing in the data file must animal 0 25 appear in the pedigree file When all the pedi gree information individual male parent female parent appears as the first three fields of the data file the data file can double as the pedigree file In this example the line harvey ped ALPHA could be replaced with harvey dat ALPHA Typically additional individuals providing additional genetic links are present in the pedigree file 9 Command file Genetic analysis 166 9 3 The pedigree file The pedigree file is used to define the genetic relationships for fitting a genetic animal model and is required if the P qualifier is associated with a da
357. o o o j 7 ce o o 8 o o00 e ga So g 7 o o o E o 4099 Bb go Soo o3 g g g88 0 o e885 828 oo 8 3 on 0 Ej ra E a ona 8 880 58 oo 8 6 0 998 o o Figure 16 1 Residual plot for the rat data We refit the model without the dose sex term Note that the variance parame ters are re estimated though there is little change from the previous analysis 16 Examples 287 Source Model terms Gamma Component Comp SE C dam 27 27 0 595157 0 9792 79E 01 2 93 OP Variance 322 317 1 00000 0 164524 12 13 0 P Wald F statistics Source of Variation NumDF DenDF_con F_inc F_con M P_con 7 mu 1 2 0 8951 48 1093 05 lt 001 3 littersize 1 31 4 27 85 46 43 A lt 001 1 dose 2 24 0 12 05 11 42 A lt 001 2 sex 1 301 7 58 27 58 27 A lt 001 Part 4 shows what happens if we wrongly drop dam from this model Even if a random term is not significant it should not be dropped from the model if it represents a strata of the design as in this case Source Model terms Gamma Component Comp SE C Variance 322 317 1 00000 0 253182 12 59 OP Wald F statistics Source of Variation NumDF DenDF_con F_inc F_con M P_con 7 mu nl 317 0 47077 31 3309 42 lt 001 3 littersize 1 317 0 68 48 146 50 A lt 001 1 dose 2 317 0 60 99 58 43 A lt 001 2 sex 1 317 0 24 52 24 52 A lt 001 16 4 Source of variability in unbalanced data Volts In this example we illustrate an analysis of unbalanced data in which the main aim is to determine t
358. ob servations missing in different patterns and these are handled internally during analy sis the R structure must be ordered traits within units that is the R structure defini tion line for units must be specified before the line for Trait variance parameters are variances not vari ance ratios the R structure definition line for units that is 1485 O ID could be replaced by Oor O O ID this tells ASReml to fill in the number of units and is a useful option when the exact number of units in the data is not known to the user Orange Wether Trial 1984 8 SheepID IL TRIAL BloodLine I TEAM YEAR GFW YLD FDIAM wether dat skip 1 GFW FDIAM Trait Trait YEAR lIr Trait TEAM Trait SheepID predict YEAR Trait 1 2 2 1 R and 2 G structures 1485 0 ID units Trait 0 US traits 3 0 Trait TEAM 2 ist G structure Trait 0 US GP 3 0 TEAM O ID Trait SheepID 2 2nd G struct Trait 0 US GP 3 0 SheepID 0 ID the error variance matrix is specified by the model Trait 0 US the initial values are for the lower triangle of the symmetric matrix speci fied row wise finding reasonable initial values can be a problem If initial values are written on the next line in the form q O where q is 1 2 and t is the number of traits ASReml will take half of the phenotypic variance matrix of the data as an initial value see as file in code box for example 8 Command file Multivariate
359. ocess the equa tions in the order they are specified in the model Generally this will make a job much slower if it can run at all It is useful if the model has a suitable order as in the IBD model Y m r giv id id giv id invokes a dense inverse of an IBD matrix and id has a sparse structured inverse of an additive relationship matrix While EQORDER 3 generates a more sparse solution EQORDER 1 runs faster forces another mod n 10 rounds of iteration after apparent convergence The default for n is 1 This qualifier has lower priority than MAXIT and ABORTASR NOW see MAXIT for de tails Convergence is judged by changes in the REML log likelihood value and variance parameters However sometimes the vari ance parameter convergence criteria has not been satisfied 5 Command file Reading the data 84 Table 5 5 List of rarely used job control qualifiers qualifier action ASReml3 FOWN allows the user to specify the test reported in the F con col umn of the Wald F Statistics table It has the form FOWN terms to test background terms placed on a separate line immediately after the model line Multiple FOWN statements should appear together It gener ates a Wald F statistic for each model term in terms to test which tests its contribution after all other terms in terms to test and background terms conditional on all terms that ap pear in the SPARSE equations It should only specify terms whi
360. oefficients in the same factor The reported log likelihood value may be positive or negative and typically ex cludes some constants from its calculation It is sometimes reported relative to an offset when its magnitude exceeds 10000 any offset is reported in the asr file Twice the difference in the likelihoods for two models is commonly used as 14 Description of output files 224 version amp title date workspace data summary the basis for a likelihood ratio test see page 17 This is not valid for gener alised linear mixed models as the reported LogL does not include components relating to the reweighting Furthermore it is not appropriate if the fixed effects in the model have changed In particular if fixed effects are fitted in the sparse equations the order of fitting may change with a change in the fitted variance structure resulting in non comparable likelihoods even though the fixed terms in the model have not changed The iteration sequence terminates when the max imum iterations see MAXIT on page 70 has been reached or successive LogL values are less than 0 002 apart The following is a copy of nin89a asr ASReml 3 01d 01 Apr 2008 Build e 01 Apr 2008 10 Apr 2008 16 47 40 140 32 bit 32 Mbyte Windows Licensed to NSW Primary Industries NIN alliance trial 1989 nin89a permanent FA GI I A I A A kkk kkk kk kkk Contact support asreml co uk for licensing and support a
361. oesooo 66629 6 9 0 10 0 ooo SGoeoeaceoooocoooocooe Ss o 0 i ooo oooDuOoooDp OOOO OOO OS te 0 0 ooo SOOSoeoeecosoooesoecos The sln file contains estimates of the fixed and random effects with their stan dard errors in an array with four columns ordered as 14 Description of output files 227 variety estimates intercept missing value estimates factor_name level estimate standard_error Note that the error presented for the estimate of a random effect is the square root of the prediction error variance In a genetic context for example where a relationship matrix A is involved the accuracy is 1 ae where s is the standard error reported with the BLUP u for the ith individual f is the inbreeding coefficient reported when DIAG qualifier is given on a pedigree file line 1 f is the diagonal element of A and oc is the genetic variance The sln file can easily be read into a GENSTAT spreadsheet or an S PLUS data frame Below is a truncated copy of nin89a sln Note that e the order of some terms may differ from the order in which those terms were specified in the model statement e the missing value estimates appear at the end of the file in this example e the format of the file can be changed by specifying the SLNFORM qualifier In particular more significant digits will be reported e Use of the OUTLIER qualifier will generate extra columns containing the outlier statistics d
362. of hypotheses variance parameters Inference concerning variance parameters of a linear mixed effects model usu ally relies on approximate distributions for the RE ML estimates derived from asymptotic results It can be shown that the approximate variance matrix for the REML estimates is given by the inverse of the expected information matrix Cox and Hinkley 1974 section 4 8 Since this matrix is not available in ASReml we replace the expected information matrix by the Al matrix Furthermore the REML estimates are con sistent and asymptotically normal though in small samples this approximation appears to be unreliable see later A general method for comparing the fit of nested models fitted by REML is the REML likelihood ratio test or REMLRT The REMLRT is only valid if the fixed effects are the same for both models In ASReml this requires not only the same fixed effects model but also the same parameterisation If lro is the REML log likelihood of the more general model and g is the REML log likelihood of the restricted model that is the REML log likelihood under the null hypothesis then the REMLRT is given by D 2log lr2 lr1 2 log r2 log r1 2 14 which is strictly positive If r is the number of parameters estimated in model i then the asymptotic distribution of the REMLRT under the restricted model gt 2 1S Xr r The REMLRT is implicitly two sided and must be adjusted when the test inv
363. olves an hypothesis with the parameter on the boundary of the parameter space It can be shown that for a single variance component the theoretical asymptotic distribution of the REMLRT is a mixture of y variates where the mixing prob abilities are 0 5 one with 0 degrees of freedom spike at 0 and the other with 1 degree of freedom The approximate P value for the REMLRT statistic D is 0 5 1 Pr x lt d where d is the observed value of D This has a 5 crit ical value of 2 71 in contrast to the 3 84 critical value for a y variate with 1 degree of freedom The distribution of the REMLRT for the test that k variance components are zero or tests involved in random regressions which involve both variance and covariance components involves a mixture of xy variates from 0 to k degrees of freedom See Self and Liang 1987 for details 2 Some theory 18 Outliers ASReml3 Tests concerning variance components in generally balanced designs such as the balanced one way classification can be derived from the usual analysis of vari ance It can be shown that the REMLRT for a variance component being zero is a monotone function of the F statistic for the associated term To compare two or more non nested models we can evaluate the Akaike Infor mation Criteria AIC or the Bayesian Information Criteria BIC for each model These are given by AIC BIC 2lri 2ti 2lpri logy 2 15 where t is the number of variance param
364. om effect This increased the log likelihood 3 71 P lt 0 05 with the spl age 7 smoothing constants heading to the boundary There is a possible explanation in the season factor When this is added Model 3 it has an F ratio of 107 5 P lt 0 01 while the fac age term goes to the boundry Notice that the inclusion of the fixed term season in models 3 to 6 means that comparisons with models 1 and 2 on the basis of the log likelihood are not valid The spring 16 Examples 329 21 Predicted values of circ 3055 x 1582 Figure 16 14 Plot of fitted cubic smoothing spline for model 1 measurements are lower than the autumn measurements so growth is slower in winter Models 4 and 5 successively examined each term indicating that both smoothing constants are significant P lt 0 05 Lastly we add the covariance parameter between the intercept and slope for each tree in model 6 This ensures that the covariance model will be translation invariant A portion of the output file for model 6 is 8 LogL 87 4291 S2 5 6303 32 df Source Model terms Gamma Component Comp SE C spl age 7 5 5 2 17239 12 2311 1 09 OP spl age 7 Tree 25 25 1 38565 7 80160 1 47 OP Variance 35 32 1 00000 5 63028 1 72 O P Tree UnStru 1 1 5 62219 31 6545 1 26 0 U Tree UnStru 2 1 0 124202E 01 0 699290E 01 0 85 Q U Tree UnStru 2 2 O L08377E 03 0 610192E 03 1 40 OU Covariance Variance Correlation Matrix UnStructured 31 65 0 5032 0 6993E
365. omly assigned to the four sub plots within each whole plot The data is presented in Table 16 1 Table 16 1 A split plot field trial of oat varieties and nitrogen application nitrogen block variety 0 0cwt O0 2cwt 0 4cwt 0 6cwt GR 111 130 157 174 l M 117 114 161 141 V 105 140 118 156 GR 61 91 97 100 ll M 70 108 126 149 V 96 124 121 144 GR 68 64 112 86 IlI M 60 102 89 96 V 89 129 132 124 GR 74 89 81 122 IV M 64 103 132 133 V 70 89 104 117 GR 62 90 100 116 V M 80 82 94 126 V 63 70 109 99 GR 53 74 118 113 Vi M 89 82 86 104 V 97 99 119 121 A standard analysis of these data recognises the two basic elements inherent in the experiment These two aspects are firstly the stratification of the experiment units that is the blocks whole plots and sub plots and secondly the treatment 16 Examples 280 structure that is superimposed on the experimental material The latter is of prime interest in the presence of stratification Thus the aim of the analysis is to examine the importance of the treatment effects while accounting for the stratification and restricted randomisation of the treatments to the experimental units The ASReml input file is presented below split plot example blocks 6 Coded 1 6 in first data field of oats asd nitrogen A 4 Coded alphabetically subplots Coded 1 4 variety A 3 Coded alphabetically wplots Coded 1 3 yield oats asd SKIP 2 yie
366. on up to 5 way a b is expanded toa b a b a b c d is expanded to abcda ba ca db c b d c d a b c a b d a c d b c d a b c d indicates nested expansion a b is expanded to a a b a b c d e is expanded to a b a c a d e This syntax is detected by the string and the closing parenthesis must occur on the same line and before any comma indicating continuation Any number of terms may be enclosed Each may have prepended to suppress it from the model Each enclosed term may have initial values and qualifiers following For example yield site site lin row r variety at esite 1 trow lt 3 col 2 expands to yield site site lin row r site variety at site 1 row 3 at site 1 col 2 6 Command file Specifying the terms in the mixed model 102 ASReml2 Important ASReml3 Conditional factors A conditional factor is a factor that is present only when another factor has a particular level e individual components are specified using the at f function see Table 6 2 for example at site 1 row will fit row as a factor only for site 1 e a complete set of conditional terms are specified by omitting the level spec ification in the at f function provided the correct number of levels of f is specified in the field definitions Otherwise a list of levels may be specified at f b creates a series of model terms representing b nested within a for any model term b A model term is created for each level
367. on of the data and prediction from the model 178 Revised 08 Random factors may contribute to predictions in several ways They may be evaluated at levels specified by the user they may be averaged over or they may be ignored omitting all model terms that involve the factor from the prediction Averaging over the set of random effects gives a prediction specific to the random effects observed We call this a conditional prediction Omitting the term from the prediction model produces a prediction at the population average often zero that is substituting the assumed population mean for an predicted random effect We call this a marginal prediction Note that in any prediction some random factors for example Genotype may be evaluated as conditional and others for example Blocks at marginal values depending on the aim of prediction For fixed factors there is no pre defined population average so there is no natural interpretation for a prediction derived by omitting a fixed term from the fitted values Therefore any prediction will be either for specific levels of the fixed factor or averaging in some way over the levels of the fixed factor The prediction will therefore involve all fixed model terms Covariates must be predicted at specified values If interest lies in the relationship of the response variable to the covariate predict a suitable grid of covariate values to reveal the relationship Otherwise predict at
368. only required for combination into earlier fields in transformations or when ASReml attempts to read more fields than it needs to is required when reading a binary data file with pedigree iden tifiers that have not been recoded according to the pedigree file It is not needed when the file was formed using the SAVE option but will be needed if formed in some other way see Section 4 2 5 Command file Reading the data 67 ASReml2 Table 5 2 Qualifiers relating to data input and output qualifier action RREC n causes ASReml to read n records or to read up to a data ASReml2 reading error if n is omitted and then process the records it has This allows data to be extracted from a file which con tains trailing non data records for example extracting the predicted values from a pvs file The argument n speci fies the number of data records to be read If not supplied ASReml reads until a data reading error occurs and then pro cesses the data it has Without this qualifier ASReml aborts the job when it encounters a data error See RSKIP ASReml2 ROTE Telp allows ASReml to skip lines at the heading of a file down to and including the nth instance of string s For example to read back the third set predicted values in a pvs file you would specify IRREC RSKIP 4 Ecode since the line containing the 4th instance of Ecode imme diately precedes the predicted values The RREC qualifier means that ASRem
369. onse is permitted and it must be specified first Selected output follows Distribution and link Binomial Logit Mu P 1 1 exp XB V Mu 1 Mu N Warning The LogL value is unsuitable for comparing GLM models 1 LogL 894 974 S2 1 0000 5014 df Dev DF 0 6196 2 LogL 894 554 S2 1 0000 5014 df Dev DF 0 6194 3 LogL 890 600 S2 1 0000 5014 df Dev DF 0 6178 4 LogL 884 431 S2 1 0000 5014 df Dev DF 0 6144 5 LogL 885 759 S2 1 0000 5014 df Dev DF 0 6109 6 LogL 892 413 S2 1 0000 5014 df Dev DF 0 6085 7 LogL 896 969 S2 1 0000 5014 df Dev DF 0 6077 8 LogL 897 941 S2 1 0000 5014 df Dev DF 0 6076 9 LogL 897 962 S2 1 0000 5014 df 1 components restrained 10 LogL 897 962 S2 1 0000 5014 df Dev DF 0 6076 11 LogL 897 961 S2 1 0000 5014 df Dev DF 0 6076 Deviance from GLM fit 5014 3046 50 Variance heterogeneity factor Deviance DF 0 61 Results from analysis of Scorel YVar Notice While convergence of the LogL value indicates that the model has stabilized its value CANNOT be used to formally test differences between Generalized Linear Mixed Models 16 Examples 338 Source Model terms Gamma Component Comp SE C Residual UnStructured 2 1 0 162615E 03 0 162615E 03 0 03 OP Residual UnStructured 2 2 0 255609 0 255609 35 20 OP Trait SIRE UnStructured 1 1 0 166092 0 166092 2 73 0 y Trait SIRE UnStructured 2 1 0 330313E 02 0 330313E 02 0 07 0 U Trait SIRE UnStructured 2 2 0 303900 0 303900 3 76 0 U Covarianc
370. opment of many of the approaches for the analysis of multi section trials We also thank Ian White for his contribution to the spline methodology and Simon Harding for the licensing and installation software and for his development of the WinASReml environment for running ASReml The Mat rn function material was developed with Kathy Haskard a PhD student with Brian Cullis and the denominator degrees of freedom mate rial was developed with Sharon Nielsen a Masters student with Brian Cullis Damian Collins contributed the PREDICT PLOT material Greg Dutkowski has contributed to the extended pedigree options The asremload d11 functionality is provided under license to VSN Alison Kelly has helped with the review of the XFA models Finally we especially thank our close associates who continually test the enhancements Preface I Arthur Gilmour thank Jesus Christ for His forgiveness and personal support over many years As He has said Behold I stand at the door and knock If any man hear my voice and open the door I will come in and sup with him and he with me Revelation 3 20 I thank the Lord for the privilege of collaborating with several very gifted people including those involved in the ASReml project acknowledging their acceptance generosity patience and perseverence toward a boy from Boree Creek The heavens declare the glory of God and the firmament earth shows His handiwork Psalm 19 1 Be exalted O God above the heavens and
371. or a group of m variates or factor variables IG m l is used when m contiguous data fields comprise a set to ASReml3 be used together The variables will be treated as fac tor variables if the second argument l setting the num ber of levels is present it may be For example i and X1 X2 X3 X4 X5 y X G5y data dat data dat y mu X1 X2 X3 X4 X5 y mu X are equivalent DATE specifies the field has one of the date formats dd mm yy dd mm ccyy dd Mon yy dd Mon ccyy and is to be converted into a Julian day where dd is a 1 or 2 digit day of the month mm is a 1 or 2 digit month of the year Mon is a three letter month name Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec yy is the year within the century 00 to 99 cc is the century 19 29 or 20 The separators an must be present as indicated The dates are converted to days starting 1 Jan 1900 When the century is not specified yy of 0 32 is taken as 2000 2032 33 99 taken as 1933 1999 DMY specifies the field has one of the date formats dd mm yy or dd mm ccyy and is to be converted into a Julian day MDY specifies the field has one of the date formats mm dd yy or mm dd ccyy and is to be converted into a Julian day TIME specifies the field has the time format hh mm ss and is to be con 5 Command file Reading the data 51 ASReml2 ASReml2 ASReml2 verted to seconds past midnight where hh is hours 0 to 23 mm is minutes 0 59 and ss i
372. or each sampling unit The columns contain variates and covariates numeric factors alphanumeric traits response vari ables and weight variables in any order that is convenient to the user The data file may be free format fixed format or a binary file Free format data files The data are read free format SPACE COMMA or TAB separated unless the file name has extension bin for real binary or db1 for double precision binary see 4 Data file preparation 44 ASReml2 below Important points to note are as follows files prepared in Excel must be saved to comma or tab delimited form blank lines are ignored column headings field labels or comments may be present at the top of the file provided that the skip qualifier Table 5 2 is used to skip over them NA and are treated as coding for missing values in free format data files if missing values are coded with a unique data value for example 0 or 9 use M to flag them as missing or DV to drop the data record containing them see Table 5 1 comma delimited files whose file name ends in csv or for which the CSV qualifier is set recognise empty fields as missing values a line beginning with a comma implies a preceding missing value consecutive commas imply a missing value a line ending with a comma implies a trailing missing value if the filename does not end in csv or the CSV qualifier is not set commas are treated as white s
373. or one dimensional structures in this case the giv structure can be directly associated with the term using the giv f 7 model function which associates the ith giv file with factor f for example giv animal 1 0 12 is equivalent to the first of the preceding examples It is imperative that the GIV GRM matrix be defined with the correct row column order the order that matches the order of the levels in the factor it is associated with The easiest way to check this is to compare the order used in the GIV GRM file with the order reported in the s1n file when the model is fitted 9 Command file Genetic analysis 173 Genetic groups in GIV matrices If a user creates a GIV file outside ASReml which has fixed degrees of freedom associated with it a GROUPSDF n qualifier is provided to specify the number of fixed degrees of freedom n incorporated into the GIV matrix The GROUPSDF qualifier is written into the first line of the giv matrix produced by the GIV qualifier of the pedigree line if the pedigree includes genetic groups and will be honoured from there when reusing a GIV matrix formed from a pedigree with genetic groups in ASReml When groups are constrained then it will be the number of groups less number of constraints For example if the pedigree file qualified by GROUPS 7 begins AOO BOO coo ABC O O ABC is not present in the subsequent pedigree lines DOO EOG DE O O DE is not present in the subsequent pedigr
374. ordered sequence of variance structures for the NIN variety trial see Section 7 3 This is to introduce variance modelling in practice We then present the topics in detail Non singular variance matrices When undertaking the REML estimation ASReml needs to invert each variance matrix For this it requires that the matrices be negative definite or positive definite They must not be singular Negative definite matrices will have neg ative elements on the diagonal of the matrix and or its inverse The exception is the XFA model which has been specifically designed to fit singular matrices Thompson et al 2003 Let xv Ag represent an arbitrary quadratic form for x 1 n The quadratic form is said to be nonnegative definite if x Ax gt 0 for all x R If x Ax is nonnegative definite and in addition the null vector 0 is the only value of x for which x Ax 0 then the quadratic form is said to be positive definite Hence the matrix A is said to be positive definite if x Ax is positive definite see Harville 1997 pp 211 7 Command file Specifying the variance structures 119 7 2 Variance model specification in ASReml The variance models are specified in the AS NIN Alliance Trial 1989 Reml command file after the model line as variety A shown in the code box In this case just one variance model is specified for replicates see column 11 nin89 asd skip 1 r ield mu variety r repl tabu
375. ore AS Reml will use estimates in the rsv file for certain models to provide starting values for certain more general models in serting reasonable defaults where necessary The transitions recognised are listed and discussed in Section 7 10 5 Command file Reading the data 69 Table 5 3 List of commonly used job control qualifiers qualifier action DIAG to FA1 DIAG to CORUH uniform heterogeneous CORUH to FA1 and to XFA1 FAi to FAi 1 XFAi to XFAi 1 FAi to CORGH full heterogeneous FAi to US full heterogeneous CORGH heterogeneous to US CONTRAST s t p provides a convenient way to define contrasts among treat ASReml2 ment levels CONTRAST lines occur as separate lines between the datafile line and the model line s is the name of the model term being defined t is the name of an existing factor p is the list of contrast coefficients For example CONTRAST LinN Nitrogen 3 1 1 3 defines LinN as a contrast based on the 4 implied by the length of the list levels of factor Nitrogen Missing values in the factor become missing values in the contrast Zero values in the factor no level assigned become zeros in the contrast The user should check that the levels of the factor are in the order assumed by contrast check the ass or sln or tab files It may also be used on the implicit factor Trait in a multivariate analysis provided it implicitly identifies the number of levels of Trait the number of traits
376. otype has two factors and so the matrix G is comprised of two component matrices defining the variance structure for each factor in the term Models for the component matrices G include the standard model for which Gi ilq and direct product models for correlated random factors given by Gi Gi 8 Giz Gi for three component factors The vector w is therefore assumed to be the vector representation of a 3 way array For two factors the vector u is simply the vec of a matrix with rows and columns indexed by the component factors in the term where vec of a matrix is a function which stacks the columns of its matrix argument below each other A range of models are available for the components of both R and G They include correlation C models that is where the diagonals are 1 or covariance 2 Some theory 11 V models and are discussed in detail in Chapter 7 Some correlation models include e autoregressive order 1 or 2 e moving average order 1 or 2 e ARMA 1 1 e uniform e banded e general correlation Some of the covariance models include e diagonal that is independent with heterogeneous variances e antedependence e unstructured e factor analytic There is the facility within ASReml to allow for a nonzero covariance between the subvectors of u for example in random regression models In this setting the intercept and say the slope for each unit are assumed to be correlated and it is more natural
377. ous sections have introduced variance modelling in ASReml using the NIN data for demonstration In this and the remaining sections the syntax is described formally still using the example where appropriate Recall from Equation 2 2 on page 7 that the variance for the random effects in the linear mixed model was defined including an overall scale parameter 0 When this parameter is 1 0 R and G are defined in terms of variances Otherwise they are defined relative to this scale parameter Typically 0 is 1 if there are several residual variances as in the case of multivariate analysis a different residual variance for each trait or multienvironment trials a different residual variance for each trial However for simple analyses with a single residual variance 6 is modelled as the residual variance so that R becomes a correlation matrix 7 Command file Specifying the variance structures 127 General syntax Variance model specification in ASReml has the following general form variance header line R structure definition lines G structure header and definition lines variance parameter constraints e variance header line specifies the number of R and G structures e R structure definition lines define the R structures variance models for error as specified in the variance header line e G structure header and definition lines define the G structures variance models for the additional random terms in the model as specifi
378. ovided for specifying GLM attributes for it The ASUV qualifier is required in this situation for the GLM weights to be utilized 6 Command file Specifying the terms in the mixed model 112 Caution Generalized Linear Mixed Models This section was written by Damian Collins A Generalized Linear Mixed Model GLMM is an extension of a GLM to in clude random terms in the linear predictor Inference concerning GLMMs is impeded by the lack of a closed form expression for the likelihood ASReml cur rently uses an approximate likelihood technique called penalized quasi likelihood or PQL Breslow and Clayton 1993 which is based on a first order Taylor se ries approximation This technique is also known as Schalls technique Schall 1991 pseudo likelihood Wolfinger and OConnell 1993 and joint maximisa tion Harville and Mee 1984 Gilmour et al 1985 Implementations of PQL are found in many statistical packages for instance in the GLMM Welham 2005 and the IRREML procedures of Genstat Keen 1994 the MLwiN pack age Goldstein et al 1998 the GLMMIX macro in SAS Wolfinger 1994 and in the GLMMPQL function in R The PQL technique is well known to suffer from estimation biases for some types of GLMMs For grouped binary data with small group sizes estimation biases can be over 50 e g Breslow and Lin 1995 Goldstein and Rasbash 1996 Rodriguez and Goldman 2001 Waddington et al 1994 For other GLMMs PQL has bee
379. pace characters following on a line are ignored so this character may not be used in alphanumeric fields blank spaces tabs and commas must not be used embedded in alphanumeric fields unless the label is enclosed in quotes for example the name Willow Creek would need to be appear in the data file as Willow Creek to avoid error the symbol must not be used in the data file alphanumeric fields have a default size of 16 characters Use the LL qualifier to extend the size of factor labels stored extra data fields on a line are ignored if there are fewer data items on a line than ASReml expects the remainder are taken from the following line s except in csv files were they are taken as missing If you end up with half the number of records you expected this is probably the reason all lines beginning with followed by a blank are copied to the asr file as comments for the output their contents are ignored 4 Data file preparation 45 Fixed format data files The format must be supplied with the FORMAT qualifier which is described in Table 5 5 However if all fields are present and are separated the file can be read free format Preparing data files in Excel Many users find it convenient to prepare their data in Excel or Access How ever the data must be exported from these programs into either csv Comma separated values or txt TAB separated values form for ASReml to read it ASReml can conver
380. predicted values As in the asr file date time and trial information are given the title line The Ecode for each prediction column 4 is usually E indicating the prediction is of an estimable function Predictions of non estimable functions are usually not printed see Chapter 10 NIN alliance trial 1989 04 Apr 2008 17 00 47 nin89 Ecode is E for Estimable for Not Estimable Predicted values of yield The predictions are obtained by averaging across the hypertable calculated from model terms constructed solely from factors in the averaging and classify sets The ignored set repl Use AVERAGE to move table factors into the averaging set 3 A guided tour 41 predicted variety effects variety LANCER BRULE REDLAND CODY ARAPAHOE NE83404 NE83406 NE83407 CENTURA SCOUT66 COLT NE87613 NE87615 NE87619 NE87627 29 25 31 20 SED Overall Standard Error of 5625 0750 5000 2125 4375 3875 2750 6875 6500 5250 0000 4000 6875 2625 2250 Difference Predicted_Value Standard_Error 28 26 30 21 29 27 24 22 21 27 27 8557 8557 8557 8557 8557 8557 lt 8557 8557 8557 8557 8557 8557 8557 8557 8557 s979 Ecode wo gt A A a A A A A A A HHH Data file preparation Introduction The data file Free format Fixed format Preparing data files in Excel Binary format 42 4 Data file preparation 43 4 1 Introduction Th
381. process MYOWNGDG files Failed when sorting pedigree Failed when processing pedigree file Failed while ordering equations FORMAT error reading factor Definitions G structure header Factor order G structure ORDER O MODEL GAMMAS G structure size does not match Getting Pedigree GLM Bounds failure May be an unrecognised factor model term name or variance structure name or wrong count of initial values possible on an earlier line May be insufficient lines in the job Check your MYOWNGDG program and the gdg file Maybe increase WORKSPACE Messages may identify a problem with the pedigree This indicates the job needs more memory than was allocated or is available Try increas ing the workspace or simplifying the model Likely causes are bad syntax or invalid characters in the vari able labels variable labels must not include any of these symbols and the data file name is misspelt there are too many variables declared or there is no valid value supplied with an arithmetic transformation option there is a problem reading G structure header line An earlier error for example insufficient initial values may mean the actual line read is not actually a G header line at all A G header line must contain the name of a term in the linear model spelt exactly as it appears in the model a G structure line cannot be interpreted The size of the structure defined does not agre
382. quired to classify the alphabetic labels For example Sire I skip 1 would skip the field before the field which is read as Sire This qualifier is ignored when reading binary data 5 5 Transforming the data Revised 08 Transformation is the process of modifying the data for example dividing all of the data values in a field by 10 forming new variables for example summing the data in two fields or creating temporary data for example a test variable used to discard some records from analysis and subsequently discarded Occasional users may find it easier to use a spreadsheet to calculate derived variables than to modify variables using ASReml transformations Transformation qualifiers are listed after data field labels and the field_type if present They define an operation e g often involving an argument a constant or another variable which is performed on a target variable For a G group of variables the target is the first variable in the set The target is usually implicit the current field but can be changed to a new variable with the TARGET qualifier Using transformations will be easier if you understand the process As ASReml parses the variable definitions it sequentially assigns them column positions in the internal data array It notes which is the last variable which is not created by say the transformation and that determines how many fields are read from the data file unless overridden by
383. rameters respectively Gilmour et al 1997 recommend revision of the current spatial model based on the use of diagnostics such as the sample variogram of the residuals from the current model This diagnostic and a summary of row and column residual trends are produced by default with graphical versions of ASReml when a spatial model has been fitted to the errors It can be suppressed by the use of the n option on the command line We have produced the following plots by use of the g22 option Slate Hall example Rep 6 Six replicates of 5x5 plots in 2x3 arrangement RowBlk 30 Rows within replicates numbered across replicates ColBlk 30 Columns within replicates numbered across replicates row 10 Field row column 15 Field column variety 25 yield barley asd skip 1 DOPATH 1 PATH 1 AR1 x AR1 y mu var 12 15 column AR1 0 1 Second field is specified so ASReml can sort 10 row AR1 0 1 records properly into field order PATH 2 AR1 x AR1 units y mu var r units 12 15 column AR1 0 1 10 row AR1 0 1 PATH 3 incomplete blocks y mu var r Rep Rowblk Colblk PATH 0 predict variety TWOSTAGEWEIGHTS Table 16 6 Field layout of Slate Hall Farm experiment Column Replicate levels Row 1 2 3 4 5 6 T 8 9 10 11 12 13 14 15 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 2 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 5 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 6 4 4 4
384. re several ways L can be defined to construct a test for a particular model term two of which are available in ASReml These Wald F statistics are labelled F inc 2 Some theory 21 for incremental and F con for conditional respectively For balanced designs these Wald F statistics are numerically identical to the F statistics obtained from the standard analysis of variance The first method for computing Wald statistics for each term is the so called incremental form For this method Wald statistics are computed from an incremental sum of squares in the spirit of the approach used in classical regression analysis see Searle 1971 For example if we consider a very simple model with terms relating to the main effects of two qualitative factors A and B given symbolically by y 1 A B where the 1 represents the constant term u then the incremental sums of squares for this model can be written as the sequence R 1 R A 1 R 1 A R 1 R BI1 A R 1 A B R 1 A where the R operator denotes the reduction in the total sums of squares due to a model containing its argument and R denotes the difference between the reduction in the sums of squares for any pair of nested models Thus R B 1 A represents the difference between the reduction in sums of squares between the so called maximal model y 1 A B and y l A Implicit in these calculations is that e we only compute Wald statistics for estima
385. re of differing sizes number of effects For example for traits weaning weight and yearling weight an animal model with maternal weaning weight should specify model terms Trait animal at Trait 1 dam when fitting a genetic covariance between the direct and maternal effects The model can be split into submodels with SM i qualifiers 6 Command file Specifying the terms in the mixed model 101 6 5 ASReml2 Interactions and conditional factors Interactions 3 interactions are formed by joining two or more terms with a or a for example a b is the interaction of factors a and b interaction levels are arranged with the levels of the second factor nested within the levels of the first labels of factors including interactions are restricted to 31 characters of which only the first 20 are ever displayed Thus for interaction terms it is often necessary to shorten the names of the component factors in a systematic way for example if Time and Treatment are defined in this order the interaction between Time and Treatment could be specified in the model as Time Treat remember that the first match is taken so that if the label of each field begins with a different letter the first letter is sufficient to identify the term interactions can involve model functions Expansions is ignored makes sure the following term is defined but does notinclude it in the model indicates factorial expansi
386. re the progeny of 92 sires and 3561 dams produced from 4871 litters over 49 flock year combinations Not all traits were measured on each group No pedigree data was available for either sires or dams The aim of the analysis is to estimate heritability h of each trait and to estimate the genetic correlations between the five traits We will present two approaches a half sib analysis and an analysis based on the use of an animal model which 16 Examples 342 directly defines the genetic covariance between the progeny and sires and dams The data fields included factors defining sire dam and lamb tag covariates such as age the age of the lamb at a set time brr the birth rearing rank 1 born single raised single 2 born twin raised single 3 born twin raised twin and 4 other sex M F and grp a factor indicating the flock year combination Half sib analysis In the half sib analysis we include terms for the random effects of sires dams and litters In univariate analyses the variance component for sires is denoted by 2 s dams is denoted by o iaa 02 where o is the maternal variance component of to where o is the additive genetic variance the variance component for and the variance component for litters is denoted by o and represents variation attributable to the particular mating For a multivariate analysis these variance components for sires dams and litters are in theory replaced by unstructur
387. red with only one other variety 22 with two other varieties and the remaining 14 with three different varieties In the next three sections we present an exhaustive analysis of these data using 16 Examples 312 equivalent univariate and multivariate techniques It is convenient to use two data files one for each approach The univariate data file consists of factors pair run variety tmt unit and variate rootwt The factor unit labels the individual trays pair labels pairs of trays to which varieties are allocated and tmt is the two level bloodworm treatment factor control treated The multivariate data file consists of factors variety and run and variates for root weight of both the control and exposed treatments labelled yc and ye respectively Preliminary analyses indicated variance heterogeneity so that subsequent analyses were conducted on the square root scale Figure 16 8 presents a plot of the treated and the control root area on the square root scale for each variety There is a strong dependence between the treated and control root area which is not surprising The aim of the experiment was to determine the tolerance of varieties to bloodworms and thence identify the most tolerant varieties The definition of tolerance should allow for the fact that varieties differ in their inherent seedling vigour Figure 16 8 The original approach of the scientist was to regress the treated root area against the control root area and d
388. ropriate variance models for spatial data Cressie 1991 Gilmour et al 1997 demonstrate its usefulness for the identification of the sources of variation in the analysis of field experiments If the elements of the data vector and hence the residual vector are indexed by a vector of spatial coordinates s i 1 n then the ordinates of the sample variogram are given by 1 7 4 or Vas si amp ls j l n i435 The sample variogram reported by ASReml has two forms depending on whether the spatial coordinates represent a complete rectangular lattice as typical of a field trial or not In the lattice case the sample variogram is calculated from the triple lij1 lij2 vij where liji Si1 sj1 and lij2 si2 Sj2 are the displacements As there will be many vij with the same displacements ASReml calculates the means for each displacement pair 1 1 l 2 either ignoring the signs default or separately for same sign and opposite sign TWOWAY after grouping the larger displacements 9 10 11 14 15 20 The result is displayed as a perspective plot see page 238 of the one or two surfaces indexed by absolute displacement group In this case the two directions may be on different scales Otherwise ASReml forms a variogram based on polar coordinates It calculates the distance between points dij Vj ip and an angle 6 180 lt 4 lt 180 subtended by the line from 0 0 to l j1 lij2 with the x axis The angle
389. rot on the Normal scale as a weighted analysis to mimic analysis of the ungrouped data Using 56 of the 68 records ignoring Group 4 there are 1960 56 x 35 00 observations and so we use the IDF 1904 1960 56 qualifier to get the correct residual degrees of freedom for this analysis of the proportion with footrot The YSS 62 54249 qualifier adds 62 54249 67 4 45751 to the Total Sum of Squares so that it includes the extra variation associated with the extra degrees of freedom There were 67 56 x 1 196 cases of foot rot so the Total uncorrected Sum of Squares for a binary variable should be 67 However the weighted sum of squares for the pRot values is only 4 45751 for example the first record contributes 1 39 1 39 x39 instead of 1 0 4 45751 was discovered from the as1 file on the line 4 45751 SSPD before inserting the YSS qualifier The transformations in the code which follows convert Scald and Rot to missing for group 4 Lamb data from ARG thesis page 177 8 Year GRP 5 y99 V2 4 1M1 SEX SIRE I Total FS1 FS2 Scald V99 Rot V99 pRot Rot Total 1 1 1 101 3933 6 6 1 LAMB DAT skip 1 IDF 1904 YSS 62 54249 pRot TOTAL Total mu SEX GRP r SIRE predict SEX 0 1 GRP 1235 The pertinant results are Univariate analysis of pRot Summary of 56 records retained of 68 read Model term Size miss zero MinNonO Mean MaxNonO StndDevn 1 Year 0 O 1 000 1 536 2 000 0 5032 2 GRP 5 0 0 1 3 1429 5 3 SEX 0 28 1 000 0
390. rs 8 and 9 describe special commands for multivari ate and genetic analyses respectively Chapter 10 deals with prediction of linear functions of fixed and random effects in the linear mixed model and Chapter 13 presents the syntax for forming functions of variance components Chapter 11 demonstrates running an ASReml job features available and Chapter 14 gives a detailed explanation of the output files Chapter 15 gives an overview of the error messages generated in ASReml and some guidance as to their probable cause The guide concludes with the most extensive chapter which presents the examples Briefly the improvements in Release 2 include more robust variance parameter updating so that Convergence Failure is less likely extensions to the syntax inclusion of the Mat rn correlation model ability to plot predicted values im provements for testing fixed effects improvements to the handling of pedigrees and some increases in computational speed Release 3 contains some extensions to data handling merging files pedigree pro cessing model specification theshold models prediction and examining residuals The data sets and ASReml input files used in this guide are available from Preface http www vsni co uk products asreml as well as in the examples direc tory of the distribution CD ROM They remain the property of the authors or of the original source but may be freely distributed provided the source is acknowl edged Th
391. rthur gilmour dpi nsw gov au JES OCGA O HS SCKG ooo oook aK ARG k Folder C data asr3 ug3 manex variety A QUALIFIERS SKIP 1 DISPL QUALIFIER DOPART 1 is active Reading nin89aug asd FREE FORMAT skipping Univariate analysis of yield AY 15 Summary of 242 records retained of 242 read Model term Size miss zero 1 variety 56 0 0 2 ad 0 0 3 pid 18 0 4 raw 18 0 5 repl 4 0 0 6 nloc 0 7 yield Variate 18 0 8 lat 0 0 9 long 0 0 10 row 22 0 0 11 column 11 0 0 12 mu 1 13 mv_estimates 18 22 AR AutoReg 5 5 0 5000 11 AR AutoReg 6 6 0 5000 MinNonOoO 1 1 000 1101 21 00 1 4 000 1 050 4 300 1 200 1 1 1 lines Mean 26 4545 26 45 2628 510 5 2 4132 4 000 25 53 25 80 13 80 11 5000 6 0000 MaxNonO StndDevn 56 56 00 4156 840 0 4 4 000 42 00 47 30 26 40 22 it 17318 1121 149 0 0 000 7 450 13 63 T 629 14 Description of output files 225 Forming 75 equations 57 dense Initial updates will be shrunk by factor 0 316 Notice 1 singularities detected in design matrix iterations 1 LogL 401 827 S2 42 467 168 df 1 000 0 5000 0 5000 2 LogL 400 780 S2 43 301 168 df 1 000 0 5388 0 4876 3 LogL 399 807 S2 45 066 168 df 1 000 0 5895 0 4698 4 LogL 399 353 S2 47 745 168 df 1 000 0 6395 0 4489 5 LogL 399 326 S2 48 466 168 df 1 000 0 6514 0 4409 6 LogL 399 324 S2 48 649 168 df 1 000 0 6544 0 4384 7 LogL 399 324 S2 48 696 168 df 1 000 0 6552 0 4377 8 LogL 399 324
392. rts incremental Wald F statistics F inc for the fixed model terms in the DENSE partition conditional on the order the terms were nominated in the model Note that probability values are only avail able when the denominator degrees of freedom is calculated and this must be explicitly requested with the DDF qualifier in larger jobs Users should study Section 2 6 to understand the contents of this table The conditional max imum model used as the basis for the conditional F statistic is spelt out in the aov file described in section 14 4 The numerator degrees of freedom NumDF for each term is easily determined as the number of non singular equations involved in the term However in general calculation of the denominator degrees of freedom DDF is not trivial ASReml will by default attempt the calculation for small analyses by one of two methods In larger analyses users can request the calculation be attempted using the DDF qualifier page 69 Use DDF 1 to prevent the calculation to save processing time when significance testing is not required T Command file Specifying the variance structures Introduction Non singular variance matrices Variance model specification in ASReml A sequence of structures for the NIN data Variance structures General syntax Variance header line R structure definition G structure header and definition lines Variance model description Forming the variance models from correlat
393. rty female rats dams were randomly split into three groups of 10 and each group randomly assigned to the three different doses All pups in each litter were weighed The litters differed in total size and in the numbers of males and females Thus the additional covariate littersize was included in the analysis The differential effect of the compound on male and female pups was also of interest Three litters had to be dropped from experiment which meant that one dose had only 7 dams The analysis must account for the presence of between dam variation but must also recognise the stratification of the experimental units pups within litters and that doses and littersize belong to the dam stratum Table 16 2 presents an indicative AOV decomposition for this experiment Table 16 2 Rat data AOV decomposition stratum decomposition type df or ne constant 1 F 1 dams dose F 2 littersize F 1 dam R 27 dams pups sex F 1 dose sex F 2 error R The dose and littersize effects are tested against the residual dam variation while the remaining effects are tested against the residual within litter variation The ASReml input to achieve this analysis is presented below Rats example dose 3 A sex 2 A littersize dam 27 pup 18 weight 16 Examples 285 rats asd DOPATH 1 Change DOPATH argument to select each PATH PATH 1 weight mu littersize dose sex dose sex r dam PATH 2 weight mu out 66 littersize dose sex dose s
394. run at all it is a setup or licensing issue which is not discussed in this chapter Coding errors can be classified as typing errors these are difficult to resolve because we tend to read what we in tended to type rather than what we actually typed Section 15 4 demonstrates the consequences of the common typographical errors that users make wrong coding this arises often from misunderstanding the guide or making assumptions arising from past experience which are not valid for ASReml The best strategy here is to closely follow a worked example or to build up to the required model Sections 15 3 and 15 2 may help as well as reviewing all the relevant sections of this Guide It may be as simple as adding one more qualifier inappropriate model the variance model you propose may not be suited to the data in which case ASReml may fail to produce a solution You can verify the model is appropriate by closer examination of the structure of the data and by fitting simpler models software problems There are many options in ASReml and some combinations have not been tested Some jobs are too big When all else fails send for support to support vsni cu uk There are over 6000 one line diagnostic messages that ASReml may print in the asr file Hopefully most are self explanatory but it will always be helpful to recognise whether they relate to parsing the input file or raise some other issue See Section 15 5 for more information
395. s SORT declared after A or I on a field definition line will cause ASReml to sort the levels so that labels occur in alphabetic numeric order for the analysis As ASReml reads the data file it encodes I and A factor levels in the order they appear in the data so that for example the user cannot tell whether SEX will be coded 1 Male 2 Female or 1 Female 2 Male without looking at the data file to see whether Male or Female appears first in the SEX field If SORT is specified ASReml creates a lookup table after reading the data to select levels in sorted order and uses this sorted order when forming the design matrices Conse quentially with the SORT qualifier the order of fitted effects will be 1 Female 2 Male in the analysis regardless of which appears first in the file However most other references to particular levels of factors will refer to the unsorted lev 5 Command file Reading the data 52 Caution ASReml2 Warning els so users should verify that ASReml has made the correct interpretation when nominating specific levels of SORTed factors In particular any transformations are performed as the data is read in and before the sorting occurs SORTALL means that the levels of this and subsequent factors are to be sorted Skipping input fields ISKIP f will skip f data fields BEFORE reading this field It is particularly useful in large files with alphabetic fields which are not needed as it saves ASReml the time re
396. s The response may also be a series of t binary where Y Ei Yj variables or a series of t variables containing counts If t counts ui E Y are supplied the total including the kth category must be given and pi Hi Hi 1 in another variable indicated by the TOTAL qualifier ASReml3 6 Command file Specifying the terms in the mixed model 110 Table 6 4 GLM distribution qualifiers qualifier action The multinomial threshold model is fitted as a cumulative prob ability model The proportions y ri n in the ordered cate gories are summed to form the cumulative proportions Y which are modelled with logit LOGIT probit PROBIT or Complemen tary LogLog CLOG link functions The implicit residual variance on the underlying scale is 1 3 3 3 underlying logistic distri bution for the logit link 1 for the probit link The distribution underlying the Complementary LogLog link is the Gumbel distri bution with implicit residual variance on the underlying svale of n 6 1 65 For example Lodging MULTINOMIAL 4 CUMULATIVE Trait Variety r block predict Variety where Lodging is a factor with 4 ordered categories Predicted values are reported for the cumulative proportions POISSON LOGARITHM IDENTITY SQRT v Natural logarithms are the default link function d 2 yln y u ASReml assumes the Poisson variable is not negative y IGAMMA INVERSE IDENTITY LOGARITHM PHI
397. s a large set of marker variables in conjunction with CYCLE processing will be much faster if the markers variables are in separate files ASReml will read 10 files containing a single field much faster than reading a single file containing 400 fields ten times to extract 10 different markers When missing values occur in the design ASReml will report this fact and abort the job unless MVINCLUDE is specified see Section 6 9 then missing values are treated as zeros Use the DV transformation to drop the records with the missing values instructs ASReml to discard records which have missing values in the design matrix see Section 6 9 suppresses the graphic display of the variogram and residuals which is otherwise produced for spatial analyses in the PC and SUN versions This option is usually set on the command line using the option letter N see Section 11 3 on graphics The text version of the graphics is still written to the res file is a mechanism for specifying the particular points to be predicted for covariates modelled using fac v leg v k spl v k and pol v k The points are specified here so that they can be included in the appropriate design matrices v is the name of a data field p is the list of values at which prediction is required See GKRIGE for special conditions per taining to fac x y prediction is used to read predict_points for several variables from a file f vlist is the names of the variables hav
398. s a variable it can be plot coordinates provided the plots are in a regular grid Thus in this example 7 Command file Specifying the variance structures 130 11 lat AR1 0 3 22 long AR1 0 3 is valid because lat gives column position and long gives row position and the positions are on a regular grid The autoregressive correlation values will still be on an plot index basis 1 2 3 not on a distance basis 10m 20m 30m if the data is sorted appropriately for the order the models are specified set field to 0 model specifies the variance model for the term for example 22 row AR1 0 3 chooses a first order autoregressive model for the row error process all the variance models available in ASReml are listed in Table 7 3 these models have associated variance parameters a error variance component g2 for the example see Section 7 3 is auto matically estimated for each section the default model is ID initial_values are initial or starting values for the variance parameters and must be supplied for example 22 row ARI 0 3 chooses an autoregressive model for the row error process see Table 7 1 with a starting value of 0 3 for the row correlation qualifiers tell ASReml to modify the variance model in some way the qualifiers are described in Table 7 4 additional_initial_values are read from the following lines if there are not enough initial values on the model line Each variance mode
399. s are not reasonably close to the REML solution ASReml has several internal strategies to cope with this problem but these are not always successful When the user needs to provide better starting values one method is to fit a simpler variance model For example it can be difficult to guess reasonable starting values for an unstructured variance matrix A first step might be to assume independence and just estimate the variances If all the variances are not positive there is little point proceeding to try and estimate the covariances The CONTINUE qualifier instructs ASReml to retrieve variance parameters from the rsv file if it exists rather than using the values in the as file When reading the rsv file if the variance structure for a term has changed it will take results from some structures as supplying starting values for other structures The transitions recognised are DIAG to CORUH DIAG to FA1 CORUH to FA1 and XFA1 FAz to FAt 1 XFA7z to XFAi 1 FAz to CORGH FAz to US CORGH to US The use of the rsv file with CONTINUE in this way reduces the need for the user to type in the updated starting values The various models may be written in various PART s of the job and controlled by the DOPART qualifier When used with the r qualifier on the command line see Chapter 11 the output from the various parts has the partnumber appended to the filename If an rsv file does not exist for the particular PART you are running
400. s for variate j j c for control and j t for treated 7 corresponds to a constant term and Uv and Ur correspond to random variety and run effects The design ma trices are the same for both traits The random effects and error are assumed to be independent Gaussian variables with zero means and variance structures var Uy oy Is var ur 0 Ies and var e o T132 The bivariate model can be written as a direct extension of 16 9 namely y Io X T 28 Zy uy I2 8 Zr up e 16 10 where y yL yj Uy ul ul ur ul ul and e el e There is an equivalence between the effects in this bivariate model and the uni variate model of 16 7 The variety effects for each trait uw in the bivariate model are partitioned in 16 7 into variety main effects and tmt variety in teractions so that u 12 u1 ug There is a similar partitioning for the run effects and the errors see table 16 9 16 Examples 318 In addition to the assumptions in the models for individual traits 16 9 the bi variate analysis involves the assumptions cov Uy Up Ova L44 COV Ur Uh Tt Ora I66 and cov ec e o J132 Thus random effects and errors are correlated between traits So for example the variance matrix for the variety effects for each trait is given by var ty oy Over Q Taq Ovet Ut This unstructured form for trait variety in the bivariate analysis is equiv alent to the variety main
401. s in the term the numerator degrees of freedom the Wald F statistic an adjusted Wald F statistic scaled by a constant reported in the next column and finally the computed denominator degrees of freedom The scaling constant is discussed by Kenward and Roger 1997 Table showing the reduction in the numerator degrees of freedom for each term as higher terms are absorbed Model Term 1 mu 2 variety LinNitr nitrogen variety LinNitr variety nitrogen oo Ww T 1 6 2 1 gt e OD CO O 5 NN WW WwW ONWWwo ABB 3 1 1 1 aa o 4 2 Marginality pattern for F con calculation Model Term DF 1 mu 2 variety 2 3 LinNitr 1 4 nitrogen 2 5 variety LinNitr 2 6 variety nitrogen Model codes 4 Model terms 1 HHHH I b 2 3 4 5 6 HHH i A at et Ht Cd I a L A F inc tests the additional variation is added to a model consisting F con tests the additional variation is added to a model consisting The terms are ignored for both F inc and F con tests Incremental F statistics calculation Source mu variety LinNitr nitrogen variety LinNitr variety nitrogen Size NumDF 1 1 3 2 1 1 4 2 3 2 12 4 C I b B explained when the term of the I terms explained when the term of the I and C c terms F value 245 ts 110 1 1409 4853 3232 3669 0 4753 2166 of Denominator degrees of freedom DenDF Lambda F 245
402. s of the vector of fixed and ran dom effects REML log likelihood residuals and inverse coef ficient matrix For arguments 4 10 19 ASReml forms the mixed model equa tions and solves them iteratively to obtain solutions for the fixed and random effects The options are n 4 forming the estimates of the vector of fixed and random effects using the Preconditioned Conjugate Gradi ent PCG Method Mrode 2005 n 10 19 forming the estimates of the vector of fixed and random effects by Gauss Seidel iteration of the mixed model equations with relaxation factor n 10 The default maximum number of iterations is 12000 This can be reset by supplying a value greater than 100 with the MAXIT qualifier in conjunction with the BLUP qualifier Iter ation stops when the average squared update divided by the average squared effect is less than le Gauss Seidel iteration is generally much slower than the PCG method 5 Command file Reading the data 81 Table 5 5 List of rarely used job control qualifiers qualifier action IDENSE n IDF n ASReml prints its standard reports as if it had completed the iteration normally but since it has not completed it some of the information printed will be incorrect In particular vari ance information on the variance parameters will always be unavailable Standard errors on the estimates will be wrong unless n 3 Residuals are not available if n 1 Use of n 3 or n 2 will halve
403. s preferred 16 9 Balanced longitudinal data Random coefficients and cubic smoothing splines Oranges We now illustrate the use of random coefficients and cubic smoothing splines for the analysis of balanced longitudinal data The implementation of cubic smoothing splines in ASReml was originally based on the mixed model formulation presented by Verbyla et al 1999 More recently the technology has been enhanced so that the user can specify knot points in the original approach the knot points were taken to be the ordered set of unique values of the explanatory variable The specification of knot points is particularly useful if the number of unique values in the explanatory variable is large or if units are measured at different times The data we use was originally reported by Draper and Smith 1998 ex24N p559 and has recently been reanalysed by Pinheiro and Bates 2000 p338 The data are displayed in Figure 16 12 and are the trunk circumferences in millimetres of each of 5 trees taken at 7 times All trees were measured at the same time so that the data are balanced The aim of the study is unclear though both previous analyses involved modelling the overall growth curve accounting for the obvious variation in both level and shape between trees Pinheiro and Bates 2000 used a nonlinear mixed effects modelling approach in which they modelled the growth curves by a three parameter logistic function of age given by _ 1
404. s seconds 0 to 59 The separator must be present e transformations are described below Storage of alphabetic factor labels Space is allocated dynamically for the storage of alphabetic factor labels with a default allocation being 2000 labels of 16 characters long If there are large A factors so that the total across all factors will exceed 2000 you must specify the anticipated size within say 5 If some labels are longer then 16 characters and the extra characters are significant you must lengthen the space for each label by specifying LL c e g cross A 2300 LL 48 indicates the factor cross has about 2300 levels and needs 48 characters to hold the level names only the first 20 characters of the names are ever printed PRUNE on a field definition line means that if fewer levels are actually present in the factor than were declared ASReml will reduce the factor size to the ac tual number of levels Use PRUNALL for this action to be taken on the current and subsequent factors up to but not including a factor with the PRUNEOFF qualifier The user may overestimate the size for large ALPHA and INTEGER coded factors so that ASReml reserves enough space for the list Using PRUNE will mean the extra undefined levels will not appear in the sln file Since it is sometimes necessary that factors not be pruned in this way for example in pedigree GIV factors pruning is only done if requested Reordering the factor level
405. s that sometimes the LogL rises to a relatively high value and then drifts away In an attempt to make the process easier these two processes have been linked as an additional meaning for the AILOADING n qualifier When fitting k factors with N gt k the first k 1 loadings are held fixed no rotation for the first k iterations Then for iterations k 1 to n loadings vectors are updated in pairs and rotated If AILOADING is not set by the user and the model is an upgrade from a lower order XFA AILOADING is set to 4 7 Command file Specifying the variance structures 144 difficult It is not unusual for users to have trouble comprehending and fitting extended factor analytic models especially with more than two factors Two examples are developed in a separate document available on request Notes on OWN models The OWN variance structure is a facility whereby users may specify their own variance structure This facility requires the user to supply a program MYOWNGDG that reads the current set of parameters forms the G matrix and a full set of derivative matrices and writes these to disk Before each iteration ASReml writes the OWN parameters to a file runs MYOWNGDG which it presumes forms the G and derivative matrix and then reads the matrices back in An example of MYOWNGDG 90 is distributed with ASReml It duplicates the AR1 and AR2 structures The following job fits an AR2 structure using this program Example of
406. s traits 7 66 5 83 13 18 66 10 TS 21 27 3 2 73 2 02 08 20 1 44 Ir tag 2 Direct animal effects PATH 2 Tr O FA1 GP 0 5 0 5 01 01 0 1 2 4 5 2 0 06 8 14 IPATH 3 Tr 0 US 2 4800 2 8 6 4 0 0128 0 03 0 06 1 22 0011 0 72 0 24 0 55 0 0026 0 0202 0 14 PATH tag 0 AINV at Tr 1 dam 2 IPATH 2 2 0 CORGH GFU 99 1 6 2 54 IPATH 3 2 0 US GU 1 1 156 31 PATH dam O AINV Maternal effects ae Tr 4 lit 2 PATH 2 4 0 FA1 Litter effects 1GP Factor Analytic 16 Examples 353 5 2 6 01 1 4 95 4 63 0 037 0 941 PATH 3 40 US Unstructured 5 073 3 545 3 914 0 1274 0 08909 0 02865 0 07277 0 05090 0 001829 1 019 PATH Lit The term Tr tag now replaces the Tr sire and picks up part of Tr dam variation present in the half sib analysis This analysis uses information from both sires and dams to estimate additive genetic variance The dam variance component is this analysis estimates the maternal variance component It is only significant for the weaning and yearling weights The litter variation remains unchanged Notice again how the maternal effect is only fitted for the first 2 traits and the litter effect for the first 4 traits The critical details are that for example with respect to dam effects the model terms that specify dam effects for particular traits at Tr 1 dam at Tr 2 dam appear together in the linear model and a variance structure is de
407. se are printed in column 3 Furthermore for multivariate analyses the residuals will be in data order traits within records However in a univariate analysis with missing values that are not fitted there will be fewer residuals than data records there will be no residual where the data was missing so this can make it difficult to line up the values unless you can manipulate them in another program spread sheet score asl file given if the DL command line option is used tables of means tab file simple averages of cross classified data are pro pvs file duced by the tabulate directive to the tab file Adjusted means predicted from the fitted model are written to the pvs file by the predict direc tive variance of variance vvp file based on the inverse of the average information parameters matrix variance parameters asr file the values at each iteration are printed in the res file res file The final values are arranged in a table printed with labels and converted if necessary to variances variogram graphics file 15 Error messages Introduction Common problems Things to check in the asr file An example Error messages Warning messages 246 15 Error messages 247 15 1 Introduction Identifying the reason ASReml does not run or does not produce the anticipated results can be a frustrating business This chapter aims to assist you by discussing four kinds of errors If ASReml does not
408. se associate factor trial within the associ ated classify factor location By contrast by specifying predict location or equivalently predict location AVERAGE region AVERAGE trial ASReml would add the average of all the trial effects and the average of the region effects into all of the location means which is not appropriate With ASSOCIATE it knows which trials to average and which region effects include to form each location mean That is ASReml knows how to construct the trial means including the appropriate region and location effects and which trials means to then average to form the location table However for region means we have a choice We can average the trial means in Table 10 4 according to region obtaining region means of 11 83 and 11 33 or we can average the location means in Table 10 5 to get region means of 12 and 11 The former is the default in ASReml produced by predict region ASSOCIATE region location trial ASAVERAGE trial or equivalently by predict region ASSOCIATE region location trial Again this is base averaging By contrast predict region ASSOC region location trial ASAVE location trial or predict region ASSOC region location trial ASAVE location produces sequential averaging giving region means of 12 and 11 respectively Similarly an overall sequential mean of 11 5 is given by 10 Tabulation of the data and prediction from the model 190 predict mu ASSOC region location
409. should also be considered This statistic is not reliable in ge netic animal models or when units is included in the linear model because then the predicted value includes some of the residual for an interaction fitted as random effects when the first outer dimension is smaller than the in ner dimension less 10 ASReml prints an observed variance matrix calculated from the BLUPs The observed correlations are printed in the upper tri angle Since this matrix is not well scaled as an es timate of the underlying variance component ma trix a rescaled version is also printed scaled ac cording to the fitted variance parameters The primary purpose for this output is to provide rea sonable starting values for fitting more complex variance structure The correlations may also be of interest After a multivariate analysis a sim ilar matrix is also provided calculated from the residuals placed in the pvc file when postprocessing with a pin file these are residuals that are more than 3 5 stan dard deviations in magnitude these in the are printed in the second column given if a predict statement is supplied in the as file the REML log likelihood is given for each iteration The REML log likelihood should have converged 14 Description of output files 245 Table 14 2 Table of output objects and where to find them ASReml output object found in comment residuals yht file and in binary form in dpr file the
410. si MatCor 2 1 Mater 86 SQR Mater 85 Mater MatCor 3 1 Mater 88 SQR Mater 85 Mater MatCor 3 2 Mater 89 SQR Mater 87 Mater defines 61 64 defines 65 69 defines 70 84 defines 85 90 0 1507 0 2581 0 3084 0 1350 0 0841 26 0 7044 29 0 2966 29 0 0136 33 0 2028 33 0 1227 33 0 1115 38 0 2703 38 0 5726 38 0 0048 38 0 6333 87 1 5168 90 1 5285 90 3 1251 NE OO COO 0 0 CO OO COO 2 oO Co OC OS 0396 0624 lt OT16 OTAT 0402 1025 iT20 1810 3513 3247 3868 2724 2022 2653 ool ho Viol 1561 7985 16 Examples 351 Animal model In this section we will illustrate the use of a pedigree file to define the genetic relationships between animals This is an alternate method of estimating additive genetic variance for these data The data file has been modified by adding 10000 to the dam ID now 10001 13561 so that the lamb sire and dam ID s are distinct They appear as the first 3 fields of the data file pcoop fmt and no historical genetic relationships are available for this data so the data files doubles as the pedigree file The multi trait additive genetic variance matrix 44 of the animals sires dams and lambs is given by var ua 54 8 A where A is the inverse of the genetic relationship matrix and u4 are the trait BLUPs ordered animals within traits There are a total of 10696 92 3561 7043 animals in the pedigree Multivariate analysis in
411. sidual POW EXP 5 436 380 Residual POW EXP 5 382 369 Covariance Variance Correlation Matrix POWER 61 11 0 8227 0 6769 0 5569 0 4156 54 88 72 80 0 8227 0 6769 0 5051 93 12 123 5 309 7 0 8227 0 6140 91 02 120 7 202 7 437 1 0 7462 63 57 84 34 211 4 305 3 382 9 Wald F statistics Source of Variation DF 8 Trait 5 1 tmt i 9 Tr tmt 4 72 9904 309 259 436 380 382 369 F_inc 127 95 0 00 4 75 1 99 222 2 52 2 74 OU OU OU OU The last two models we fit are the antedependence model of order 1 and the unstructured model These require as starting values the lower triangle of the full variance matrix We use the REML estimate of X from the heterogeneous power model shown in the previous output The antedependence model models X by the inverse cholesky decomposition 5 UDU where D is a diagonal matrix and U is a unit upper triangular matrix For an antedependence model of order q then u 0 for j gt i q 1 antedependence model of order 1 has 9 parameters for these data 5 in D and 4 in U The input is given by yl y3 y5 y7 y10 Trait tmt Tr tmt i120 14 2 Tr O ANTE 60 16 54 65 12 55 91 50 123 3 306 4 89 17 120 2 298 6 431 8 62 22 83 85 208 3 301 2 The abbreviated output file is 1 LogL 171 501 S2 1 0000 60 df 2 LogL 170 097 S2 1 0000 60 df 3 LogL 166 085 S2 1 0000 60 df 4 LogL 161 335 S2 1 0000 60 df 319 8 The 16 Examples 296 5 LogL 160 407 2 1 0000 6 LogL 160 370 2 1
412. sing a spreadsheet or data base program e Export that data as an ASCII file for example export it as a csv comma separated values file from Excel e Prepare a job file with filename extension as e Run the job file with ASReml Review the various output files revise the job and re run it or extract pertinent results for your report So you need an ASCII editor to prepare input files and review and print output files We directly provide two options ASReml W The ASReml W interface is a graphical tool allowing the user to edit programs run and then view the output before saving results It is available on the following platforms e Windows 32 bit and 64 bit e Linux 32 bit and 64 bit various incantations e Sun Solaris 32 bit ASReml W has a built in help system explaining its use ConTEXT ConTEXT is a third party freeware text editor with programming extensions which make it a suitable environment for running ASReml under Windows The ConTEXT directory on the CD ROM includes installation files and instructions for configuring it for use in ASReml Full details of ConTEXT are available from http www context cx 1 Introduction 4 1 4 How to use this guide Theory Getting started Examples Data file Linear model Variance model Prediction Output The guide consists of 16 chapters Chapter 1 introduces ASReml and describes the conventions used in the guide Chapter 2 outlines some
413. slides is presented in parallel If it were presented in series with a factor slide indexing the slides the equivalent model would be signal slide slide background xfa f k Factor analytic models are discussed in Chapter 7 There are three forms FAk FACVK and XFAk where k is the number of factors The XFAk form is a sparse formulation that requires an extra k levels to be inserted into the mixed model equations for the k factors This is achieved by the xfa f k model function which defines a design matrix based on the design matrix for f augmented with k columns of zeros for the k factors 6 Command file Specifying the terms in the mixed model 108 6 7 Weights caution Weighted analyses are achieved by using WT weight as a qualifier to the response variable An example of this is y WIT wt mu A X where y is the name of the response variable and wt is the name of a variate in the data containing weights If these are relative weights to be scaled by the units variance then this is all that is required If they are absolute weights that is the reciprocal of known variances use the S2 1 qualifier described in Table 7 4 to fix the unit variance When a structure is present in the residuals the weights are applied as a matrix product If X is the structure and W is the diagonal matrix constructed from the square root of the values of the variate weight then Rt WD W Negative weights are treated as zeros 6 8 General
414. statements are permitted either immediately before or after the linear model If a linear mixed model is not supplied tabulation is based on all records The tabulate statement has the form tabulate response_variables WT weight COUNT DECIMALS d SD RANGE STATS FILTER filter SELECT value factors e tabulate is the directive name and must begin in column 1 e response_variables is a list of variates for which means are required e WI weight nominates a variable containing weights e COUNT requests counts as well as means to be reported e DECIMALS d 1 lt d lt 7 requests means be reported with d decimal places If omitted ASReml reports 5 significant digits if specified without an argument 10 Tabulation of the data and prediction from the model 177 ASReml2 2 decimal places are reported e RANGE requests the minimum and maximum of each cell be reported e SD requests the standard deviation within each cell be reported e STATS is shorthand for COUNT SD RANGE e FILTER filter nominates a factor for selecting a portion of the data e SELECT value indicates that only records with value in the filter column are to be included e factors identifies the factors to be used for classifying the data Only factors not covariates may be nominated and no more than six may be nominated ASReml prints the multiway table of means omitting empty cells to a file with extension tab 10 3 Prediction Re
415. sumed to be indepen dent Gaussian variables with zero means and variance structures var u o Ty where b is the length of w i 1 5 and var e o In The ASReml code for this analysis is Bloodworm data Dr M Stevens pair 132 rootwt run 66 tmt 2 A id variety 44 A rice asd skip 1 DOPATH 1 IPATH 1 sqrt rootwt mu tmt r variety variety tmt run pair run tmt 000 PATH 2 sqrt rootwt mu tmt r variety tmt variety run pair tmt run uni tmt 2 002 tmt variety 2 2 0 DIAG 1 1 GU 4400 tmt run 2 20 DIAG 1 1 IGU 650 0 The two paths in the input file define the two univariate analyses we will conduct We consider the results from the analysis defined in PATH 1 first A portion of the output file is 5 LogL 345 306 52 1 3216 262 df 6 LogL 345 267 S2 1 3155 262 df 7 LogL 345 264 S52 1 3149 262 df 8 LogL 345 263 S52 1 3149 262 df Source Model terms Gamma Component Comp SE C variety 44 44 1 80947 2 37920 3 01 OP run 66 66 0 244243 0 321144 0 59 OP variety tmt 88 88 0 374220 0 492047 1 18 OP pair 132 132 0 742328 0 976057 2 01 OP run tmt 132 132 1 32973 1 74841 3 65 OP Variance 264 262 1 00000 1 31486 4 42 O P 16 Examples 315 Table 16 8 Estimated variance components from univariate analyses of bloodworm data a Model with homogeneous variance for all terms and b Model with het erogeneous variance for interactions involving tmt a b source control treated variety 2
416. t r forms natural logarithm of v r constructs MA1 design matrix for factor f forms an MA1 design matrix from plot numbers J sy ae Si Sy TR Z J 6 Command file Specifying the terms in the mixed model Table 6 1 Summary of reserved words operators and functions model term brief description common usage fixed random mbf uv 7 is a factor derived from data factor v by using the MBF qualifier J out n condition on observation n out n t condition on record n trait t Re TOR SY pol v n forms n 1 orthogonal polynomials of order 0 intercept 1 linear from the values in v the intercept polynomial is omitted if n is pre ceded by the negative sign pow z p o defines the covariable x 0 for y use in the model where is a vari able in the data p is a power and o is an offset qtl f p impute a covariable from marker y map information at position p sin v r forms sine from v with period r J sqrt v 7r forms square root of v r vA uni f forms a factor with a level for each J record where factor f is non zero uni f n forms a factor with a level for each J record where factor f has level n vect v is used in a multivariate analysis on y JV ASReml3 a multivariate set of covariates v to pair them with the variates xfa f k is formally a copy of factor f with k JV extra levels This is used when fit ting extended factor analytic mod els XFA Table
417. t an x1s file to a csv file When ASReml is invoked with an xls file as the filename argument and there is no csv file or as with the same basename it exports the first sheet as a csv file and then generates a template as command file from any column headings it finds see page 196 It will also convert a Genstat gsh spreadsheet file to csv format The data extracted from the x1s file are labels numerical values and the results from formulae Empty rows at the start and end of a block are trimmed but empty rows in the middle of a block are kept Empty columns are ignored A single row of labels as the first non empty row in the block will be taken as column names Empty cells in this row will have default names C1 C2 etc assigned Missing values are commonly represented in ASReml data files by NA or ASReml will also recognise empty fields as missing values in csv x1s files Binary format data files Conventions for binary files are as follows e binary files are read as unformatted Fortran binary in single precision if the filename has a bin or BIN extension Fortran binary data files are read in double precision if the filename has a db1 or DBL extension e ASReml recognises the value 1e37 as a missing value in binary files Fortran binary in the above means all real bin or all double precision db1 variables mixed types that is integer and alphabetic binary representation of variables is not allowed in bi
418. t are BLUPs Combining variance models Inference Random effects Tests of hypotheses variance parameters Diagnostics Inference Fixed effects Introduction Incremental and Conditional Wald Statistics Kenward and Roger Adjustments Approximate stratum variances 2 Some theory 7 2 1 The linear mixed model Introduction If y denotes the n x 1 vector of observations the linear mixed model can be written as y XT Zut e 2 1 where T is the p x 1 vector of fixed effects X is an n x p design matrix of full column rank which associates observations with the appropriate combination of fixed effects u is the q x 1 vector of random effects Z is the n x q design matrix which associates observations with the appropriate combination of random effects and e is the n x 1 vector of residual errors The model 2 1 is called a linear mixed model or linear mixed effects model It is assumed elorol o rol 22 where the matrices G and R are functions of parameters y and respectively The parameter 0 is a variance parameter which we will refer to as the scale parameter In mixed effects models with more than one residual variance arising for example in the analysis of data with more than one section see below or variate the parameter is fixed to one In mixed effects models with a single residual variance then is equal to the residual variance o In this case R must be a correlation matrix see Table 2 1 for a discussion
419. t field i default 0 0 is the increment applied to the transformation argument The default for n is the number of variables in the current field definition ENDDO is formally equivalent to DO 1 and is implicit when another DO appears or the next field definition be gins Note that when several transformations are repeated the processing order is that each is performed n times before the next is processed contrary to the implication of the syntax However the target is reset for each transformation so that the transformations apply to the same set of variables 5 Command file Reading the data 61 Y1 Y2 Y3 Y4 Y5 Repeat 5 times incrementing just Ymean 0 DO 5 0 1 Y1 ENDDO 5 the argument is equivalent to YL Y2 Y3 YA YS Ymean 0 Y1 Y2 Y3 Y4 Y5 5 YO Yi Y2 Y3 Y4 Y5 TARGET Y1 do 5 1 O YO ENDDO Take YO from rest Markers G 12 do D ENDDO Delete records with missing marker values The default arguments 12 1 0 are used The initial target is the first marker Other rules and examples Other rules include the following e variables that are created should be listed after all variables that are read in Revised 08 unless the intention is to overwrite an input field missing values are unaffected by arithmetic operations that is missing values in the current or target column remain missing after the transformation has been performed except in assignment 3 will leave missing values NA and as
420. t of Residuals 24 8730 15 9145 vs Fitted values 16 7724 35 9355 RvE ss sii inti ie i ie i 4 1 1 i 1 12 2 1211 121 1 1 t 1 112 15 1 311 121 1 1 i 312 111221 3 1 i i amp 4 122121 4112 14 2 2 1 1 11 2112 23 11 2 2 i 12 A 21 2 1213 1 49 Z 14 SAADAA a a a ges a a a ii a i 1 111 11 41 2 12 f 1 1 1 11 1 3 2 1 i 4 vie Sa 12 1 1 111 1 2 if 14 Description of output files 236 uo a SLOPES FOR LOG ABS RES on LOG PV for Section 1 0 15 SLOPES FOR LOG SDi on LOG PVBari for Section 1 w37 xk kkk x xk kkk OK xk kkk kkk kkk OK JR KR KK KOK KOK kkk KOK 2 2 2 K K k kK k k k k k kK kK kK K k k OK x DK k kK k k k k k k kk k kK kK k k kK x ORK xk kk kk RK k k kk kkk kkk k kk k kk k k kk 2 kK k k kK k xk Min Mean Max 24 873 0 27954 15 915 omitting 18 zeros Spatial diagnostic statistics of Residuals 22 11 Residual Plot and Autocorrelations lt LOo xXH gt se 0 077 xxx X OF x tx x gt X lo XXX X x Xxx g lt bt f serie txxxt xXx x xX x o XxxXXx xXXK JooL lt Oo x x xXx x H lt lt lt lt lt O0 xX x 0 lt lt LLLoo lt o L lt lt lt lt 0 OL o x x 1 0 28 0 38 0 50 0 65 O 77 1 00 0 77 0 65 0 50 0 38 0 28 2 0 17 0 27 0 39 0 51 0 56 0 64 0 56 0 50 0 40 0 32 0 26 3 0 05 0 11 0 19 0 28 0 35 42 0 40 0 35 0 30 0 24 0 19 w Residuals Percentage of sig
421. t the top of the file causes ASReml to sort the pedigree into an acceptable order that is par ents before offspring before forming the A Inverse The sorted pedigree is written to a file whose name has srt appended to its name requests the formation of the inverse relationship matrix for the X chro mosome as described by Fernando and Grossman 1990 for species where the male is XY and the female is XX This NRM inverse matrix is formed in addition to the usual A and can be accessed as GIV1 or as specified in the output The pedigree must include a fourth field which codes the SEX of the individual The actual code used is up to the user and deduced from the first line which is assumed to be a male Thus whatever string is found in the fourth field on the first line of the pedigree is taken to mean MALE and any other code found on other records is taken to mean FEMALE 9 Command file Genetic analysis 171 9 6 Reading a user defined inverse relationship matrix ASReml2 ASReml3 Sometimes an inverse relationship matrix is required other than the one ASReml can produce from the pedigree file We call this a GIV G inverse matrix The user can prepare a giv file containing this matrix and use it in the analysis Alternatively the user can prepare the relationship matrix in a grm file and ASReml will invert it to form the GIV matrix The syntax for specifying a G matrix file say name grm or the G inverse file say name
422. t year 5 crop 1 pasture lime AVE month 0 22 0 53 70 22 0 51 16 51 0 0 but to average over years as well we need one of the following predict statements predict crop 1 pasture lime PRES year month IPRUTS 86 55 56 53 57 63 0 0 0 0 0 O 36 0 O 53 23 24 54 54 43 35 0 0 70 02117 0 0 070 0 053 53 56 22 92 19 44 0 036 0 0 49 O22 0 537022 651 16 51 0 OFS predict crop 1 pasture lime PRES month year IPRWTS 56 36 70 53 0 55 0 0 56 22 56 O 21 22 0 53 53 17 92 53 57 23 0 19 70 63 24 0 44 22 54 0 0 0 54 70 0 51 43 0 36 16 35 0 0 51 053 0 O 0 0 49 O 5 predict crop 1 pasture lime PRES year month PRWIS YMprwts txt 0 0 0 0 0 0 where YMprwts txt contains 11 2 11 0 11 2 10 6 11 4 12 6 0 0 QO 0 0 6 0 0 0 0 0 7 2 0 0 0 0 10 6 4 6 4 8 10 8 10 8 8 6 7 0 0 0 06 0 14 0 0 4 2 3 4 0 0 0 0 0 0 14 0 0 0 0 10 6 0 0 10 6 11 2 4 4 18 4 3 8 8 8 0 0 fiz Q 0 2 5 0 4 4 0 10 6 14 4 4 0 10 2 3 2 10 2 0 0 We have presented both sets of predict statements to show how the weights were derived and presented Notice that the order in PRESENT year month implies that the weight coefficients are presented in standard order with the levels for months cycling within levels for years There is a check which reports if non zero weights are associated with cells that have no data The weights are reported in the pvs file PRESENT counts are reported in the res file 10 Tabulation of the data and prediction from the model 193
423. ta field The pedigree file e has three fields the identities of an individual its sire and its dam or maternal grand sire if the MGS qualifier Table 9 1 is specified in that order e an optional fourth field may supply inbreeding selfing information used if the FGEN qualifier Table 9 1 is specified e a fourth field specifying the SEX of the individual is required if the XLINK qualifier Table 9 1 is specified e is sorted so that the line giving the pedigree of an individual appears before any line where that individual appears as a parent e is read free format it may be the same file as the data file if the data file is free format and has the necessary identities in the first three fields see below e is specified on the line immediately preceding the data file line in the command file e use identity O or for unknown parents harvey ped harvey dat 101 SIRE_1 0 101 SIRE_1 O 1 3 192 390 2241 102 SIRE_1 0 102 SIRE_1 0 1 3 154 403 2651 103 SIRE_1 0 103 SIRE_1 O 1 4 185 432 2411 104 SIRE_1 0 104 SIRE_1 O 1 4 183 457 2251 105 SIRE_1 0 105 SIRE_1 0 1 5 186 483 2581 106 SIRE_1 0 106 SIRE_1 O 1 5 177 469 2671 107 SIRE_1 0 107 SIRE_1 0 1 5 177 428 2711 108 SIRE_1 0 108 SIRE_1 0 1 5 163 439 2471 109 SIRE_2 0 109 SIRE_2 0 1 4 188 439 2292 110 SIRE_2 0 110 SIRE 2 0 1 4 178 407 2262 111 SIRE_2 0 111 SIRE 2 0 1 5 198 498 1972 112 SIRE_2 0 112 SIRE 2 0 1 5 193 459 2142 113 SIRE_2 0 113 SIRE 2 0 1 5 186 459 2442 114 SIRE_
424. ta sets the evaluation of the trace terms in either 2 7 or 2 8 is either not feasible or is very computer intensive To overcome this problem ASReml uses the Al algorithm Gilmour Thompson and Cullis 1995 The matrix denoted by Z4 is obtained by averaging 2 7 and 2 8 and approximating y PH Py by its expectation tr PHj in those cases when H 0 For variance components models that is those linear with respect to variances in H the terms in Z4 are exact averages of those in 2 7 and 2 8 The basic idea is to use T4 kj in place of the expected information matrix in 2 9 to update kK The elements of Z4 are 1 DA ie Kj zY PHiPH Py 2 10 2 Some theory 14 The Z4 matrix is the scaled residual sums of squares and products matrix of y Y1o Ye where y is the working variate for k and is given by y H Py H R R R t kiE Q ZGiG l Kev where y X7 Zu 7 and are solutions to 2 11 In this form the Al matrix is relatively straightforward to calculate The combination of the Al algorithm with sparse matrix methods in which only non zero values are stored gives an efficient algorithm in terms of both computing time and workspace Estimation prediction of the fixed and random effects To estimate T and predict u the objective function log fy y u T R log fu u G is used The is the log joint distribution of Y u Differentiating with respect to
425. tected Each error is discussed with reference to the output written to the asr file Briefly the errors are 1 there is no file nine asd in the working folder 2 unrecognised qualifier should be SKIP 3 incorrectly defined factor A required be cause factor is alphanumeric 4 comma missing from first line of model in dicating model is incomplete 5 misspelt variable label in linear model Repl should be rep1 nin alliance trial variety 56 3 id pid raw repl 4 nloc yield lat long row 22 column 11 nine asd slip 1 dopart 1 1 amp 2 tpartit 1 yield mu variety 4 Ir Repl 5 001 Repl 1 6 2 O IY 0 1 Ta part 2 yield mu variety 9 12 11 row AR1 1 10 22 col ARI 1 part predict voriety 8 6 misspelt variable label in G structure header line Repl should be rep1 7 wrong levels declared in G structure model line Rep1 has 4 levels 8 misspelt variable label in predict statement voriety should be variety 9 mv omitted from spatial model 10 wrong levels declared in R structure model lines Data file not found Running this job produces the asr file in Sec tion 15 1 The first problem is that ASReml cannot find the data file nine asd in the cur rent working folder as indicated in the error message above the Fault line ASReml reports nin alliance trial nine asd slip 1 yield mu variety 15 Error messages
426. ted with a variate v and k knot points s v k in ASReml v is included as a covariate in the model and spl v k as a random term The knot points can be explicitly specified using the SPLINE qualifier Table 5 4 If kis specified but SPLINE is not specified equally spaced points are used If kis not specified and there are less than 50 unique data values they are used as knot points If there are more than 50 unique points then 50 equally spaced points will be used The spline design matrix formed is written to the res file An example of the use of spl1 is price mu week r spl week sqrt v 7r forms the square root of v r This may also be used to transform the response variable Trait is used with multivariate data to fit the individual trait means It is formally equivalent to mu but Trait is a more natural label for use with multivariate data It is interacted with other factors to estimate their effects for all traits 6 Command file Specifying the terms in the mixed model 107 Table 6 2 Alphabetic list of model functions and descriptions model function action units creates a factor with a level for every record in the data file This is used to fit the nugget variance when a correlation structure is applied to the residual uni ff 0 n creates a factor with a new level whenever there is a level present for the factor f Levels effects are not created if the level of factor fis 0 missing or
427. terms are considered The output see page 225 is a report to the asr file with a line for every submodel showing the sums of squares degrees of freedom and terms in the model There is a limit of d 20 model terms in the screen ASReml will not allow interac tions to be included in the screened terms For example to identify which three of my set of 12 covariates best explain my dependent variable given the other terms in the model specify SCREEN 3 SMX 3 The number of models evaluated quickly increases with d but ASReml has an arbitrary limit of 900 submodels evaluated Use the DENSE qualifier to control which terms are screened The screen is conditional on all other terms those in the SPARSE equations being present 5 Command file Reading the data 88 Table 5 5 List of rarely used job control qualifiers qualifier action ASReml2 ASReml2 ASReml2 ASReml2 ASReml2 SLNFORM n I SPATIAL TABFORM n TXTFORM n TWOWAY IVCC n modifies the format of the s1n file SLNFORM 1 prevents the sln file from being written SLNFORM 1 is TAB separated sln becomes sln txt SLNFORM 2 is COMMA separated sln becomes _sln csv SLNFORM 3 is Ampersand separated sln becomes _s1n tex See TXTFORM for more detail increases the amount of information reported on the residuals obtained from the analysis of a two dimensional regular grid field trial The information is written to the res fil
428. th output Notice 1 singularities detected in design matrix 1 LogL 105 631 S2 1 0000 129 df Dev DF 1 082 2 LogL 105 632 S2 1 0000 129 df Dev DF 1 082 3 LogL 105 631 S2 1 0000 129 df Dev DF 1 081 4 LogL 105 628 S2 1 0000 129 df Dev DF 1 080 5 LogL 105 627 S2 1 0000 129 df Dev DF 1 079 6 LogL 105 627 S2 1 0000 129 df Dev DF 1 078 Deviance from GLM fit 129 139 09 Variance heterogeneity factor Deviance DF 1 08 Results from analysis of F51 F862 Notice While convergence of the LogL value indicates that the model has stabilized its value CANNOT be used to formally test differences between Generalized Linear Mixed Models Source Model terms Gamma Component Comp SE C SIRE 34 34 0 174697 0 174697 2 80 0 P Wald F statistics Source of Variation NumDF DenDF F_inc Prob 11 Trait 2 Ti 405 40 lt 00f 3 SEX 1 129 0 5 61 0 020 2 GRP 4 30 0 8 03 lt 001 Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using numerical derivatives Warning These Wald F statistics are based on the working variable and are not equivalent to an Analysis of Deviance Standard errors are scaled 16 Examples 341 by the variance of the working variable not the residual deviance Solution Standard Error T value T prev 2 GRP 2 0 7T27155 0 273336 2 66 3 1 76491 0 356573 4 95 2 93 4 1 19399 0 273168 4 37 1 61 5 0 915605 0 242677 e 1 16 3 SEX i 0 197719 0 856093E 01
429. the 5 heights The ASReml input file up to the specification of the R structure is This is plant data multivariate tmt A Diseased Healthy plant 14 yi y3 y5 y7 y10 grass asd skip 1 ASUV The focus is modelling of the error variance for the data Specifically we fit the multivariate regression model given by Y DT E 16 1 16 Examples 291 This is plant data multivariate _Y yl Xoga cS tm Y axis 21 0000 130 500 axis 0 5000 5 5000 1 2 j Figure 16 3 Trellis plot of the height for each of 14 plants where Y 4 is the matrix of heights D14 2 is the design matrix T is the matrix of fixed effects and E is the matrix of errors The heights taken on the same plants will be correlated and so we assume that var vec E I4 8 X 16 2 where is a symmetric positive definite matrix The variance models used for are given in Table 16 4 These represent some commonly used models for the analysis of repeated measures data see Wolfinger 1986 The variance models are fitted by changing the last four lines of the input file The sequence of commands for the first model fitted is yl y3 y5 y7 y10 Trait tmt Tr tmt r units 120 14 Trait The split plot in time model can be fitted in two ways either by fitting a units term plus an independent residual as above or by specifying a CORU variance model for the R structure as follows yi ye y5 y7 yiO Trait tmt Tr tmt 120 14 Trait O CORU 5
430. the data and prediction from the model 176 10 1 Introduction This chapter describes the tabulate directive and the predict directive intro duced in Section 3 4 under Prediction Tabulation is the process of forming simple tables of averages and counts from the data Such tables are useful for looking at the structure of the data and numbers of observations associated with factor combinations Multiple tabulate directives may be specified in a job Prediction is the process of forming a linear function of the vector of fixed and random effects in the linear model to obtain an estimated or predicted value for a quantity of interest It is primarily used for predicting tables of adjusted means If a table is based on a subset of the explanatory variables then the other variables need to be accounted for It is usual to form a predicted value either at specified values of the remaining variables or averaging over them in some way 10 2 Tabulation Revised 08 ASReml2 A tabulate directive is provided to enable simple summaries of the data to be formed for the purpose of checking the structure of the data The summaries are based on the same records as are used in the analysis of the model fitted in the same run In particular it will ignore records that exist in the data file but were dropped as the data was read into ASReml either explicitly using DV or implicitly because the dependent variable had missing values Multiple tabulate
431. the residual likelihood The estimate of 7 is found by equating y to its conditional expectation and after some algebra we find 7 X H X X H y Estimation of x y is based on the log residual likelihood 1 lr 5 log det L H Lz y3 L H L2 y2 1 5 log det X H X logdet H y Py 2 4 where P H H1X X H X X H Note that y Py y X7 H y X7 The log likelihood 2 4 depends on X and not on the particular non unique transformation defined by L The log residual likelihood ignoring constants can be written as 1 lp 5 log det C log det R log det G y Py 2 5 We can also write P R R WC W R 2 Some theory 13 with W X Z Letting k y the REML estimates of x are found by calculating the score 1 U ri lr ki 9 ltt PH y PH Py 2 6 and equating to zero Note that H 0H rk The elements of the observed information matrix are OLR 1 1 a tr PH lt tr PH PH OKiOK 9 r j 2 r j 1 y PH PH Py zY PHijPy 2 7 where Hj OH OKiOK The elements of the expected information matrix are p fn _ 1 tr PH PH 2 8 OKOK 2 ae Given an initial estimate an update of k k using the Fisher scoring FS algorithm is KO RO 4 T 6O KOTU KO 2 9 where U is the score vector 2 6 and T K is the expected infor mation matrix 2 8 of k evaluated at 6 For large models or large da
432. the word Error indicate that something is inconsistent as far as ASReml is concerned It may be a coding error that the user can fix easily or a processing error which will generally be harder to diagnose Often the error reported is a symptom of something else being wrong Table 15 2 List of warning messages and likely meaning s warning message likely meaning Notice ASReml has merged design points closer than Warning e missing values generated by transformation Warning 7 singularities in AI matrix Warning m variance structures were modified Warning n missing values were detected in the design Warning n negative weights Warning r records were read from multiple lines WARNING term has more levels than expected Warning term in the predict IGNORE list Warning term in the predict USE list This is to reduce the number of knot points used in fitting a spline data values should be positive usually means the variance model is overpa rameterized Look up AISING the structures are probably at the boundary of the parameter space either use MVINCLUDE or delete the records it is better to avoid negative weights unless you can check ASReml is doing the correct thing with them check the data summary has the correct num ber of records and all variables have valid data values If ASReml does not find sufficient val ues on a data line it continues reading from
433. their approximate prediction variance matrix corresponding to the dense portion It is only written if the VRB qualifier is specified The file is formatted for reading back for post processing The number of equations in the dense portion can be increased to a maximum of 800 using the DENSE option Table 5 5 but not to include random effects The matrix is lower triangular row wise in the order that the parameters are printed in the s1n file It can be thought of as a partitioned lower triangular matrix o2 where 3 p is the dense portion of 8 and C is the dense portion of C This is the first 20 rows of nin89a vrb Note that the first element is the estimated error variance that is 48 6802 see the variance component estimates in the asr output 14 Description of output files 242 0 486802E 02 0 807551E 01 0 313123E 00 0 295404E 01 0 743616E 01 0 472519E 01 0 330076E 01 0 768275E 01 0 395693E 01 0 226478E 01 0 402503E 01 0 508553E 01 0 428826E 01 0 855241E 01 0 384055E 01 0 392097E 01 0 000000E 00 0 470711E 01 0 000000E 00 0 000000E 00 0 163302E 01 0 402696E 01 0 347471E 01 0 310018E 00 0 383429E 01 0 000000E 00 0 440539E 01 0 000000E 00 0 417864E 01 0 243687E 01 0 330171E 01 0 406762E 01 0 000000E 4 0 000000E 4 0 410031E 4 0 343331E 4 0 000000E 4 0 837281E 4 0 357605E 4 0 000000E 4 0 458492E 4 0 379286E 4 0 362391E
434. theory 23 are marginal to at least one term in a higher group and so forth For example in the table model term A B has M code B because it is marginal to model term A B C and model term A has M code A because it is marginal to A B A C and A B C Model term mu M code is a special case in that its test is conditional on all covariates but no factors Following is some ASReml output from the aov table which reports the terms in the conditional statistics Marginality pattern for F con calculation Model terms Model Term DF 12 3 4 5 6 7 8 1 mu 1 E 2 water 1 I C C c 3 variety 7 I I C c 4 sow 2 I I I i 5 water variety 7 I I I I C C 6 water sow 2 I I I I I C 7 variety sow 14 I I I I I I 8 water variety sow 14 I I I I I I I F inc tests the additional variation explained when the term is added to a model consisting of the I terms F con tests the additional variation explained when the term is added to a model consisting of the I and C c terms Any c terms are ignored in calculating DenDF for F con using numerical derivatives for computational reasons The terms are ignored for both F inc and F con tests Consider now a nested model which might be represented symbolically by y 1 REGION REGION SITE For this model the incremental and conditional Wald F statistics will be the same However it is not uncommon for this model to be presented to ASReml as y 1 REGION SITE with SITE i
435. tion lines 131 7 5 Variance model description oao o a 20000000 132 Contents xi Forming variance models from correlation models 137 Notes on the variance models 0 138 Notes on Mat rn aaa 139 Notes on power models 0 0 0 00000 00 141 Notes on Factor Analytic models 142 Notes on OWN models 2 2 0 2 ee 144 7 6 Variance structure qualifiers ooo aa 146 7 7 Rules for combining variance models 2 4 147 7 8 G structures involving more than one random term 148 7 9 Constraining variance parameters 2 204 150 Parameter constraints within a variance model 150 Constraints between and within variance models 151 Equating variance structures 0 0 0000 152 7 10 Model building using the CONTINUE qualifier 154 7 11 Convergence issues 1 a a a 155 Command file Multivariate analysis 157 8 1 Introdtiction lt 4 p 26528 22948 bbe ee bk ea ee eR Os 158 Repeated measures on rats 2 2 a e a 158 Wether trial data o ses 26 4 ee ace amp Be Soe Sa SMS poe eS 158 8 2 Model specification 2 2 2 0 0000 ee ee 159 Contents xii 8 3 Varlanc structures o e r s eo Ee ko Be Soe eee baw ee Os 160 Specifying multivariate variance structures in ASReml 160 8 4 The output for a multivariate analysis o0 aa 161 9 Command file Genetic an
436. tistic has a chi square distribution on r degrees of freedom These are marginal tests so that there is an adjustment for all other terms in the fixed part of the model It is also anti conservative if p values are constructed because it assumes the variance parameters are known The small sample behaviour of such statistics has been considered by Kenward and Roger 1997 in some detail They presented a scaled Wald statistic to gether with an F approximation to its sampling distribution which they showed performed well in a range though limited in terms of the range of variance models available in ASReml of settings In the following we describe the facilities now available in ASReml for conducting inference concerning terms which are the in dense fixed effects model component of the general linear mixed model These facilities are not available for any terms in the sparse model These include facilities for computing two types of Wald F statistics and partial implementation of the Kenward and Roger adjustments Incremental and Conditional Wald F Statistics The basic tool for inference is the Wald statistic defined in equation 2 17 ASReml produces a test of fixed effects that reduces to an F statistic in special cases by dividing the Wald statistic constructed with 0 by r the numerator degrees of freedom In this form it is possible to perform an approximate F test if we can deduce the denominator degrees of freedom However there a
437. tle for the job and is purely descriptive for future reference NIN Alliance trial 1989 variety A id pid raw repl 4 nloc yield lat long row 22 column 11 nin89 asd skip 1 tabulate yield variety yield mu variety r repl predict variety 001 repl 1 repl 0 IDV 0 1 NIN Alliance trial 1989 variety A id 3 A guided tour 32 See Section 5 7 See Section 5 8 See Chapter 10 Reading the data The data fields are defined before the data file name is specified Field definitions must be given for all fields in the data file and in the order in which they appear in the data file Data field definitions must be indented In this case there are 11 data fields variety column in nin89 asd see Section 3 3 The A after variety tells ASReml that the first field is an alphanumeric factor and the 4 after repl tells ASReml that the field called repl the fifth field read is a numeric factor with 4 levels coded 1 4 Similarly for row and column The other fields include variates yield and various other variables The data file line The data file name is specified immediately after the last data field definition Data file qualifiers that relate to data input and out put are also placed on this line if they are re quired In this example skip 1 tells ASReml to ignore skip the first line of the data file nin89 asd the line containing the field labels The data file line
438. tructures need to be modified Basic multi environment trial analysis site 5 sites coded 1 5 column columns coded 1 row rows coded 1 variety A variety names yield met dat SECTION site ROWFAC row COLFAC col yield site r variety site variety f mv site 2 0 variance header line ASReml inserts the 10 lines required to define the R structure lines for the five sites here defines a spline model term with an explicit set of knot points The basic form of the spline model term sp1 v is defined in Table 6 1 where v is the underlying variate The basic form uses the unique data values as the knot points The extended form is spl1 v n which uses n knot points Use this SPLINE qualifier to supply an explicit set of n knot points p for the model term t Using the extended form without using this qualifier results in n equally spaced knot points being used The SPLINE qualifier may only be used on a line by itself after the datafile line and before the model line 5 Command file Reading the data 78 Table 5 4 List of occasionally used job control qualifiers qualifier action ASReml3 ASReml2 ISTEP r SUBGROUP t v p SUBSET t v p WMF When knot points are explicitly supplied they should be in increasing order and adequately cover the range of the data or ASReml will modify them before they are applied If you choose to spread them over several lines use a comma at the e
439. ualifiers 68 key output files 223 likelihood comparison 223 convergence 70 log residual 12 offset 223 Index 366 residual 12 longitudinal data 2 balanced example 323 marginal distribution 12 Mat rn variance structure 140 measurement error 124 MERGE 211 MET 9 meta analysis 2 9 missing values 44 105 112 228 NA 44 in explanatory variables 113 in response 112 mixed effects 7 model 7 mixed model 7 equations 14 multivariate 159 specifying 33 model animal 165 351 correlation 10 covariance 11 formulae 94 random regression 11 sire 165 model building 154 moving average 105 multi environment trial 2 9 multivariate analysis 158 317 example 341 half sib analysis 342 Nebraska Intrastate Nursery 27 Negative binomial 110 non singular matrices 118 nonidentifiable 16 objective function 14 observed information matrix 13 operators 96 options command line 197 ordering of terms 114 Ordinal data 109 orthogonal polynomials 106 outliers 244 output files 36 multivariate analysis 161 objects 243 output file extension aov 221 229 apj 221 ask 221 asl 221 232 asp 221 asr 36 221 223 ass 221 dbr 221 dpr 221 232 pvc 221 pvs 221 232 233 res 221 233 rsv 221 240 sln 38 221 226 spr 221 tab 221 240 veo 221 vll1 222 vrb 241 VVp 222 242 was 222 yht 38 221 228 overspecified 16 o
440. ualifiers which relate the linear predictor 7 scale to the observation u E y scale Table 6 4 lists the distribution and other qualifiers Table 6 4 GLM distribution qualifiers The default link is listed first followed by permitted alternatives qualifiers action INORMAL IDENTITY LOGARITHM INVERSE allows the model to be fitted on the log inverse scale but with the residuals on the natural scale NORMAL IDENTITY is the default BINOMIAL LOGIT IDENTITY PROBIT COMPLOGLOG TOTAL n v p 1 p n Proportions or counts r ny are indicated if TOTAL specifies the d 2n yln y p variate containing the binomial totals Proportions are assumed if 1 y In no response value exceeds 1 A binary variate 0 1 is indicated if TOTAL is unspecified The expression for d on the left applies when y is proportions or binary The logit is the default link function The variance on the underlying scale is 17 3 3 3 underlying logistic distribution for the logit link MULTINOMIAL k CUMULATIVE LOGIT PROBIT COMPLOGLOG TOTAL n fits a multiple threshold model with t k 1 thresholds to vij p l uj n polytomous ordinal data with k categories assuming a multinomial fori lt j lt t distribution Typically the response variable is a single variable containing the d 2nd _ ordinal score 1 k or a set of k variables containing counts r yln yi pi in the k categorie
441. ug asd skip 1 yield mu variety 12 11 column AR1 424 22 row AR1 904 e is used to annotate the input all characters following a symbol on a line are ignored comments for the output e a blank is the usual separator TAB is also a separator e maximum line length is 2000 characters lines without can be joined with with lines beginning with followed by a blank are copied to the asr file as e acomma as the last character on the line is sometimes used to indicate that the current list is continued on the next line a comma is not needed when ASReml knows how many values to read they need to be typed exactly as defined they may not be abbreviated e a qualifier is a letter sequence beginning with an which sets an option some qualifiers require arguments qualifiers must appear on the correct line qualifier identifiers are not case sensitive qualifier identifiers may be truncated to 3 characters reserved words used in specifying the linear model Table 6 1 are case sensitive 5 Command file Reading the data 48 5 3 Title line The first 40 characters of the first nonblank NIN Alliance Trial 1989 text line in an ASReml command file are taken variety A as a title for the job Use this to document sre pl the analysis for future reference An optional qualifier line see section 11 3 may precede the title line It is recognised by the presence oF the qualifier pr
442. ulated ignoring fixed boundary singular variance parameters using algebraic derivatives 4 dam 27 effects fitted SLOPES FOR LOG ABS RES on LOG PV for Section 1 2 27 16 Examples 286 3 possible outliers see res file The iterative sequence has converged and the variance component parameter for dam hasn t changed for the last three iterations The incremental Wald F statistics indicate that the interaction between dose and sex is not significant The F_con column helps us to assess the significance of the other terms in the model It confirms littersize is significant after the other terms that dose is significant when adjusted for littersize and sex but ignoring dose sex and that sex is significant when adjusted for littersize and dose but ignoring dose sex These tests respect marginality to the dose sex interaction We also note the comment 3 possible outliers see res file Checking the res file we discover unit 66 has a standardised residual of 8 80 see Fig ure 16 1 The weight of this female rat within litter 9 is only 3 68 compared to weights of 7 26 and 6 58 for two other female sibling pups This weight appears erroneous but without knowledge of the actual experiment we retain the obser vation in the following However part 2 shows one way of dropping unit 66 by fitting an effect for it with out 66 Rats example Residuals vs Fitted values Residuals Y 3 02 1 22 Fitted values X 5 04 7 63 o 6 8
443. unless the algorithm has at least produced estimates for the fixed and random effects in the model Note that residuals are not included in the output forced by this qualifier This option is primarily intended to help debugging a job that is not converging properly When forming a design matrix for the spl1 model term ASReml uses a standardized scale independent of the actual scale of the variable The qualifier SCALE 1 forces ASReml to use the scale of the variable The default standardised scale is appropriate in most circumstances 5 Command file Reading the data 91 Table 5 6 List of very rarely used job control qualifiers qualifier action ASReml2 ASReml2 ASReml2 SCORE ISLOW n TOLERANCE s1 s2 VRB requests ASReml write the SCORE vector and the Average Information matrix to files basename SCO and basename AIM The values written are from the last iteration reduces the update step sizes of the variance parameters more persistently than the STEP r qualifier If specified ASReml looks at the potential size of the updates and if any are large it reduces the size of r If n is greater than 10 ASReml also modifies the Information matrix by multiplying the diagonal elements by n This has the effect of further reducing the updates In the iteration subroutine if the calculated LogL is more than 1 0 less than the LogL for the previous iteration and SLOW is set and NIT gt 1 ASReml imme
444. use the notation a b n to represent the sequence of values from a to n with step size b a The default stepsize is 1 in which case b may be omitted A colon may replace the ellipsis An increasing sequence is assumed When giving particular values for factors the default is 10 Tabulation of the data and prediction from the model 181 to use the coded level 1 n rather than the label alphabetical or integer To use the label precede it with a quote Where a large number of values must be given they can be supplied in a separate file and the filename specified in quotes The file form does not allow label coding or sequences See the discussion of PRWTS for an example Having identified the explanatory variables in the classify set the second step is to check the averaging set The default averaging set is those explanatory variables involved in fixed effect model terms that are not in the classify set By default variables that are not in any ASSOCIATE list and that only define random model terms are ignored Use the AVERAGE ASSOCIATE or PRESENT qualifiers to force variables into the averaging set The third step is to check the linear model terms to use in prediction The default is that all model terms based entirely on variables in the classifying and averaging sets are used Two qualifiers allow this default to be modified by adding USE or removing IGNORE model terms The qualifier ONLYUSE expl
445. ut objects and where to find them Table 14 2 presents a list of objects produced with each ASReml run and where to find them in the output files Table 14 2 ASReml output objects and where to find them output object found in comment Wald F statistics ta asr file This table contains Wald F statistics for each term ble in the fixed part of the model These provide for an incremental or optionally a conditional test of significance see Section 6 11 data summary asr file includes the number of records read and retained ass file for analysis the minimum mean maximum number of zeros number of missing values per data field factor variate field distinction An extended report of the data is written to the ass file if the SUM qualifier is specified It in cludes cell counts for factors histograms of vari ates and simple correlations among variates eigen analysis res file When ASReml reports a variance matrix to the res file asr file it also reports an eigen analysis of the matrix eigen values and eigen vectors to the res file elapsed time asr file this can be determined by comparing the start asl file time with the finishing time The execution times for parts of the Iteration pro cess are written to the asl file if the DEBUG LOGFILE command line qualifiers are invoked fixed and random ef sln file if BRIEF 1 is invoked the effects that were in fects cluded in the dense portion of the solution
446. values TURNINGPOINTS n requests ASReml to scan the predicted values from a fitted line for possible turning points and if found report them and save them internally in a vector which can be accessed by subsequent parts of the same job using TPn This was added to facilitate location of putative QTL Gilmour 2007 TWOSTAGEWEIGHTS is intended for use with variety trials which will subsequently ASReml2 be combined in a meta analysis It forms the variance matrix for the predictions inverts it and writes the predicted variety means with the corresponding diagonal elements of this matrix to the pvs file These values are used in some variety testing programs in Australia for a subsequent second stage analysis across many trials Smith et al 2001 A data base is used to collect the results from the individual trials and write out the combined data set The diagonal elements scaled by the variance which is also reported and held in the data base are used as weights in the combined analysis VPV requests that the variance matrix of predicted values be printed to the pvs file 10 Tabulation of the data and prediction from the model 186 PLOT graphic control qualifiers This functionality was developed and this section was written by Damian Collins ASReml2 The PLOT qualifier produces a graphic of the predictions Where there is more than one prediction factor a multi panel trellis arrangement may be used Al ternative
447. values are not deleted but ASReml drops the missing observation and uses the appropriate unstruc tured R inverse matrix For regular spatial analysis we prefer to retain separability and therefore estimate the missing value s by including the special term mv in the model out n out n out n t establishes a binary variable which is out n t out i 1 if data relates to observation i trait 1 else is 0 ASReml2 out i t 1 if data relates to observation i trait t else is 0 The intention is that this be used to test remove single observations for example to remove the influence of an outlier or influential point Possible outliers will be evident in the plot of residuals versus fitted values see the res file and the appropriate record numbers for the out term are reported in the res file Note that 7 relates to the data analysed and will not be the same as the record number as obtained by counting data lines in the data file if there were missing observations in the data and they have not been estimated To drop records based on the record number in the data file use the D transformation in association with the VO transformation 6 Command file Specifying the terms in the mixed model 106 Table 6 2 Alphabetic list of model functions and descriptions model function action pol v n forms a set of orthogonal polynomials of order n based on the unique p v n values in variate or factor v and any additional i
448. vari lah Stange trial 1397 gul Bots taza ete Outer displacement Figure 14 2 Variogram of residuals 32 33 52 56 35 52 Inner displacement Pe FF Ee Shee Ja SD SD SD SD SD SD 23 0311757288330 14 Description of output files 238 Figures 14 2 to 14 5 show the graphics derived from the residuals when the I DISPLAY 15 qualifier is specified and which are written to eps files by run ning ASReml g22 nin89a as The graphs are a variogram of the residuals from the spatial analysis for site 1 Figure 14 2 a plot of the residuals in field plan order Figure 14 3 plots of the marginal means of the residuals Figure 14 4 and a histogram of the resid uals Figure 14 5 The selection of which plots are displayed is controlled by the DISPLAY qualifier Table 5 4 By default the variogram and field plan are displayed The sample variogram is a plot of the semi variances of differences of residuals at particular distances The 0 0 position is zero because the difference is identically zero ASReml displays the plot for distances 0 1 2 8 9 10 11 14 15 20 The plot of residuals in field plan order Figure 14 3 contains in its top and right margins a diamond showing the minimum mean and maximum residual for that row or column Note that a gap identifies where the missing values occur The plot of marginal means of residuals shows residuals for each row column as well as th
449. variables Response variables may be grouped using the G factor definition qual ifier so that more than 20 actual variables can be analysed this message occurs when there is an error forming the inverse of a variance structure The probable cause is a non positive definite initial variance structure US CHOL and ANTE models It may also occur if an identity by un structured ID US error variance model is not specified in a multivariate analysis including ASMV see Chapter 8 If the failure is on the first iteration the problem is with the start ing values If on a subsequent iteration the updates have caused the problem You can specify GP to force the matrix positive def inite and try reducing the updates by using the STEP qualifier Otherwise you could try fitting an alternative parameterisation The CORGH model may be more stable than the US model generally refers to a problem setting up the mixed model equations Most commonly it is caused by a non positive definite matrix Use better initial values or a structured vari ance matricx that is positive definite 15 Error messages 277 Table 15 3 Alphabetical list of error messages and probable cause s remedies error message probable cause remedy XFA model not permitted in R You may use FA or FACV The R structure must structures be positive definite XFA may not be used as an R structure 16 Examples Introduction Split plot desig
450. variate data no longer having an n x t n subjects with t traits each structure This will be a problem if the R structure model assumes n x t data structure the matrix may be OK but ASReml has not checked it this indicates that there are some lines on the end of the as file that were not used The first extra line is displayed This is only a problem if you intended ASReml to read these lines The RSKIP qualifier requested skipping header blocks which were not present ASReml increases to the correct value indent them to avert this message user nominated more levels than are permit ted constraint parameter is probably wrongly as signed fix the argument The model term Trait was not present in the multivariate analysis model you may need more iterations restart to do more iterations see CONTINUE 15 Error messages 266 Table 15 2 List of warning messages and likely meaning s warning message likely meaning Notice LogL values are reported relative to a base of Warning Missing cells in table Warning More levels found in term Warning PREDICT LINE IGNORED TOO MANY Warning PREDICT statement is being ignored Warning Second occurrence of term dropped Warning Spatial mapping information for side Warning Standard errors Warning SYNTAX CHANGE text may be invalid Warning The A qualifier ignored when reading BINARY data Warning The SPLINE qualif
451. ve are detected and the value is then fixed at a small positive value This is shown in the output in that the parameter will have the code B rather than P appended to the value in the variance component table IGU unrestricted does not limit the updates to the parameter This allows variance parameters to go negative and correlation parameters to exceed 1 Negative variance components may lead to problems the mixed model coefficient matrix may become non positive definite In this case the sequence of REML log likelihoods may be erratic and you may need to experiment with starting values IGF fixes the parameter at its starting value IGZ only applies to FA and FACV models and fixes the corresponding parameter in to zero 0 00 For multiple parameters the form GXXXX can be used to specify F P Uor Z for the parameters individually A shorthand notation allows a repeat count before a code letter Thus GPPPPPPPPPPPPPPZPPPZP could be written as G14PZ3PZP For a US model GP makes ASReml attempt to keep the matrix posi tive definite After each AI update it extracts the eigenvalues of the updated matrix If any are negative or zero the AI update is discarded and an EM update is performed Notice that the EM update is applied to all of the variance parameters in the particular US model and cannot be applied to only a subset of them is used to associate a label f with a variance structure so that the same structure can be used e
452. vised 08 Revised 08 Underlying principles Our approach to prediction is a generalization of that of Lane and Nelder 1982 who consider fixed effects models They form fitted values for all combinations of the explanatory variables in the model then take marginal means across the explanatory variables not relevent to the current prediction Our case is more general in that we also consider the case of associated factors see page 102 and options for random effects that appear in our mixed models A formal description can be found in Gilmour et al 2004 and Welham et al 2004 Associated factors have a particular one to many association such that the levels of one factor say Region define groups of the levels of another factor say Location In prediction it is necessary to correctly associate the levels of associated factors Terms in the model may be fitted as fixed or random and are formed from explanatory variables which are either factors or covariates For this exposition we define a fixed factor as an explanatory variable which is a factor and appears in the model in terms that are fixed it may also appear in random terms a random factor as an explanatory variable which is a factor and appears in the model only in terms that are fitted as random effects Covariates generally appear in fixed terms but may appear in random terms as well random regression In special cases they may appear only in random terms 10 Tabulati
453. volving several strata here animal direct additive ge netic dam maternal and litter typically involves several runs The ASReml input file presented below has two parts which show the use of FA1 and US vari ance structures but omits earlier runs involved with linear model selection and obtaining initial values This model is not equivalent to the sire dam litter model with respect to the animal litter components for gfw fd and fat WORK 100 RENAME CONTINUE ARG 2 3 DOPATH 1 Multivariate Animal model tag IP sire dam P grp 49 sex brr 4 litter 4871 age wwt mO ywt mO MO identifies missing values giw mO fdm mO fat mO pcoop fmt read pedigree from first three fields pcoop fmt MAXIT 20 STEP 0 01 1 allows selection of PATH as a command line argument IPATH 3 EXTRA 4 Force 4 more iterations after convergence criterion met PATH wwt ywt gfw fdm fat Trait Tr age Tr brr Tr sex Tr age sex r Tr tag at Tr 1 dam at Tr 2 dam lP it atlTy 1 1at at Tr 2 11t at ir 3 1it at ir 4 lie I at Trait 1 age grp 0024 16 Examples 352 at Trait 2 age grp 0019 at Trait 4 age grp 0020 at Trait 5 age grp 00026 at Trait 1 sex grp 93 at Trait 2 sex grp 16 0 at Trait 3 sex grp 28 at Trait 5 sex grp 1 18 tf Tr grp 123 One multivariate R structure 3 G structures 000 No structure across lamb records First zero lets ASReml count te number of records Tr 0 US General structure acros
454. w Ndat 0 Normal 4 5 is equivalent to Ndat Normal 4 5 Rate REPLACE 9 0 Rate RESCALE 10 0 1 ISEED 848586 treat LCAB CvR treat SET 1 1 1 group treat SET 1 22334 Anorm A SETN 2 5 10 Aeff A SETU 5 10 year 3 SUB 66 67 68 5 Command file Reading the data 59 Table 5 1 List of transformation qualifiers and their actions with examples qualifier argument action examples SEQ TARGET ASReml3 UNIFORM ASReml2 Vtarget value Vfield replaces the data values with a sequen tial number starting at 1 which incre ments whenever the data value changes between successive records the current field is presumed to define a factor and the number of levels in the new factor is set to the number of levels identified in this sequential process see Other ex amples below Missing values remain missing changes the focus of subsequent trans formations to variable field v replaces the variate with uniform ran dom variables having range 0 v assigns value to data field target over writing previous contents subsequent transformation qualifiers will operate on data field target assigns the contents of data field field to data field target overwriting previ ous contents subsequent transforma tion qualifiers will operate on data field target If field is 0 the number of the data record is inserted plot V3 SEQ sqrtA meanAB A 2 TAR
455. wed here Multiple trait mapping problem Negative Sum of Squares NFACT out of range Maybe increase workspace or restruc ture simplify the model Numerical problems calculating the Mat rn function If rescaling the X Y cordinates so that the step size is closer to 1 0 does not re solve the issue try AEXP instead special structures are weights the Ainverse and GIV structures The limit is 98 and so no more than 96 GIV structures can be defined The limit is 1500 It may be possible to re structure the job so the limit is not exceeded assuming that the actual number of parame ters to be estimated is less ASReml failed to read the first data record Maybe it is a heading line which should be skipped by using the SKIP qualifier or maybe the field is an alphanumeric field but has not been declared so with the A qualifier You need to identify which design terms con tain missing values and decide whether to delete the records containing the missing val ues in these variables or if it is reasonable to treat the missing values as zero by using MVINCLUDE More missing values in the response were found than expected missing observations have been dropped so that direct product R structure does not match the multivariate data structure Maybe a trait name is repeated This is typically caused by negative variance parameters try changing the starting values or using the STEP option If the problem oc
456. wn models 145 OWN variance structure 144 F2 145 IT 145 Index 367 parameter scale 7 variance 7 Path DOPATH 206 PATH 207 PC environment 195 pedigree 165 file 166 Performance issues 208 power 141 Predict TP 106 ITP 185 TURNINGPOINTS 185 PLOT suboptions 186 PRWTS 191 predicted values 39 prediction 33 176 qualifiers 183 predictions estimable 40 prior mean 15 product direct 9 qualifier UpArrow 56 1 lt 56 lt 56 lt gt 56 56 gt 56 gt 56 Ix 56 1 56 1 56 1 7 56 s 146 55 ABS 56 ADJUST 81 ATLOADINGS 79 ATSINGULARITIES 79 ALPHA 168 AOD Analysis of Deviance 110 ARCSIN 56 ARGS 198 ASK 198 ASMV 72 ASSIGN 205 ASSOCIATE in PREDICT 188 ASSOCIATE 183 ASUV 73 1 AS 50 1A 49 BINOMIAL GLM 109 BLOCKSIZE 151 BLUP 80 BMP 79 IBRIEF 80 198 CHECK 212 ICINV 89 ICOLFAC 73 COMPLOGLOG 109 COMPLOGLOG 109 I CONTINUE 68 154 198 CONTRAST 69 ICOS 56 ICSV 64 CYCLE 205 IDATAFILE 64 IDDF 69 DEBUG 198 IDEC 184 IDEFINE 215 DENSEGIV 171 DENSE 81 DEVIANCE residuals 111 IDF 81 332 IDIAG 168 Index 368 IDISPLAY 73 DISP dispersion 110 DOM dominance 60 DOPART 206 DOPATH 206 DO 57 IDV 56 ID 56 EMFLAG 82 ENDDO 57 IEPS 73 EXP 57 EXTRA 83 FACPOINTS 89 FACTOR 75 FCON 24 70 FGEN 16
457. xcel 45 execution time 243 F statistics 20 Factor qualifier DATE 50 DMY 50 LL Label Length 51 MDY 50 PRUNE 51 SKIP fields 52 SORT 51 SORTALL 52 TIME 50 factors 43 file Index 365 GIV 171 pedigree 166 Fisher scoring algorithm 13 fixed effects 7 Fixed format files 65 fixed terms 94 99 multivariate 159 primary 99 sparse 100 Forming a job template 35 forum 5 free format 43 functions of variance components 39 214 correlation 217 heritability 217 linear combinations 216 syntax 216 G structure 118 definition lines 127 131 header 131 more than one term 148 Gamma distribution 110 Generalized Mixed Linear Models 108 genetic data 2 groups 168 links 165 models 165 qualifiers 165 relationships 166 genetic markers 75 GIV 171 GLM distribution Binomial 109 Gamma 110 Negative Binomial 110 Normal 109 Ordinal data 109 Poisson 110 GLMM 112 graphics options 199 half sib analysis 342 help via email 4 heritability 217 243 heterogeneity error variance 9 identifiable 16 IID 7 inbreeding coefficients 168 227 Incremental F Statistics 20 Information Criteria 18 information matrix 13 expected 13 observed 13 initial values 130 input file extension BIN 45 DBL 45 bin 43 45 csv 44 dbl 43 45 pin 215 interactions 101 Introduction 20 isotropic covariance model 10 job control options 201 q
458. y D d D 0 i4j l lt k lt w l L 1 Ly l 1 lt i j lt k FA 1 i k order DCD wtw FAk k factor C FF E kw w analytic F contains k correlation factors E diagonal DD diag X FACV 1 i k order IT Y wtw FACVk k factor T contains covariance factors kw w analytic W contains specific variance covariance form XFA 1 i k order S T H ww XFAk k extended T contains covariance factors kw w factor W contains specific variance analytic covariance form Inverse relationship matrices AINV inverse relationship matrix derived from pedigree 0 1 GIV1 generalized inverse number 1 0 1 GIV6 generalized inverse number 6 0 1 t This is the number of values the user must supply as initial values where w is the dimension of the matrix The homogeneous variance form is specified by appending V to the correlation basename the heterogeneous variance form is specified by appending H to the correlation basename t These must be associated with 1 variance parameter unless used in direct product with another structure which provides the variance 7 Command file Specifying the variance structures 137 Revised 08 Forming variance models from correlation models The base identifiers presented in the first part of Table 7 3 are used to specify the correlation models The corresponding homogeneous and heterogeneous variance models are specified by appending V and H to the base identifiers respectively and append
459. y a modified Cholesky diag onalisation of the average information matrix That is if F is the average infor mation matrix for let U be an upper triangular matrix such that F U U We define U D U where D is a diagonal matrix whose elements are given by the inverse elements of the last column of U ie deii 1 uir i 1 r The matrix Ue is therefore upper triangular with the elements in the last column equal to one If the vector o is ordered in the natural way with o being the last element then we can define the vector of so called pseudo stratum variance components by E U 0 Th ence var D The diagonal elements can be manipulated to produce effective stratum degrees of freedom Thompson 1980 viz vi 2E de In this way the closeness to an orthogonal block structure can be assessed 3 A guided tour Introduction Nebraska Intrastate Nursery NIN field experiment The ASReml data file The ASReml command file The title line Reading the data The data file line Specifying the terms in the mixed model Tabulation Prediction Variance structures Running the job Description of output files The asr file The sln file The yht file Tabulation predicted values and functions of the variance components 26 3 A guided tour 27 3 1 Introduction Revised 08 ASReml2 This chapter presents a guided tour of ASReml from data file preparation and basic aspects of the ASR
460. y for site 3 use the expression at site 3 row The string is equivalent to at for this function ASReml2 at f at f is expanded to a series of terms like at f 7 where i takes the f values 01 to the number of levels of factor f Since this command is interpreted before the data is read it is necessary to declare the number of levels correctly in the field definition This extended form may only be used as the first term in an interaction at f m n at f i j k is expanded to a series of terms at f i at f j Cf m n at f k Similarly at f i X at f j X at f k X can be written as at f i j k X provided at f i 7 k is written as the first component of the interaction Any number of levels may be listed cos v r forms cosine from v with period r Omit r if v is radians If v is degrees r is 360 con f apply sum to zero constraints to factor f It is not appropriate for random c f factors and fixed factors with missing cells ASReml assumes you specify the correct number of levels for each factor The formal effect of the con function is to form a model term with the highest level formally equal to minus the sum of the preceding terms 6 Command file Specifying the terms in the mixed model 104 Table 6 2 Alphabetic list of model functions and descriptions model function action ASReml2 fac v fac v y giv f n g f n h f ide f ilf inv v r With sum to zero constraints a missi
461. y linNitr 2 45 0 0 48 0 48 b 0 625 10 variety nitrogen 4 45 0 0 22 0 22 B 0 928 The analysis shows that there is a significant linear response to nitrogen level but the lack of fit term and the interactions with variety are not significant In this example the conditional Wald F statistic is the same as the incremental one because the contrast must appear before the lack of fit and the main effect before the interaction and otherwise it is a balanced analysis The first part of the aov file the FMAP table only appears if the job is run in DEBUG mode There is a line for each model term showing the number of non singular effects in the terms before the current term is absorbed For example variety nitrogen initially has 12 degrees of freedom non singular effects mu takes 1 variety then takes 2 linNitr takes 1 nitrogen takes 2 variety linNitr takes 2 and there are four degrees of freedom left This information is used to make sure that the conditional Wald F statistic does not contradict marginality principles 14 Description of output files 231 The next table indicates the details of the conditional Wald F statistic The conditional Wald F statistic is based in the reduction in Sums of Squares from dropping the particular term indicated by from the model also including the terms indicated by I C and c The next two tables based on incremental and conditional sums of squares report the model term the number of effect
462. y of snapper in and around a marine reserve using a log linear mixed effects model Australian and New Zealand Journal of Statistics 41 383 394 Mrode R 2005 Linear models for the prediction of animal breeding values 2nd edition CAB international Wallingford Oxfordshire OX10 8DE UK Nelder J A and Wedderburn R W M 1972 Generalised linear models Journal of the Royal Statistical Society Series A 135 370 384 Bibliography 360 Patterson H D and Nabugoomu F 1992 REML and the analysis of series of crop variety trials Proceedings from the 25th International Biometric Conference pp 77 93 Patterson H D and Thompson R 1971 Recovery of interblock information when block sizes are unequal Biometrika 58 545 54 Piepho H P Denis J B and van Eeuwijk F A 1998 Mixed biadditive models Proceedings of the 28th International Biometrics Conference Pinheiro J C and Bates D M 2000 Mixed Effects Models in S and S PLUS Berlin Springer Verlag Quaas R L 1976 Computing the diagonal elements and inverse of a large numerator relationship matrix Biometrics 32 949 953 R Development Core Team 2005 R A language and environment for statistical computing R Foundation for Statistical Computing Vienna Austria ISBN 3 900051 07 0 Robinson G K 1991 That BLUP is a good thing The estimation of random effects Statistical Science 6 15 51 Robson D S 1959 A simple m
463. y will be assumed base non inbred individuals unless their inbreeding level is set with FGEN f where 0 lt f lt 1 is the inbreeding level of such individuals IGIV instructs ASReml to write out the A inverse in the format of giv files If GROUPS is also specified this giv file will include the GROUPSDF qualifier on its first line GOFFSET o An alternative to group constraints see GROUP below is to shrink the ASReml3 group effects by adding the constant o gt 0 to the diagonal elements of A pertaining to groups When a constant is added no adjustment of the degrees of freedom is made for genetic groups Use GOFFSET 1 to add no offset but to suppress insertion of constraints where empty groups appear The empty groups are then not counted in the DF adjustment GROUPS g includes genetic groups in the pedigree The first g lines of the pedigree identify genetic groups with zero in both the sire and dam fields All other lines must specify one of the genetic groups as sire or dam if the actual parent is unknown You may insert Groups with no members to define constraints on groups that is to associate groups into supergroups where the supergroup fixed ef fect is formally fitted separately in the model A constraint is added to the inverse which causes the preceding set of groups which have members to have effects which sum to zero The issue is to get the degrees of freedom correct and to get the correct calculation of the
464. ying the variance structures 156 two components In models with many variance parameters there may not be enough information to effectively estimate all the parameters or the natural estimates of the param eters may fall outside the conceptual parameter space If there are no actual block effects a block variance component is just an independent estimate of the residual variance ib few degrees of freedom In summary the following strategies are available e review starting values are they in the right order and of the right magnitude can ASReml generate better ones can you get better values from a simpler model hold some parameters fixed for the initial iterations review the model try a simpler structure and test where the variation is has something important been omitted e review input structures is the GIV file positive definite and arranged in the right order review the summary of the data tabulate and plot the data check handling of missing values in response and in design review the iteration sequence 8 Command file Multivariate analysis Introduction Repeated measures on rats Wether trial data Model specification Variance structures Specifying multivariate variance structures in ASReml The output for a multivariate analysis 157 8 Command file Multivariate analysis 158 8 1 Introduction Multivariate analysis is used here in the narrow sense of a multivariate mixed model Ther
465. you could do the prediction in parts predict var 1 525 column 5 5 predict var 526 532 column 5 5 SED to examine the matrix of pairwise prediction errors of variety differences 16 8 Paired Case Control study Rice This data is concerned with an experiment conducted to investigate the tolerance of rice varieties to attack by the larvae of bloodworms The data have been kindly provided by Dr Mark Stevens Yanco Agricultural Institute A full description of the experiment is given by Stevens et al 1999 Bloodworms are a significant pest of rice in the Murray and Murrumbidgee irrigation areas where they can cause poor establishment and substantial yield loss The experiment commenced with the transplanting of rice seedlings into trays Each tray contained 32 seedlings and the trays were paired so that a control tray no bloodworms and a treated tray bloodworms added were grown in a controlled environment room for the duration of the experiment At the end of this time rice plants were carefully extracted the root system washed and root area determined for the tray using an image analysis system described by Stevens et al 1999 Two pairs of trays each pair corresponding to a different variety were included in each run A new batch of bloodworm larvae was used for each run A total of 44 varieties was investigated with three replicates of each Unfortunately the variety concurrence within runs was less than optimal Eight varieties occur
466. ysed see Section 6 2 with the value y where y is the number of the data field containing the trait to be analysed This facilitates analysis of several traits under the same model The value of y is appended to the basename so that output files are not overwritten when the next trait is analysed Workspace command line options S W The workspace requirements depend on problem size and may be quite large An initial workspace allocation may be requested on the command line with the S or W options if neither is specified 32Mbyte 4 million double precision words is allocated Wm WORKSPACE m sets the initial size of the workspace in Mbytes For example W1600 requests 1600 Mbytes of workspace the maximum typically available under Windows W2000 is the maximum available on 32bit Unix Linux systems On 64bit systems the argument if less than 32 is taken as Gbyte Alternatively Ss can be used to set the initial workspace allocation s is a digit The workspace allocated is 2 x 8 Mbyte S3 is 64Mb S4 is 128Mb S5 is 256Mb S6 is 512Mb S7 is 1024Mb S8 is 2048Mb S9 is 4096Mb This option was in Release 1 0 the more flexible option Wm has been introduced in Release 2 0 The W option is ignored if the S option is also specified Otherwise additional workspace may be requested with the Ss or Wm options or the WORKSPACE m qualifier on the top job control line if not specified on the command line If your system cannot provide the r

ASReml User Guide - VSN International

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