Home

Manual for SIENA version 1.98

1. 10 5 where pm A s and pm A s represent respectively the rate at which an actor of cur rent out degree s increases or decreases his out degree by 1 The parameter pm is a multiplicative effect of the observation period Function xi is called the distributional tendency function and is represented accord ing to Snijders 2003 formula 17 by amp s exp a azlog s 1 2 where the names given in SIENA are e a out degrees effect e ay logarithmic out degree effect e a3 factorial out degree effect The reasons for these names and interpretation of the effects can be found in Snijders 2003 To the exponent also effects of actor covariates can be added The so called volatility function v nu is defined as ue a Also to this exponent effects of actor covariates can be added Exponential random graph distribution The exponential random graph distribution which is used if there is only one observation is defined by the probability function Po X z exp 6 u x 9 where u x is a vector of statistics The following statistics are available Note that SIENA will note whether the observed graph 2 is symmetric or not and choose accordingly between the statistics for undirected and directed graphs Formulas for effects Title Page Page 42 of 60 Sisan PEN Bie 10 11 IL For undirected graphs the number of edges gt i lt j Tij
2. part of the gratification function The usual order of importance of these effects is 3 is most important then 1 and 2 then 4 and 5 For each dyadic covariate three effects can be included in the model 5 f Title Page 1 the effect in the objective function 2 the interaction effect of this covariate with reciprocity part of the objective function 3 the effect on dissolution of relations part of the gratification function Page 14 of 60 The first of these three is usually the most important Full Screen 4 2 Model Type The Model Type is part of what is specified in the advanced options as the Model Code This distinguishes between the model of Snijders 2001 Model Type 1 and that of Snijders 2003 Model Type 2 In the latter model the decisions by the actors to increase or decrease their number of outgoing ties are determined on the basis of only their current degree the probabilities of increasing or decreasing the out degree are expressed by the distributional tendency function indicated in the output as zi and the volatility function v indicated as nu Which new tie to create or which existing tie to withdraw depends in the usual way on the objective and gratification functions Thus the outdegree distribution is governed by parameters that are not connected to the parameters for the structural dynamics The use of such an approach in statistical modeling minimizes the influence of the ob
3. One should be aware however that such a data driven approach leads to fa gt capitalization on chance Since the selected effects were chosen on the basis of the large ee Eee deviation between observed and expected values the t tests based on the same data set Page 26 of 60 6 9 E 4 Page 26 of 60 will tend to give significant results too easily _ The generated statistics for each run are also written to the file pname sdt sdt for GoBack simulation data so you can inspect them also more precisely This file is overwritten each time you are simulating again A brief history of what the program does is again FullScreen e written to the file pname log me E 6 1 Conditional and unconditional simulation The distinction between conditional and unconditional simulation is the same for the sim ulation as for the estimation option of SIENA If the conditional simulation option was chosen which is the default and the simu lations do not succeed in achieving the condition required by its stopping rule see Sec tion 5 3 3 then the simulation is terminated with an error message saying This distance is not achieved for this parameter vector In this case you are advised to change to uncon ditional simulation Simulation Title Page 7 One observation exponential random graph models By choosing only one observation moment the user specifies that not a model for network evolution is studied bu
4. Rate parameter 5 4292 0 6920 Other parameters 1 f density out degree O T648 EO 295 2 reciprocity 2m0 Gu O 55119 3 f number of distances 2 Ot Om Gu O oe Or7p The rate parameter is the parameter called p in section 10 2 below The value 5 4292 indicates that the estimated number of changes per actor i e changes in the choices made by this actor as reflected in the row for this actor in the adjacency matrix between the two observations is 5 43 rounded in view of the standard error 0 69 Note that this refers to unobserved changes and that some of these changes may cancel make a new choice and then withdraw it again so the average observed number of differences per actor will be somewhat smaller than this estimated number of unobserved changes The other three parameters are the weights in the objective function The terms in the Title Page objective function in this model specification are the density effect defined as s in section 10 1 the reciprocity effect s 2 and the number of distances 2 indirect relations effect defined as s 5 Therefore the estimated objective function here is Page 21 of 60 Sisan 0 76 sii x 2 31 si2 x 0 59 515 x f The standard errors can be used to test the parameters For the rate parameter testing the hypothesis that it is 0 is meaningless because the fact that there are differences between the two observed networks implies that the rate of change must be pos
5. thereby reading the basic information file Data description is carried out by SIENA02 EXE which executes Describe In the StOCNET operation the model specification is carried out by StOCNET changing the mo3 file and then running SIENA04 EXE SIENA04 EXE reads the mo3 file and writes the corresponding mo2 and mo4 files If you change pname mo3 by an text editor outside of StOCNET it is advisable to run SIENA04 EXE before proceeding The simulation is carried out by SIENA05 EXE which executes Simulate The estimation is carried out by executing SIENA07 EXE which executes Estimate Some essential procedures Unit S_BASE contains the simulation procedures The main procedures in this unit are the following 1 Function FRAN which generates the required statistics and is called by procedure Simulate in S_SIM and by Estimate in S_EST 2 Procedure Statistics which calculates the statistics from a generated network or adjacency matrix and which is called by FRAN 3 Procedure Runepoch which generates a random network for given parameter values and a given initial situation by simulating the actor oriented evolution model for one period between two observations This procedure is called by procedure FRAN 4 Procedure Runstep which makes one stochastic step according to the actor oriented evolution model i e it choosed stochastically one entry i j of the adjacency matrix to be changed This procedure is called by procedure Runepoc
6. 2002 For this model the estimation procedure does not always perform satisfactorily for reasons described in Snijders 2002 and investigated further in Snijders and van Duijn 2002 This manual is about SIENA version 1 98 February 2003 The program and this manual can be downloaded from the web site http stat gamma rug n stocnet The best way to run SIENA is as part of the StOCNET program collection Boer Huisman Snijders amp Zeggelink 2003 which can also be downloaded from this website For the operation of StOCNET the reader is referred to the corresponding manual If desired SIENA can be operated also independently of StOCNET This manual consists of two parts the user s manual and the programmer s manual There are two parallel pdf versions s_man_s pdf for screen viewing and s_man_p pdf for printing They were made with the ATpX pdfscreen sty package of C V Radhakrishan iA which made it possible e g to insert various hyperlinks within the manual Both versions gt can be viewed and printed with the Adobe Acrobat reader This is the screen version Note RE a that section numbering may differ between the two versions Page 2 of 60 e 1This program was first presented at the International Conference for Computer Simulation and the l Social Sciences Cortona Italy September 1997 which originally was scheduled to be held in Siena See Full Screen e Snijders amp van Duijn 1997 The background pictu
7. 832 842 Geyer C J and E A Thompson 1992 Constrained Monte Carlo maximum likelihood for dependent data Journal of the Royal Statistical Society ser B 54 657 699 Huisman M E and T A B Snijders 2003 Statistical analysis of longitudinal network data with changing composition Submitted for publication Snijders T A B 2001 The statistical evaluation of social network dynamics Pp 361 395 in Sociological Methodology 2001 edited by M E Sobel and M P Becker Boston and London Basil Blackwell Snijders T A B 2002 Markov Chain Monte Carlo Estimation of Exponential Random Graph Models Journal of Social Structure Vol 3 2002 No 2 ae Available from http www2 heinz cmu edu project INSNA joss index1 html Snijders T A B 2003 Accounting for Degree Distributions in Empirical Analysis of Network Dynamics Proceedings of the National Academy of Sciences USA to be published Available from http stat gamma rug nl snijders siena html gt Snijders T A B and M A J Van Duijn 1997 Simulation for statistical inference in dynamic Page 59 oF 60 network models Pp 493 512 in Simulating Social Phenomena edited by R Conte R l Hegselmann and P Terna Berlin Springer GoBack Snijders T A B and van Duijn M A J 2002 Conditional maximum likelihood estimation under various specifications of exponential random graph models Full Screen e Pp 117 134 in Jan Hagberg ed Contribu
8. Duijn 1997 This defines a linear function of the out degree parametrized in such a way that it is necessarily positive For a general dependence on the out degree in degree and number of reciprocated relations one can use an average of such terms the second and third one depending in the analogous way on 74 and Zir respectively 10 3 Gratification function The gratification function denoted g in Snijders 2001 is the way of modeling effects which operate in different strengths for the creation and the dissolution of relations The potential effects in this function are the following 1 J1 tij tji indicator of a reciprocated relation a negative value of 7 reflects the costs associated with breaking off a reciprocated relation 2 y2 1 Tij X p ZihTnj the number of actors through whom 1 is indirectly related to j a positive value of y2 reflects that it is easier to establish a new tie to another actor j if i has many indirect ties to j via others who can serve as an introduction 3 73 Zij Wij the value w for another actor to whom 7 has a tie e g a negative value of 73 reflects the costs for i associated with breaking off an existing tie to other actors j with a high value for wij 10 4 Rate function for Model Type 2 For Model Type 2 see Section 4 2 the rate function is defined according to Snijders 2003 by v s 1 aiaa ale sae 4 Tih Formulas for effects Title Page Page 41 of 60 Sisan
9. Snijders 2001 The results were obtained in an independent repetition of the estimation for this data set and this model specification since the repetition was independent the results are slightly different illustrating the stochastic nature of the estimation algorithm Title Page Page 18 of 60 e rsen Pee oe 1 Convergence check In the first place a convergence check is given based on phase 3 of the algorithm This check considers the deviations between simulated values of the statistics and their observed values the latter are called the targets Ideally these deviations should be 0 Because of the stochastic nature of the algorithm when the process has properly converged the deviations are small but not necessarily exactly 0 The program calculates the averages and standard deviations of the deviations and combines these in a t statistic in this case average divided by standard deviation For longitudinal modeling convergence is excellent when these t values are less than 0 1 in absolute value good when they are less than 0 2 and satisfactory when they are less than 0 3 The corresponding part of the output is the following Total of 1857 iterations Parameter estimates based on 1357 iterations basic rate parameter as well as covariance and derivative matrices based on 500 iterations Information for convergence diagnosis Averages standard deviations and t statistics for deviations from targ
10. a constant rate function indicated in the screen as the basic rate parameter without additional rate function effects e gratification function Advice start modeling without a gratification function THAE FEGE The output file contains a list of all available effects given after the report of the data input In addition the model specification comprises the current parameter values and the Model Type see Section 4 2 After data input the constant rate parameter and the density effect in the objective function have default initial values depending on the data GoBack All other parameter values initially are 0 The estimation process changes the current value of the parameters to the estimated Full Screen e values Values of effects not included in the model are not changed by the estimation n Page 13 of 60 It is possible for the user to change parameter values and to request that some of the parameters are fixed in the estimation process at their current value 4 1 Effects associated with covariates Model specification For each individual covariate five effects can be included in the model 1 the effect on the actor s activity in the objective function out degree 2 the effect on the actor s popularity in the objective function in degree the dissimilarity effect in the objective function the effect on the rate of change of the actor CUS Sec the dissimilarity effect on dissolution of relations
11. files even for observation times where the actor is not a part of the network e g when the actor did not yet join or the actor already left the network In other words the adjacency matrix for each observation time has dimensions n x n Input data Title Page Page 9 of 60 Full Screen on At these times where the actor is not in the network the entries of the adjacency matrix can be specified in two ways First as missing values using missing value code s In the estimation procedure these missing values of the joiners before they joined the network are regarded as 0 entries and the missing entries of the leavers after they left the network are fixed at the last observed values This is different from the regular missing data treatment Note that in the initial data description the missing values of the joiners and leavers are treated as regular missing observations This will increase the fractions of missing data and influence the initial values of the density parameter A second way is by giving the entries a regular observed code representing the absence or presence of an arc in the digraph as if the actor was a part of the network In this case additional information on relations between joiners and other actors in the network before joining or leavers and other actors after leaving can be used if available Note that this second option of specifying entries always supersedes the first specification if a valid code nu
12. i is tied 8i7 2 DL Haj Oj Se De A out degree up to c where c is some constant defined by sig x max Zi square root out degree cx o d where c is some constant defined by Sig x Ti CTi where c is chosen to diminish the collinearity between this and the density effect squared out degree c where c is some constant defined by si1o zi where c is chosen to diminish the collinearity between this and the density effect Formulas for effects Title Page Page 38 of 60 Sisan 11 number of 3 cycles i11 2 a Lig Ljh Thi The constants c can be chosen and changed by the user The main effect for a dyadic covariate w is 12 covariate centered defined by the sum of the values of w for all others to whom i is tied 412 2 Dy Tij Wij W where w is the mean value of wy For each actor dependent covariate vj recall that these are centered there are three potential effects in the objective function indicated in the following list 13 14 15 covariate related popularity defined by the sum of the covariate over all actors to whom i has a tie Si13 J j Tij vj covariate related activity defined by it s out degree weighted by his covariate value Si14 2 v Ti covariate related dissimilarity defined by the sum of absolute covariate differences between 7 and the others to whom he is tied sns 2 X zig lv v
13. is rn 2d 1 d where r is a constant which can be changed in the advanced options and called Run length in the advanced options screen n is the number of actors and d is the density of the graph truncated to lie between 0 05 and 0 95 The default value of r is 10 This value can be increased when it is doubted that the run length is sufficient to achieve convergence of the MCMC algorithm Exponential random Title Page Page 29 of 60 rsen 8 Advanced options There are some advanced options available in Siena The main advanced options determine the following il 2 There is a choice between conditional and unconditional simulation and estimation The use of standard initial values suitable estimates for the density and reciprocity parameters and zero values for all other parameters rather than the default use of the current parameter values as initial values for estimating new parameter values The Model Code This defines the Model Type and an associated output option The meaning of this code is Model Code 1 Model Type 1 default output Model Code 2 Model Type 2 extra output for evaluating the fit of the out degree distribution Model Code 3 Model Type 1 extra output for evaluating the fit of the out degree distribution The number of subphases in phase 2 of the estimation algorithm This determines the precision of the estimate Advice 3 for quick preliminary inves tigations 4 or 5
14. network effects reciprocity transitivity etc to get an impression of what the network looks like and later add effects of covariates Fixing parameters Sometimes an effect must be present in the model but its precise numerical value is not well determined E g if the network at time t would contain only reciprocated choices then the model should contain a large positive reciprocity effect but whether it has the value 3 or 5 or 10 does not make a difference This will be reflected in the estimation process by a large estimated value and a large standard error a derivative which is close to 0 and sometimes also by lack of convergence of the algorithm This type of problem also occurs in maximum likelihood estimation for logistic regression and certain other generalized linear models see Geyer and Thompson 1992 Section 1 6 and Albert and Anderson 1984 In such cases this effect should be fixed to some large value and not left free to be estimated This can be specified in the model specification under the Advanced button As another example when the network observations are such that ties are formed but not dissolved some entries of the adjacency matrix change from 0 to 1 but none or hardly any change Getting started Title Page EEEH 3 a a an 9 1 2 from 1 to 0 then it is possible that the density parameter must be fixed at some high positive value Exploring which effects to include For an expl
15. project using mol mo3 and data files 2 S_BASE contains the basic model definition and procedures to write mo2 and mo4 files 3 S_SIM contains the procedure for straight simulation 4 S_EST contains the procedure for estimation 5 S_DESC contains procedures for data description Then there is an intermediate unit 6 S START contains the procedure ReadWriteData to start a project by reading the pname in file and the initial data files and writing the internally used files It uses only S_DAT Since S_START was programmed so that it uses only S_DAT it does not contain the default parameters included in some of the effects and it writes only files mol and mo3 not mo2 and mo4 Procedure ReadWriteData from S_START therefore must be followed always by procedure BeforeFirstModelDefinition from S_BASE This writes files mo2 and mo4 Further there are three units containing specific kinds of utilities Page 55 oF 60 7 SLIB is a library of various computational and input output utilities GoBack 8 RANGEN is a library for generation of random variables It uses the URNS suite for random numbers generation Full Screen e 9 EIGHT is a unit for storing te data Its name was chosen for historical reasons Close Units and executable files Title Page 15 1 15 2 Executable files The basic data input is carried out by executing SIENAO1 EXE This program executes ReadWriteData and BeforeFirstModelDefinition
16. specification SIENA05 EXE for simulations with fixed parameter values iS Se SIENAO7 EXE for parameter estimation In these executable programs the project name must be given in the command line e g SEENA POZNE SIENAO1 bunt if bunt is the name of the project and there exists a bunt in file This bunt is called a command line parameter There are the following three ways to specify a command with a command line parameter in Windows The command line can be given at the DOS prompt in a Windows environment it can be given in the Windows Run command for Windows 98 and higher and it can be indicated in the target in the properties of a shortcut UUES Page 46 of 60 Sisan 13 SIENA files Internally the following files are used Recall that pname is the name of the project which the user can choose at will 13 1 Basic information file The basic information file is called pname in and contains the definition of the numbers of cases and variables the names of the files in which data are initially stored and their codes and the names of the variables This file is written by StOCNET when the data are defined and can also be written by any text editor that can produce ASCII files It is read by SIENAO1 EXE It must have the following contents 1 First a line with six numbers number of observations 2 or more denoted by M of the network SIENA files number of vertices denoted further by n
17. If there are problems in reading the basic input file delete blanks that may be present after the last number in the lines containing the codes See to it that the basic input file is an ASCII text file with numbers separated by blanks lines separated by hard returns Title Page Page 48 of 60 tse An example for the basic input file is the following This refers to data files that are included with the program collected by Gerhard van de Bunt This example which contains a file with three covariates is used in van de Bunt 1999 and in van de Bunt van Duijn and Snijders 1999 232 OOO vrnd32t2 dat ib PES si tg vrnd32t4 dat T2 D vars dat 3 gender program smoke The basic data input is carried out by executing SIENA01 EXE This programs reads the basic information file Some preliminary output is given in the pname out file SIENA files Title Page Disan 13 2 13 3 Definition files The program writes and reads for internal use the following four definition files e pname mol Defines numbers of actors and variables and variable names e pname mo2 Defines names of effects e pname mo3 Defines model specification and parameter values e pname mo4 Contains parameter values and names The four pname mox files are read in a format where certain lines are skipped entirely and other lines are skipped after reading a certain number These skipped parts are between square brackets Th
18. Manual for SIENA version 1 98 Tom A B Snijders Mark Huisman ICS Department of Sociology Grote Rozenstraat 31 9712 TG Groningen The Netherlands t a b snijders ppsw rug nl February 6 2003 Abstract SIENA for Simulation Investigation for Empirical Network Analysis is a computer pro gram that carries out the statistical estimation of models for the evolution of social networks according to the dynamic actor oriented model of Snijders 2001 2003 It also carries out MCMC estimation for the exponential random graph model according to the procedures described in Snijders 2002 This manual gives some information about SIENA version 1 98 We are grateful to Peter Boer and Evelien Zeggelink for their cooperation in the development of the StOCNET and SIENA programs Sisan 1 General information General information SIENA for Simulation Investigation for Empirical Network Analysis is a computer program that carries out the statistical estimation of models for repeated measures of social net works according to the dynamic actor oriented model of Snijders and van Duijn 1997 and Snijders 2001 Some examples are presented in van de Bunt 1999 and van de Bunt van Duijn and Snijders 1999 The program also carries out MCMC estimation for the exponential random graph model also called p model of Frank and Strauss 1986 Frank 1991 and Wasserman and Pattison 1996 This procedure is described in Snijders
19. and then either want to check again whether the statistics used for estimation have expected values very close to their observed values or want to compute expected values of other statistics The statistics to be simulated can be specified in a special screen in StOCNET The number of runs is set at a default value of 1 000 and can be changed in the advanced options The user can break in and terminate the simulations early The output file contains means variances covariances and correlations of the selected statistics The output file also contains t statistics for the various statistics these can be regarded as tests for the simple null hypothesis that the model specification with the current parameter values is correct The simulation feature can be used in the following way Specify a model and esti mate the parameters After this estimation supposing that it converged properly add a number of potential effects This number might be too large for the estimation algo rithm Therefore do not Estimate but choose Simulate instead The results will indicate which are the statistics for which the largest deviations as measured by the t statistics occurred between simulated and observed values Now go back to the model specification and return to the specification for which the parameters were estimated earlier The ef Simulation fects corresponding to the statistics with large t values are candidates for now being added iA to the model
20. are constant within SIENA runs but can be changed by the user If you change a constant in the pname mo3 file you must run SIENA04 EXE to get the correct corresponding pname mo2 and pname mo4 files The end of the pname mo3 file contains specifications of various estimation options Most of these are accessible in StOCNET e g through the advanced options mentioned above in Section 8 The consecutive options are the following 1 Estimation method 0 for unconditional 1 for conditional estimation for exponential random graphs another available option is to include incidental vertex parameters 10 for unconditional 11 for conditional estimation with incidental vertex parameters SIENA files 2 Initial value for estimation 0 current value 1 standard Standard means that a good starting value is chosen for the density effect and in the one observation exponential random graph case also for the reciprocity effect the other effects then have a 0 0 starting value 3 A code for the type of model ds For longitudinal data this is the Model Code described in the section on advanced options s z 3 For exponential random graph models this code defines the steps used in the one Page 51 of 60 observation case for simulating a random di graph see also the description above J 1 Gibbs steps for single relations GoBack 2 Gibbs steps for dyads 3 Gibbs steps for triplets Full Screen e 4 Metropolis Hastings steps for single r
21. ber All code numbers must be in the range from 0 to 9 This implies that if the data are already in 0 1 format the single code number 1 must be given As another example if the data matrix contains values 1 to 5 and only the values 4 and 5 are to be interpreted as present arcs then the code numbers 4 and 5 must be given Code numbers for missing numbers also must be indicated These must of course be different from the code numbers representing present arcs Dyadic covariates Each dyadic covariate also must be contained in a separate input file with a square data matrix i e n lines each with n integer numbers separated by blanks each line ended by a hard return The diagonal values are meaningless but must be present The reasons for restricting dyadic covariates to integer values from 0 to 255 has to do with how the data are stored internally If the user wishes to use a dyadic covariate with a different range this variable first must be transformed to integer values from 0 to 255 E g for a continuous variable ranging from 0 to 1 the most convenient way probably is to multiply by 100 so the range becomes 0 100 and round to integer values In the present implementation this type of recoding cannot easily be carried out within StOCNET but the user must do it in some other program Input data Title Page el gt rr Ls a e 3 3 Individual covariates Individual i e actor bound covariates can be combined
22. d where d is the mean of all v v values The interaction effect of a dyadic covariate w with reciprocity is 16 covariate centered defined by the sum of the values of wij for all others to whom i is tied sielt D1 Tij Tji Wij W where w again is the mean value of wy Formulas for effects Title Page Page 39 of 60 rsen 10 2 Rate function The rate function lambda is defined for Model Type 1 which is the default Model Type as a product Vi p a m Ai i2 i3 of factors depending respectively on period m actor covariates and actor position see Snijders 2001 p 383 The corresponding factors in the rate function are the following 1 The dependence on the period can be represented by a simple factor i Pm Formulas for effects for m 1 M 1 If there are only M 2 observations the basic rate parameter is called p 2 The effect of actor covariates with values vp can be represented by the factor Ai exp gt Qh Uhi h 3 The dependence on the position of the actor can be modeled as a function of the actor s out degree in degree and number of reciprocated relations Define these by Ti Deis Ti Sie Li r Sissi 3 Jj J recalling that zi 0 for all i Denoting the corresponding parameter by a the dependence on the out degree is represented by toe mer Tag erp Title Page This formula is motivated in Snijders and Van
23. d something like 5 parameters the estimation process takes a few minutes on a fast PC The number of actors n should not give a problem up to say 200 For large data sets and models the estimation process may take more minutes up to several hours Section 16 indicates the constants in the program that define limitations for the data sets used Limitations and time use Title Page rt scue Part II Programmer s manual The programmer s manual will not be important for most users It is intended for those who wish to run SIENA outside of the StOCNET environment for those who want to know what all the pname files are all about and for those who want to have a look inside the source code The program consists of a basic computation part programmed by the author in Turbo Pascal and Delphi and the StOCNET windows shell programmed by Peter Boer in Delphi with first Evelien Zeggelink and then Mark Huisman as the project leader The computa tional part can be used both directly and from the windows shell The StOCNET windows shell is much easier for data specification and model definition Limitations and time use Title Page Sisan 12 Executable programs The present computational part is composed of 4 executable programs The programs are 1 SIENAO1 EXE for the basic data input using an existing basic information file see below 2 SIENA02 EXE for data description SIENA04 EXE for confirmation of the model
24. eir purpose is to give information to the human reader about the meaning of the lines Note however that SIENA does not check for the brackets but skips information on the basis of line numbers and reading numerical information File pname mol is written at the initial project definition and not changed further Files pname mo2 and pname mo4 are used for model specification and converted internally to pname mo3 All these files must correspond they contain some overlapping information File pname mo3 is read and changed in the computational part of SIENA Model specification through the mo3 file To change the model specification outside the StOCNET shell you can change the pname mo3 file by an ASCII text editor In this way you can used advanced SIENA options which are not yet available through StOCNET whether such options exist will depend on the versions of SIENA and StOCNET When looking at the pname mo3 file with some good will you can see that this file contains lines corresponding to the various effects each line has a 0 1 entry denoting that the effect is excluded included another 0 1 entry denoting that the effect is not fixed or SIENA files Title Page P10 a a fixed during the estimation process and the value of the parameter For effects in the objective function also a 0 1 entry indicates if the effect contains a constant parameter value if so this parameter value also is included Such parameters
25. elations 5 Metropolis Hastings steps for dyads in which symmetric dyads remain symmetric Close and asymmetric dyads remain asymmetric appropriate for undirected graphs and for tournaments i e antisymmetric graphs 6 Metropolis Hastings steps conditional on in degrees and out degrees To each of these values the number 10 may be added so the values become 11 16 In that case a continuous chain is used i e the last generated graph is used as the intial value in the MCMC sequence for simulating the next graph Otherwise i e for the values 1 6 the initial value is an independently generated random graph A number r proportional to the number of steps used for generating one graph in the one observation case The number of steps is r n 2d 1 d where n is the nunber of actors and d is the observed density of the graph if the observed density is less than 05 or more than 95 the value d 05 is used The number of subphases in phase 2 of the estimation algorithm advice 4 The number of phase 3 iterations for the estimation algorithm advice 500 for lon gitudinal data 1000 for modeling one observation data by an exponential random graph The initial value of the gain parameter in the estimation algorithm advice 0 1 The default number of simulations for straight simulation advice 1000 SIENA files Title Page Preset Disan 13 4 Data files After the initial project defini
26. ets Ae 07236 7 006 0 034 2 0 204 7 059 0 029 She Sabo 22 242 9 072 Good convergence is indicated by the t statistics being close to zero In this case the t statistics are 0 034 0 029 and 0 072 which is less than 0 1 in absolute value so the convergence is excellent In data exploration if one or more of these t statistics are larger in absolute value than 0 3 it is advisable to restart the estimation process For results that are to be reported it is advisable to carry out a new estimation when one or more of the t statistics are larger in absolute value than 0 1 Large values of the averages and standard deviations are not at all a reason for concern Estimation Title Page Soare a a For the exponential random graph or p model the convergence of the algorithm is more problematic than for longitudinal modeling A sharper value of the t statistics must be found before the user may be convinced of good convergence It is advisable to try and obtain t values which are less than 0 15 If even with repeated trials the algorithm does not succeed in producing t values less than 0 15 then the estmation results are of doubtful value Estimation Title Page 2 Parameter values and standard errors The next crucial part of the output is the list of estimates and standard errors For this data set and model specification the following result was obtained 3 Estimates and standard errors Estimation 0
27. files used are the two networks vrnd32t2 dat vrnd32t4 dat The networks are coded as 0 unknown 1 best friend 2 friend 3 friendly relation 4 neutral 5 troubled relation 6 item non response 9 actor non response In the Transformations screen of StOCNET choose the values 1 2 3 as the values to be coded as 1 for the first as well as the second network Choose 6 9 as missing data codes The actor attributes are in the file vars dat Variables are respectively gender 1 F 2 M program and smoking 1 yes 2 no See the references mentioned above for further information about this network and the actor attributes Specify the data in StOCNET by using subsequently the Data Transformation and Model menus do not forget to click Apply when finishing each of these parts and then choose the Specifications button in the Model menu You will be requested to make some choices for the specification the meaning of which should be clear given what is explained above In the specification of the rate function choose a constant rate in the specification of the objective function choose the out degree effect the reciprocity effect and one other effect In the specification of the gratification function choose no effects at all Leave the specification of the rate function as it is see Getting started Title Page Section 4 in which it was advised to start modeling with a constant rate function Then le
28. for directed graphs the number of arcs 7j4 Vij The number of reciprocated relations Vij Uji The number of out twostars X X pcp Tih Tik The number of in twostars J pcp Uni Tki The number of two paths mixed twostars 57 gt gt fk Thi Lik For undirected graphs the number of transitive triads SS igh Vij Lih Ljh for directed graphs the number of transitive triplets J p Vij Tin jh The number of three cycles ign Tij jh Thi For each dyadic covariate wij the sum Tij Wij For each dyadic covariate w the associated reciprocity effect defined by Doig Tij Zji Wij For each individual covariate v changing or constant recall that all covariates are centered three effects are included The first is the v related popularity effect 57 744 vi next is the v related activity effect X xi4 vi finally the v related dissimilarity effect J i lt Vij v v d where d is the mean of all v vj values Formulas for effects Title Page Page 43 of 60 rt scue 11 Limitations and time use The estimation algorithm being based on iterative simulation is time consuming The time needed is approximately proportional to p2n C where p is the number of parameters n is the number of actors the power a is some number between 1 and 2 and C is the number of relations that changed between time m and time m 1 summed over m 1 to M 1 For data sets with 30 to 40 actors an
29. for serious estimations The number of runs in phase 3 of the estimation algorithm This determines the precision of the estimated standard errors and covariance matrix of the estimates and of the t values reported as diagnostics of the convergence Advice 200 for preliminary investigations when precise standard errors and t values are not important 500 or 1000 for serious estimations The initial gain value which is the step size in the starting steps of the Robbins Monro procedure indicated in Snijders 2001 by ay Advanced options Title Page Page 30 of 60 Pons Sisan Pee a 7 The number of runs in the straight simulations Advice the default of 1000 will usually be adequate These options are used through StOCNET in the Advanced window of the Estimation spec ification For one observation moment where SIENA tries to estimate parameters of an exponen tial random graph model the Model Code defines the kind of steps made in the MCMC algorithm Further there is in this case an additional advanced option Advanced options 8 The multiplication factor r for the run length used in the MCMC algorithm Title Page rsen 9 Getting started For getting a first acquaintance with the model one may use the data set collected by Gerhard van de Bunt discussed extensively in van de Bunt 1999 and van de Bunt van Duijn and Snijders 1999 The data files are provided with the program The digraph data
30. h Units and executable files Title Page P10 a a 5 Procedure ChangeTie which called at the end of procedure RunStep carries out the required change of the adjacency matrix and the associated updates of various statistics 6 Function Lambda which is the rate function for each actor and is used in procedure Runstep For Model Type 2 it uses functions xi and nu 7 Function contr_f which defines the contribution sin x of each given effect h to the objective function and is used in procedure Runstep 8 Function contr_g which defines the contribution of each given effect to the gratifica tion function and is also used in procedure Runstep In unit S_EST the Robbins Monro algorithm is contained in the procedure POLRUP for Polyak Ruppert see Snijders 2001 Units and executable files Title Page rt scue 16 Constants The program contains the following constants Trying to use a basic information file that implies a data set going beyond these constants leads to an error message in the output file and stops the further operation of SIENA name meaning in unit nmax maximum number n of actors EIGHT nrg maximum array size for random number generation RANGEN pmax maximum number p of included effects SLIB ccmax maximum number of possible statistics SLIB nzmax maximum number nz of individual covariates EIGHT nzzmax maximum number nzz of dyadic covariates EIGHT The constant individual c
31. hanging to Model Type 2 see Section 4 2 Getting started Title Page Page 34 of 60 Pons rsen Pee oe 9 2 Convergence problems If there are convergence problems this may have several reasons e The data specification was incorrect e g because the coding was not given properly e The starting values were poor Try restarting from the default values calculated at the initial data input a certain non zero value for the density parameter and zero values for the other parameters or from values obtained as the estimates for a simpler model that gave no problems You can obtain the initial default parameter values by choosing the advanced option standard initial values When starting estimations with Model Type 2 see Section 4 2 there may be some problems to find suitable starting values For Model Type 2 it is advised to start with unconditional estimation see the advanced options and a simple model and to turn back to conditional estimation using the current parameter values as initial estimates for new estimation runs only when satisfactory estimates for a simple model have been found Getting started e Too many weak effects are included Use a smaller number of effects delete non significant ones and increase complexity step by step Retain parameter estimates from the last simpler model as the initial values for the new estimation procedure provided for this model the algorithm converged withou
32. he other strongly correlated effect It is possible that the standard error of the retained effect becomes much smaller by omitting the other effect which can also mean a change of the t test from non sigificance to significance Estimation Title Page Prete Sisan 5 3 5 3 1 5 3 2 Other remarks about the estimation algorithm Changing initial parameter values for estimation When you wish to change initial parameter values for running a new estimation procedure this can be done in StOCNET as an advanced option Automatic fixing of parameters If the algorithm encounters computational problems sometimes it tries to solve them au tomatically by fixing one or more of the parameters This will be noticeable because a parameter is reported in the output as being fixed without your having requested this This automatic fixing procedure is used when in phase 1 one of the generated statistics seems to be insensitive to changes in the corresponding parameter This is a sign that there is little information in the data about the precise value of this parameter when considering the neighborhood of the initial parameter values However it is possible that the problem is not in the parameter that is being fixed but is caused by an incorrect starting value of one of the other parameters When the warning is given that the program automatically fixed one of the parameter try to find out what is wrong In the first place chec
33. idual covari ates the grand mean is calculated stored and subtracted during the program calculations Thus dyadic covariates are treated by the program differently than individual covariates in the sense that the mean is subtracted at a different moment but the effect is exactly the same The formula for balance is a kind of dissimilarity between rows of the adjacency matrix The mean dissimilarity is subtracted in this formula and also reported in the output This mean dissimilarity is calculated by a formula given in Section 10 Title Page Page 12 of 60 sou 4 Model specification After defining the data the next step is to specify a model In StOCNET this is done by going to the Model menu defining the two or more networks to be used as the repeated observations of the evolving network possibly choosing one or more dyadic covariates and Model specification possibly a file with actor attributes clicking first on the Apply button and then clicking on the Specifications button The model specification consists of three kinds of effects see Snijders 2001 e objective function This is the main focus of model selection The objective function normally should always contain the density or out degree effect to account for the observed density It is also advisable usually to include the reciprocity effect this being one of the most fundamental network effects e rate function Advice start modeling with
34. in one or more files If there are k covariates in one file then this data file must contain n lines with on each line k numbers which all are read as real numbers i e a decimal point is allowed The numbers in the file must be separated by blanks and each line must be ended by a hard return A distinction is made between constant and changing covariates which refers to changes over time Each constant covariates has one value per actor valid for all observation mo ments Changing covariates can change between observation moments but are assumed to have constant values from one observation moment to the next If observation moments for the network are tj tg t 7 then the changing covariates should refer to the M 1 moments t through tm and the m th value of the changing covariates is assumed to be valid for the period between moment tm and moment t 41 Changing covariates are meaningful only if there are 3 or more observation moments Each changing covariate must be given in one file containing k M 1 variables The mean is always subtracted from the covariates See the section on Centering below Input data Title Page Page 8 of 60 Sarsan 3 4 Missing data 3 5 Missing data are not allowed in the covariate data In the network data it is allowed that there are some missing data These must be indicated by a missing data code not by blanks in the data set In the current implementation of SIENA miss
35. ing data are treated in a simple way trying to minimize their influence on the estimation results The simulations are carried out over all actors Missing data are treated separately for each period between two consecutive observations of the network In the initial observation for each period missing entries in the adjacency matrix are set to 0 In the course of the simulations however these values are allowed to become 1 For the calculation of the statistics used for the parameter estimation and the simulations if a given element is missing in the adjacency matrix for the observation at the start and or the observation at the end of this period this element in set to 0 in both of these observations Composition change SIENA can also be used to analyze networks of which the composition changes over time because actors join or leave the network between the observations as described in Huisman and Snijders 2002 For this case a data file is needed in which the times of composition change are given For networks with constant composition no entering or leaving actors this file is omitted and the current subsection can be disregarded Network composition change due to actors joining or leaving the network is handled separately from the treatment of missing data The digraph data files must contain all actors who are part of the network at any observation time denoted by n and each actor must be given a separate and fixed line in these
36. itive The weights in the objective function can be tested by t statistics defined as estimate divided by its standard error Do not confuse this t test wth the t test for checking convergence these are completely different although both are t ratios Here the t values are respectively 0 7648 0 2957 2 59 2 3071 0 5319 4 34 and 0 5923 0 1407 4 21 Since these are larger than 2 in absolute value all are significant at the 0 05 significance level It follows that there is evidence that the actors have a preference for reciprocal relations and for networks with a small number of other actors at a distance 2 The value of the density parameter is not very important it is important that this parameter is included to control for the density in the network but as all other statistics are correlated with the density the density is difficult to interpret by itself When for some effects the parameter estimate as well as the standard error are quite large say when both are more than 2 and certainly when both are more than 5 then it is possible that this indicates poor convergence of the algorithm in particular it is possible that the effect in question does have to be included in the model to have a good fit but the precise parameter value is poorly defined hence the large standard error and the significance of the effect cannot be tested with the t ratio This can be explored by estimating the model without this parameter and also with
37. k that your data were entered correctly and the coding was given correctly and then respecify the model or restart the estimation with other e g 0 parameter values Sometimes starting from different parameter values e g the default values implied by the advanced option of standard initial values will lead to a good result Sometimes however it works better to delete this effect altogether from the model It is also possible that the parameter does need to be included in the model but its precise value is not well determined Then it is best to give the parameter a large or strongly negative value and indeed require it to be fixed see section 9 1 Estimation Title Page Page 24 of 60 a rsen Pee a 5 3 3 5 3 4 Conditional and unconditional estimation SIENA has two methods for estimation and simulation conditional and unconditional They differ in the stopping rule for the simulations of the network evolution In unconditional estimation the simulations of the network evolution in each time period carry on until the predetermined time length chosen as 1 0 has elapsed In conditional estimation the simulations run on until the number of different entries between the initially observed network of this period and the simulated network is equal to the number of entries in the adjacency matrix that differ between the initially and the finally observed networks of this period Conditional means here co
38. mber is specified this will always be used For joiners and leavers crucial information is contained in the times they join or leave the network i e the times of composition change which must be presented in a separate input file This data file must contain n lines each line representing the corresponding actor in the digraph files with on each line four numbers The first two concern joiners the last two concern leavers 1 the last observation moment at which the actor is not yet observed 2 the time of joining expressed as a fraction of the length of the period 3 the last observation moment at which the actor is observed 4 the time of leaving also expressed as a fraction Also actors who are part of the network at all observation moments must be given values in this file In the following example the number of observation moments is considered to be M 5 which means there are four periods period m starts at observation moment m and ends at m 1 for m 1 2 4 M 1 Input data Title Page A imoa Pons Disan a Example of file with times of composition change Present at all five observation times Oy OKO Joining in period 2 at fraction 0 6 of length of period 2 06 5 0 0 Leaving in period 3 at fraction 0 4 of length of period 0 1 0 3 0 4 Input data Joining in per 1 0 7 and leaving in per 4 0 2 i We 4 Ow Leaving in per 2 0 6 and joining in per 3 0 8 3 Os 26 Note that for j
39. n 1 95 are 1 the advanced option modeltype is added implementing methods in Snijders 2003 2 maximum number of actors increased to 500 Title Page 2 Parts of the program The operation of the SIENA program is comprised of four main parts Program parts 1 input of basic data description 2 model specification 3 simulation of the model with given and fixed parameter values 4 estimation of parameter values using stochastic simulation The normal operation is to start with data input then specify a model and estimate parameters and then continuing with new model specifications followed by estimation or simulation The program is organized in the form of projects A project consists of data and the current model specification All files internally used in a given project have the same root name which is called the project name and indicated here by pname The main output is written to the text file pname out Title Page sou 3 Input data The main statistical method implemented in SIENA is for the analysis of repeated measures of social networks and requires network data collected at two or more time points There Input data fore two or more data files with digraphs are necessary the observed networks one for each time point The number of time points is denoted M For the exponential random graph model one observed network data set is required In addition various kinds of covariates are allowed 1 ac
40. nditional on the observed number of changes Conditional estimation is slightly more stable and efficient because the basic rate pa rameter is not estimated by the Robbins Monro algorithm so this method decreases by 1 the number of parameters estimated by this algorithm Therefore this is the default The possibility to choose between conditional and unconditional estimation is an advanced option If there are changes in network composition see Section 3 5 only the unconditional estimation procedure is available Automatic changes from conditional to unconditional estimation Even though conditional estimation is the default and slightly more efficient than uncon ditional estimation there is one kind of problem that sometimes occurs with conditional estimation and which is not encountered by unconditional estimation It is possible but fortunately rare that the initial parameter values were chosen un fortunately in such a way that the conditional simulation does not succeed in getting to the condition required by its stopping rule see Section 5 3 3 This is detected by SIENA which then switches automatically to unconditional estimation after some time it switches back again to conditional estimation Estimation Title Page 516 a 6 Simulation The simulation option simulates the network evolution for fixed parameter values This is meaningful mainly at the point that you have already estimated parameters
41. nly on the set of all symmetric or all antisymmetric graphs respectively The program has six possibilities for the definition of the steps in the MCMC procedure Exponential random Title Page Page 28 of 60 1 Gibbs steps for single relations xij 2 Gibbs steps for dyads Tij zji 3 Gibbs steps for triplets Lij jh zih and Lij Ejh Zhi 4 Metropolis Hastings steps for single relations ij Full Screen Pee oe 5 Metropolis Hastings steps for dyads x 2j in which symmetric dyads remain sym metric and asymmetric dyads remain asymmetric This is appropriate for symmetric and antisymmetric graphs 6 Metropolis Hastings steps keeping the in degrees and out degrees fixed see Snijders and van Duijn 2002 The choice between these types of steps is made in the advanced options Some other options are available by modifying the pname mo3 file as indicated in Section below In the conditional option where the number of arcs is fixed options 1 and 4 exchange values of arcs xi and tx with i j h k with probabilities defined by the Gibbs and Metropolis Hastings rules respectively option 2 changes values of dyads xij ji and Unk Ckn With i j A h k keeping Zij vj n Len Constant and option 3 changes the value of one triplet Xij Ejh in OF Lij Ejh Zhi keeping the sum Tij jn Lin OF Tij jh Thi constant The number of steps for generating one exponential random graph
42. nt value in the estimation process The theta parameters are the statistical parameters that correspond to the effects in the current model specification These are stored in the pname mo 4 file The distinction between these two types of parameters in principle also allows linear or other restrictions between the alphas In the present version the possibility of such restrictions is not implemented but the distinction between alpha and theta allows to elaborate this possibility in a later version The names of the effects are defined in procedures DefineModel_Inames Define Model_fnames and DefineModel_gnames in unit S BASE The numbers of these effects must correspond and are defined in functions MaxEffects_l MaxEffects_f and MaxEffects_g in unit S_DAT The following procedures are all in unit S BASE The rate function is defined in pro cedures Transform_1 and Lambda the objective function in contr_f and the gratification function in contr_g For Model Type 2 the rate functions also depends on the functions Title Page xiand nu The names of the statistics are defined in DefineFunctionNames and the computation of the statistics is defined in Statistics Parameters and effects P51 a a 15 Units and executable files The basic computational parts of SIENA are contained in the following units First there are four basic units 1 S_DAT contains the basic data structures and procedures for reading and writing a
43. number of files with constant individual covariates number of files with changing individual covariates number of dyadic covariates indicator of file with times of composition change 0 means no change of network composition 1 means composition changes Title Page 2 For each of the M network observations the following three lines a line with the name of the data file a line with the codes that are regarded as a present arc in the digraph Page 47 of 60 a line with the codes that are regarded as missing data All codes should be in the range from 0 to 9 3 If there are 1 or more files with constant actor covariates for each file there must be the following lines a line with the name of the data file a line with the number of variables in this file lines with the names of these variables used in the output of the program for each variable name a separate line 4 If there are 1 or more files with changing actor covariates for each file there must be the following lines a line with the name of the data file a line with the name of this variable used in the output of the program 5 If there are 1 or more dyadic covariates for each of them there must be the following two lines a line with the name of the data file a line with the name of this variable used in the output of the program SIENA files 6 If there is a file with times of composition change a line with the name of this file must be included
44. oining the numbers 0 1 0 have a different meaning than the numbers 1 0 0 The former numbers indicate that an actor is observed at time 1 he she joined the network right before the first time point the latter indicate that an actor is not observed at observation time 1 he she joined just after the first time point The same holds for leavers 5 0 0 indicates that an actor is observed at time point 5 whereas 4 1 0 indicates that an actor left right before he she was observed at time point 5 From the example it follows that an actor is only allowed to join leave join and then leave or leave and then join the network The time that the actor is part of the network must be an uninterrupted period It is not allowed that an actor joins twice or leaves twice When there is no extra information about the time at which an actor joins or leaves in some known period there are three options set the fraction equal to 0 0 0 5 or 1 0 The second option is thought to be least restrictive Title Page Page 11 of 60 sou 3 6 Centering Individual as well as dyadic covariates are centered by the program in the following way For individual covariates the mean value is subtracted immediately after reading the me variables For the changing covariates this is the global mean averaged over all periods The values of these subtracted means are reported in the output For the dyadic covariates and the similarity variables derived from the indiv
45. oration of further effects to be included the following steps may be followed 1 Estimate a model which includes a number of basic effects 2 Simulate the model for these parameter values but also include some other relevant statistics 3 Look at the t values for these other statistics effects with large t values are candidates for inclusion in a next model It should be kept in mind however that this exploratory approach may lead to capitaliza tion on chance and also that the t value obtained as a result of the straight simulations is conditional on the fixed parameter values used without taking into account the fact that these parameter values are estimated themselves It is possible that for some model specifications the data set will lead to divergence e g because the data contains too little information about this effect or because some effects are collinear with each other In such cases one must find out which are the effects causing problems and leave these out of the model Simulation can be helpful to distinguish between the effects which should be fixed at a high positive or negative value and the effects which should be left out because they are superfluous When the distribution of the out degrees is fitted poorly which can be investigated by selecting Model Code 3 in the advanced options an improvement usually is possible either by including non linear effects of the out degrees in the objective function or by c
46. osition change Example data files for a network of changing composition are also provided with the pro gram These files are called vtest2 dat vtest3 dat and vtest4 dat They contain the same network data as the friendship data files of van de Bunt for these three observation times and with the same coding except that in these data some joiners and leavers were artifi cially created These actors were given the code 9 for the observation moment at which they were not part of the network The attribute file vtestexo dat contains the times at which the network composition changes see also the example in Section 3 5 This file is necessary for the program to correctly include the times at which actors join or leave the network For example the first line of the file contains the values 1 Off ap OnO which indicates that the first actor joins the network at fraction 0 7 of period 1 the period between the first and second observation moments and leaves the network right after the beginning of the third period i e he she does not leave the network before the last observation at the third time point Thus the first actor joins the network and then stays in during the whole period being analysed Getting started Title Page EEEH P51 a 10 10 1 Mathematical definition of effects The mathematical formulae for the definition of the effects are the following See Snijders 2001 for further background to
47. ovariates and the changing individual variables both have nzmaxz as their maximum Reasonable values for these constants are the following nmax 500 Constants nrg nmax pmax 30 cemax 16 M 12xnzmaz 3xnzzmaz where M is the number of repeated observations Tie Paz in the current version of SIENA the number of statistics is 16 M 6 x nz nzc 3 x nzz this can become higher in future specifications nzmax 10 nzzmax 10 Page 58 of 60 The number M of observations may not be higher than 99 Since the number of obser vations is dealt with by a dynamic array this is not reflected by some constant The only reason for the upper bound of 99 is that the index number of the observation is used in the internal data file extension names and may not have more than two digits But 99 seems quite a high upper bound for practical data sets 17 References Albert A and J A Anderson 1984 On the existence of the maximum likelihood estimates in logistic regression models Biometrika 71 1 10 Boer P Huisman M Snijders T A B and E P H Zeggelink 2001 StOCNET An open software system for the advanced statistical analysis of social networks Groningen ProGAMMA ICS Available from http stat gamma rug nl stocnet Frank O 1991 Statistical analysis of change in networks Statistica Neerlandica 45 283 293 Frank O and D Strauss 1986 Markov graphs Journal of the American Statistical Associ ation 81
48. r unreliable i The number of subphases in phase 2 and the number of runs in phase 3 can be changed in the advanced options Full Screen Pee a The user can break in and modify the estimation process in three ways 1 it is possible to terminate the estimation 2 in phase 2 it is possible to terminate phase 2 and continue with phase 3 3 in addition it is possible to change the current parameter values and restart the whole Estimation estimation process 5 2 Output There are three output files All are ASCII files which can be read by any text editor The main output is given in the pname out file recall that pname is the project name defined by the user A brief history of what the program does is written to the file pname log Some diagnostic output containing a history of the estimation algorithm which may be informative when there are convergence problems is written to the file siena chk chk for check This file is overwritten for each new estimation Normally you only need to look at pname out The output is divided into sections indicated by a line 1 subsections indicated by a line 2 subsubsections indicated by 3 etc For getting the main structure of the output it is convenient to have a look at the 1 marks first The primary information in the output of the estimation process consists of the following three parts Results are presented here which correspond to Table 2 column t t3 of
49. re so the results can vary This is of course not what you would like For well fitting combinations of data set and model the estimation results obtained in different trials will be very similar It is good to repeat the estimation process at least once for the models that are to be reported in papers or presentations to confirm that what you report is a stable result of the algorithm The initial value of the parameters is the current value that is the value that the parameters have immediately before you start the estimation process Usually a sequence of models can be fitted without any problems occurring Sometimes however problems may occur during the estimation process which will normally be indicated by some kind of warning in the output file In such cases the current parameter estimates may have been determined in an unsatisfactory way and using them as initial values for the new estimation process may again lead to difficulties in estimation Therefore it is advisable before starting the estimation algorithm to use a standard initial value when the current parameter values are unlikely and also when they were obtained after a divergent estimation algorithm The use of standard initial values is one of the advanced options Title Page Soare a a a 5 1 Algorithm During the estimation process StOCNET transfers control to the SIENA program The estimation algorithm has three phases 1 In phase 1 the parame
50. re in this manual is the Palazzo Pubblico with the Torre del Mangia in Siena Close Part I User s manual The user s manual gives the information for using SIENA It is advisable also to consult the user s manual of StOCNET because normally the user will operate SIENA from within StOCNET 1 1 Changes compared to earlier versions The main changes in version 1 90 compared to version 1 70 are 1 possibility to use more than two observation moments 2 inclusion of the exponential random graph p model corresponding to one obser vation moment 3 possibility to have changes of composition of the network actors leaving and or entering 4 changing actor covariates 5 arbitrary codes allowed for missing data instead of the automatic use of 6 and 9 as codes for missing data the user now has to supply these codes explicitly 6 small improvements in the user interface The main changes in version 1 95 compared to version 1 90 are 1 for the exponential random graph model some extra simulation options were added and inversion steps were added General information Title Page Page 3 of 60 Sarsan 2 some effects 3 star and 4 star counts added to the exponential random graph model General information 3 for changing covariates the global rather than the periodwise mean is subtracted 4 the program SIENAO2 for data description was added The main changes in version 1 98 compared to versio
51. served degrees on the conclusions about the structural aspects of the network dynamics This is further explained in Snijders 2003 For Model Type 2 in the rate function effects connected to these functions xi and nu are included On the other hand effects in the objective function that depend only on the out degrees are canceled from the model specification because they are not meaningful in Model Type 2 To evaluate whether Model Type 1 or Model Type 2 gives a better fit to the observed degree distribution the output gives a comparison between the observed out degrees and the fitted distribution of the out degrees as exhibited by the simulated out degrees For Model Type 2 this comparison is always given For Model Type 1 this Title Page comparison is given by specifying the Model Code in the advanced options as 3 For ATEX users the log file contains code that can be used to make a graph of the type given in Snijders 20003 Model specification Psar a 5 Estimation The model parameters are estimated under the specification given during the model speci fication part using a stochastic approximation algorithm In the following the number of parameters is denoted by p The algorithm is based on repeated and repeated and re el s peated simulation of the evolution process of the network These repetitions are called ERGUN runs in the following Note that the estimation algorithm is of a stochastic natu
52. t an exponential random graph model also called the p model Frank amp Strauss 1986 Frank 1991 Wasserman amp Pattison 1996 SIENA carries out Markov chain Monte Carlo MCMC estimation for this model as described in Snijders 2002 If the algorithm works properly the computed estimate is an approximation of the maximum likelihood estimate However it is discussed in Snijders 2002 that there often occur problems for estimating parameters of this distribution and for many data sets it is impossible to achieve satisfactory estimates i e good convergence with this method In any case it is advisable always to chose the conditional estimation simulation option which means here that the total number of ties is kept fixed To use SIENA for one observation moment it is advised first to read Snijders 2002 A further exploration of the possibilities of estimating parameters ofr this model is presented in Snijders amp van Duijn 2002 For conditional estimation in this situation the total number of arcs remains constant For unconditional estimation the total number of arcs is a random variable The choice between these two is made in the advanced options The program recognizes automatically if the data set is symmetric an undirected graph with zij j for all i j or anti symmetric a tournament with xij xj for alli 7 In such cases the MCMC estimation respects this and the exponential random graph model is considered o
53. t difficulties Title Page e Two or more effects are included that are almost collinear in the sense that they can both explain the same observed structures This will be seen in high absolute values of correlations between parameter estimates Pare ao creo e An effect is included that is large but of which the precise value is not well determined GoBack see above section on fixing parameters This will be seen in estimates and standard J errors both being large and often in divergence of the algorithm Fix this parameter FullScreen e to some large value Note large here means e g more than 5 or less than 5 l depending on the effect of course Close E 9 3 If there are problems you don t understand you could take a look at the file pname log and if the problems occur in the estimation algorithm at the file pname chk These files give information about what the program did which may be helpful in diagnosing the problem E g you may look in the pname chk file to see if some of the parameters are associated with positive values for the so called quasi autocorrelations The parameters for which this happens from subphase 2 2 onward are parameters that may have led to problems in the estimation algorithm e g because the corresponding effect is collinear with other effects or because they started from unfortunate starting values or because the data set contains too little information about their value Comp
54. t the program estimate the parameters You will see a screen with intermediate oa gt results current parameter values the differences deviation values between simulated Page 32 of 60 and observed statistics these should average out to 0 if the current parameters are close see to the correct estimated value and the quasi autocorrelations discussed in Section 5 GoBack It is possible to intervene in the algorithm by clicking on the appropriate buttons the current parameter values may be altered or the algorithm may be restarted or terminated FullScreen e In most cases this is not necessary Pee a Jae omc Some patience is needed to let the machine complete its three phases After having ob tained the outcomes of the estimation process the model can be respecified non significant effects may be excluded but it is advised always to retain the density and the reciprocity effects and other effects may be included Model choice For the selection of an appropriate model for a given data set it is best to start with a simple model including e g 2 or 3 effects delete non significant effects and add further effects in groups of 1 to 3 effects Like in regression analysis it is possible that an effect that is non significant in a given model may become significant when other effects are added or deleted When you start working with a new data set it is advisable first to investigate the main endogenous
55. ter is held constant at its initial value This phase is for estimating the matrix of derivatives In the case of longitudinal data each run requires Eaei p simulations al 2 Phase 2 consists of several subphases More subphases means a greater precision The default number of subphases is 4 The parameter values changes from run to run reflecting the deviations between generated and observed values of the statistics The changes in the parameter values are smaller in the later subphases The program searches for parameter values where these deviations average out to 0 This is reflected by what is called the quasi autocorrelations in the output screen These are averages of products of successively generated deviations between generated and observed statistics It is a good sign for the convergence of the process when the quasi autocorrelations are negative or positive but close to 0 because this means the generated values are jumping around the observed values 3 In phase 3 the parameter is held constant again now at its final value This phase is for estimating the covariance matrix and the matrix of derivatives used for the Title Page computation of standard errors In the case of longitudinal data each run again requires p simulations i The default number of runs in phase 3 is 500 This requires a lot of computing time but when the number of phase 3 runs is too low the standard errors computed are Page 17 of 60 rathe
56. these formulae They are listed in the order in which they appear in SIENA Objective function The potential effects in the objective function denoted f in Snijders 2001 are the follow ing Those which are a function only of the out degree of actor i are excluded for Model Type 2 1 density effect defined by the out degree Si Ti DY Tij 2 reciprocity effect defined by the number of reciprocated ties Si2 D1 Tij Vyas 3 transitivity effect defined by the number of transitive patterns in it s relations ordered pairs of actors j h to both of whom i is tied while also j is tied to h 43 2 Dar Lij Lih Lih 4 balance defined by the similarity between the outgoing ties of actor 7 and the outgoing ties of the other actors j to whom i is tied n n Sia r DM oo E AE ore Formulas for effects Title Page Sisan 10 where bo is a constant included to reduce the correlation between this effect and the density effect defined by number of distances two effect or indirect relations effect defined by the number of actors to whom is indirectly tied through one intermediary i e at sociometric distance 2 Sie 2 weg O waesea yp ag gt OR popularity effect defined by 1 n times the sum of the in degrees of the others to whom i is tied Sie 2 5 oy ig tj Sey Dy Tig Don Dg activity effect defined by 1 n times the sum of the out degrees of the others to whom
57. this parameter fixed at some large value see section 9 1 whether the value is large positive or large negative depends on the direction of the effect For the results of both model fits it is advisable to check the fit by simulating the resulting model and considering the statistic corresponding to this particular parameter Estimation Title Page gt a sa a 3 Collinearity check After the parameter estimates some matrices are presented The most important is the covariance matrix of the estimates In this case it is Covariance matrix of estimates correlations below diagonal 0 087 0 036 0 003 0 230 0 283 0 033 0 078 0 440 0 020 The diagonal values are the variances i e the squares of the standard errors e g 0 087 is the square of 0 2957 Below the diagonal are the correlations E g the correlation between the estimated density effect and the estimated reciprocity effect is 0 230 These correlations can be used to see whether there is an important degree of collinearity between the effects Collinearity means that several effects can represent the same data pattern in this case the same values of the network statistics When one or more of the correlations are very close to 1 0 or 1 0 this is a sign of collinearity This will also lead to large standard errors of those parameters It is then advisable to omit one of the corresponding effects from the model because it may be redundant given t
58. tion the original data files are not used any more but the project data files are used These are the following pname d01 pname d02 etc pname m01 etc pname dav pname dac pname z01 etc pname dex Data file time 1 Data file time 2 etc Data file missings time 1 etc Data files constant actor dependent covariates centered Data files changing actor dependent covariates centered Data files dyadic covariates Data file times of composition change The user does not need to care about these data files but should not delete them either 13 5 Output files The output for the user goes to pname out Extra output is written to pname log which is a log file of what the program did The estimation procedure also writes a file siena chk containing a more detailed report of the estimation algorithm The latter two files are for diagnostic purposes only The siena chk file is overwritten with each new estimation procedure SIENA files Title Page Disan 14 Parameters and effects In the source code there are two kinds of parameters alpha and theta The alpha parame ters are used in the stochastic model and each alpha parameter corresponds to one effect independently of whether this effect is included in the current model specification Their values are stored in the pname mo3 file which also indicates by 0 1 codes whether these variables are included in the model and whether they are fixed at their curre
59. tions to Social Network Analysis Information Theory and Other Topics in Statistics A Festschrift in honour of Ove Frank University Close e a of Stockholm Department of Statistics Van de Bunt G G 1999 Friends by choice An actor oriented statistical network model for friendship networks through time Amsterdam Thesis Publishers 1999 Van de Bunt G G M A J van Duijn and T A B Snijders 1999 Friendship networks through time An actor oriented statistical network model Computational and Mathematical Or ganization Theory 5 167 192 Wasserman S and P Pattison 1996 Logit models and logistic regression for social networks I An introduction to Markov graphs and p Psychometrika 61 401 425 References Title Page rt scue
60. tor bound or individual covariates also called actor attributes which can be sym bolized as v for each actor 7 these can be constant over time or changing 2 dyadic covariates which can be symbolized as wij for each ordered pair of actors i j they are allowed only to have integer values ranging from 0 to 255 The data files and the names of the variables are made available to SIENA through specifi cation of these files and variable names in StOCNET Names of variables must be composed of at most 14 characters This is because they are used as parts of the names of effects which can be included in the model and the effect names should not be too long Title Page Page 6 of 60 Sarsan Salle 3 2 Digraph data files Each digraph must be contained in a separate input file in the form of an adjacency matrix i e n lines each with n integer numbers separated by blanks each line ended by a hard return The diagonal values are meaningless but must be present The data matrices for the two digraphs must be coded in the sense that their values are converted by the program to the 0 and 1 entries in the adjacency matrix A set of code numbers is required for each digraph data matrix these codes are regarded as the numbers representing a present arc in the digraph i e a 1 entry in the adjacency matrix all other numbers will be regarded as 0 entries in the adjacency matrix Of course there must be at least one such code num

Manual for SIENA version 1.98

Contents

Download Pdf Manuals

Related Search

Related Contents