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Manual for SIENA version 2.1

1. From version 2 onward SIENA also allows dependent action variables These represent the actors behavior attitudes beliefs etc The difference between dependent action variables and changing actor covariates is that the latter change exogenously i e according to mechanisms not included in the model while the dependent action variables change endogenously depending on the changing network Unlike the changing individual covariates the values of dependent action variables are not assumed to be constant between observations Accordingly each dependent action variable must be given in one file containing k M columns corresponding to the M observation moments 4 5 Missing data SIENA allows that there are some missing data on network variables and from version 2 onward also on covariates and dependent action variables These missing data must be indicated by missing data codes to be specified in StOCNET if SIENA is operated through StOCNET not by blanks in the data set In the current implementation of SIENA missing data are treated in a simple way trying to minimize their influence on the estimation results The simulations are carried out over all actors 10 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 i e it is assumed that there is no tie Missing covariate data a
2. It is allowed that some of the values in the digraph are structurally determined i e deterministic rather than random This is analogous to the phenomenon of structural zeros in contingency tables but in SIENA not only structural zeros but also structural ones are allowed A structural zero means that it is certain that there is no tie from actor to actor j a structural one means that it is certain that there is a tie This can be e g because the tie is impossible or formally imposed respectively Structurally determined values are defined by reserved codes in the data matrix the value 10 indicates a structural zero the value 11 indicates a structural one Structurally determined values can be different for the different time points The diagonal of the data matrix always is composed of structural zeros but this does not have to be indicated in the data matrix by special codes The correct definition of the structurally determined values can be checked from the brief report of this in the output file and by looking at the file pname s01 for the first time point pname s02 second time point etc In these files the structurally determined positions structural zeros as well as structural ones are indicated by the value 1 all others i e the positions where ties are random by the value 0 Structural zeros offer the possibility of analyzing several networks simultaneously under the assumption that the parameters are identic
3. 1 In phase 1 the parameter vector is held constant at its initial value This phase is for having a first rough estimate of the matrix of derivatives In the case of longitudinal data each run requires p simulations 2 Phase 2 consists of several subphases More subphases means a greater precision The default number of subphases is 4 The parameter values change 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 vector 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 computation of standard errors In the case of longitudinal data each run again requires p simulations 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 compu
4. of numbers These have the following meaning a 0 1 entry denoting whether the effect is included 1 or excluded 0 a 0 1 entry denoting whether the effect is fixed 1 or not fixed 0 during the estimation process a 0 1 entry indicating whether a fixed effect shall be included 1 or excluded 0 in goodness of fit calculations see Section 7 the starting value of the parameter for the estimation procedure an effect specific parameter for modeling the constants c in the mathematical def inition of the effects see Section 13 1 1 Subsections 2 x 2 contain the specification of the network decision rule including the utility endowment functions and which has the following shape 2 1 2 objective function effects for dependent network variable 1 46 number of such effects first row contains label of the effect next three rows functions in which effect can be included row 1 utility function row 2 endowment function row 3 reinforcement function columns correspond to a inclusion b random effects c fixing d testing e starting value f potential extra parameters for effect calculation outdegree density 1000 1 143698 O 0000 0 000000 O 0000 0 000000 O 52 reciprocity 1000 1 467572 0 0000 0 000000 O 0000 0 000000 O Eso The section must contain first a row with the number of effects further down for each of these effects four rows on
5. 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 StCOCNET by using subsequently the Data and Transformation menus do not forget to click Apply when finishing each of these parts then select SIENA in the Model menu and click the Data specification button Select the network data in temporal sequence on the left side of the Data specification screen then click on OK Back on the SIENA main screen now click on the Model specification button You will be requested to make some choices for the specification the meaning of which should be clear given what is explained above On the left hand side of the Model specification screen you can specify utility and endowment effects indicated by two columns of checkboxes marked w and e respectively In the specification of the utility function choose the outdegree effect the reciprocity effect and one other effect In the specification of the endowment function choose no effects at all On the right hand side of the
6. It uses the URNS suite for random numbers generation 10 EIGHT is a unit for storing the data Its name was chosen for historical reasons a byte was used to store eight booleans 17 1 Executable files The basic data input is carried out by executing SIENAO1 EXE This program executes ReadWrite Data and BeforeFirstModelDefinition 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 MO file and then running SIENA04 EXE SIENA04 EXE is only used for checking admissibility of a model specification and for keeping consistency between the different session files It reads and updates the MO file and also writes the corresponding SI file If you change pname MO by an text editor outside of StOCNET it is advisable to run SIENA04 EXE before proceeding The simulation is carried out by SIENAO5 EXE which executes Simulate The estimation is carried out by executing SIENAO7 EXE which executes Estimate The multilevel combination of estimation runs for several data sets according to the same basic model specification is done by SIENA08 EXE which also executes the procedure Estimate although taking it from S_EST8 The essential difference between SIENA08 EXE and SIENAO7 EXE is con tained in the difference between units Siena_8 and Siena_7 57 18 Parameters and effects In the source
7. Results are presented here which correspond to Table 2 column t4 t3 of 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 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 exactly equal to 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 longi tudinal 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 moderate 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
8. a high positive or negative value and the effects which should be left out because they are superfluous When the distribution of the outdegrees is fitted poorly which can be investigated by the extra output requested by selecting Model Code larger than 10 in the model options an improvement 34 usually is possible either by including non linear effects of the outdegrees in the utility function or by changing to Model Type 2 see Section 5 2 11 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 standard initial values a certain non zero value for the outdegree parameter and zero values for the other parameters or from values obtained as the estimates for a simpler model that gave no problems The initial default parameter values can be obtained by choosing the model option standard initial values When starting estimations with Model Type 2 see Section 5 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 model 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 e Too many weak effects a
9. 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 current implementation this type of recoding cannot easily be carried out within StOCNET but the user must do it in some other program 4 3 Individual covariates Individual i e actor bound variables can be combined in one or more files Tf there are k variables 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 There must not be blank lines after the last data line A distinction is made between constant and changing actor variables where change refers to changes over time Each constant actor covariate has one value per actor valid for all observation moments and has the role of an independent variable Changing variables can change between o
10. determined All other effects then have a 0 0 starting value 8 An indicator allowing for tests of temporal between period homogeneity of parameters code 0 no test code m gt 0 test for period m 9 An indicator allowing for tests of actor homogeneity of parameters code 0 no test code 1 test of the outdegree density effect code 2 test of the reciprocity effect 10 A space separated list giving the row numbers of the actors for such an actor homo geneity test 11 A value determining the use of random numbers during the estimation process code 0 randomize seed code c 0 cis used as random seed If you change anything in the pname MO file you must run SIENA04 EXE to let SIENA check and if necessary censor or re define the model specification 54 16 2 2 Specification of simulations through the SI file For running simulations SIENA needs to be told which statistics it should simulate This is done by manipulating the pname Sl file by an ASCII text editor before running the simulations This file consists of two sections again marked by symbols as follows e Section 1 contains the list of possible statistics that can be simulated It looks as follows 1 statistics that can be generated 60 number of these statistics each statistic is given in two rows first row contains label of the statistic second row contains flag for inclusion Amount of change 1 Numb
11. estimate the same model another time now using the parameter values obtained under the previous Model Type 2 run as the initial values for the estimation To obtain a good model specification with respect to the rates of change in dependence of the outdegrees three effects can be included 1 the outdegrees effect 2 the factorial outdegree effect 3 the logarithmic outdegree effect 15 These are the effects defined in formula 18 of Snijders 2003b and indicated with the parameters 01 49 and a3 respectively The user has to see from the estimation results which or which two out of these effects should be included to yield a good fit for the outdegrees The Model Type is specified in the model options as part of the Model Code 16 5 2 2 Model Type non directed networks For non directed networks the Model Type has five possible values as described in Snijders 2005b 1 Forcing model one actor takes the initiative and unilaterally imposes that a tie is created or dissolved Unilateral initiative and reciprocal confirmation one actor takes the initiative and proposes a new tie or dissolves an existing tie if the actor proposes a new tie the other has to confirm otherwise the tie is not created Pairwise conjunctive model a pair of actors is chosen and reconsider whether a tie will exist between them a new tie is formed if both agree Pairwise disjunctive forcing model a pair of actors is chose
12. followed by estimation or simulation For the comparison of nested models goodness of fit indicators can be consulted 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 auxiliary output is contained in the text file pname log 4 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 It is possible to include changing actor variables representing behavior attitudes outcomes etc which also develop in a dynamic process together with the social networks As repeated measures data on social networks at the very least two or more data files with digraphs are required the observed networks one for each time point The number of time points is denoted M The other statistical method implemented in SIENA if the parameter estimation for the ex ponential random graph model ERGM For this method one observed network data set is required In addition various kinds of variables are allowed 1 actor bound or individual variables also called actor attributes which can be symbolized as v i for each actor i these can be constant over time or changing the changi
13. function for network change function ActionEffects_f in unit S_DAT procedure DefineModel_fnames in unit S_BASE and function Contr fa in unit S_BASE e For effects in the endowment function for behavior change the analogous procedures have to be changed as those for the endowment function for network change function ActionEffects_g in unit S_DAT procedure DefineModel_gnames in unit S_BASE and function Contr_ga in unit S_BASE The functions Contr_fn Contr_gna Contr_fa Contr_ga NetworkLambda and ActionLambda are evaluated very frequently by the algorithm Therefore these have been written so that very few calculations are needed to evaluate them Such calculations for a large part are replaced by updating and storing the basic numerical information needed to compute them These updates are contained in the procedure ChangeTie in unit S_BASE and the initialisation is contained in the procedure Initialise_Running_Statistics 62 19 Statistical Monte Carlo Studies According to Sir Ronald A Fisher there are three main statistical problems model specification model estimation and problems of distribution The last one concerns the distribution of statistics such as the distribution of parameter estimates around the true data generating parameter value or the distribution of test statistics and can be studied by SIENA as follows Open the unit Siena_7 and go to the procedure TEstForm FormActivate The first statement in the procedur
14. is specified and one or more parameters are restricted to some constant in most cases 0 Such restrictions on parameters can be imposed in the StOCNET program collection by pressing the Model specifications button on the main SIENA interface selecting the parameter of interest pressing the Advanced button checking the box in the column with label t corresponding to the parameter of interest and specifying the value to which the parameter is restricted Outside the StOCNET program collection parameters can be restricted by opening the pname MO file going to the parameters of interest and setting the values in the fourth column equal to 1 The goodness of fit test proceeds by simply estimating the restricted model not the unrestricted model with unrestricted parameters by the standard SIENA estimation algorithm No more information needs to be communicated When the model is restricted SIENA by default assumes that the restricted model is to be tested against the unrestricted model and by default SIENA evaluates the generalized Neyman Rao score test statistic 7 2 Example As an illustration consider the following example taken from Schweinberger 2005 The data correspond to business firms actors holding shares of other firms collected and studied by Pahor 2003 A simple baseline model was specified with some control parameters taking into account among other things that ownership ties to other firms may depend on how large the other
15. 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 variables EIGHT nzzmax maximum number nzz of dyadic covariates EIGHT The constant individual covariates and the changing individual variables both have nzmaz as their maximum Reasonable values for these constants are the following nmax 500 nrg nmax pmax 60 cemax 500 the maximum number of statistics is given by MaxFunctions which can be looked up in unit S_Dat in version 2 1 of SIENA e g for two dependent action variables and M observations the number of statistics is 53 3 x M 17 x nz nzc 5 x nzz nzmax 10 nzzmax 10 The number M of observations may not be higher than 99 Since the number of observations 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 64 21 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 Zeggeli
16. tie 6 9 code for missing friendship 4 files with constant actor covariates vars dat 3 number of covariates in this file names follow 99 code for missing gender 99 code for missing program 99 code for missing smoke The basic data input is carried out by executing SIENAO1 EXE This programs reads the basic information file Some preliminary output is given in the files pname out and pname log 16 2 Definition files The program writes and reads for internal use the following two definition files e pname MO defines model specification and options for model estimation e pname Sl defines statistics and number of runs for simulation These definition 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 Their 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 The three files pname IN pname MO and pname Sl must be compatible as they contain some overlapping information for successfully running SIENA 16 2 1 Model specification through the MO file To change the model specification outside the StOCNET shell you can change the pname MO file by an ASCII text editor In this way you can used advanced SIENA optio
17. to be reasonably close to a satisfactory value then decrease the initial gain parameter see Section 10 e g to the value 0 001 or 0 0001 30 10 Options for model type estimation and simulation There are several options available in SIENA The main options concern the model type and the estimation procedure used Options concerning model type and estimation procedure can be accessed in the StOCNET environment via the Model specification screen s option page More detailed information is given starting at page 53 1 There is a choice between conditional and unconditional estimation If there are dependent action variables the default for conditional estimation is to condition on the observed distance for the network variable but it then is possible also to condition on the distances observed for the dependent action variables The Model Code This defines the Model Type and an associated output option In the longitudinal case the meaning of this code is as follows Model Codes 10 or more give extra output for evaluating the fit of the outdegree distribution and for the explained variation Snijders 2004 the integer Model Code in the unit position i e Model Code itself if it is less than 10 and Model Code 10 if the code is more than 10 defines the Model Type defined in Section 5 2 In the ERGM non longitudinal case the Model Code defines the kind of steps made in the MCMC algorithm It is advised to use
18. 3 24 24 24 25 26 27 28 28 29 31 12 Multilevel network analysis 37 13 Formulas for effects 38 13 1 Network evolution s Le mtaa a oi ea a ea e a a a a A a E at a S a Reh 38 131 1 Network utility function azer code on ee ea ipa tale pet hie es ocala pg Ua E NE 38 13 1 2 Network endowment function 40 13 1 3 Network rate function 02 ce sea r oe odani ee ee ws 41 13 1 4 Network rate function for Model Type2 0 o e e 42 13 2 Behavioral evolution uz a Sa A A a eS SP A O 42 13 2 1 Behavioral utility function e 42 13 2 2 Behavioral endowment function 2 0 e e 43 13 2 3 Behavioral rate function 43 13 3 Exponential random graph distribution 0 0 0 0 000 ee eee 43 14 Limitations and time use 46 II Programmer s manual 47 15 Running SIENA outside of StOCNET AT 16 SIENA files 49 16 1 Basic information file 2 206 e e e Ae Re A ee E 49 L622 Detnition Mlesy 0d oo de ro Pa ede A lye iE eee Bee Daas ok Bee ek 51 16 2 1 Model specification through the MO file o o e 51 16 2 2 Specification of simulations through the SI file a 55 T6 3 Data MeS anio e ee Goel eth eo el ee ee a A A AS a le 56 16 4 Qutput fless riada he Pe ER A ERA a eh 56 17 Units and executable files 57 ECI Executablefiles na daa ic e a dl e oe A al e ieee da la 57 18 Parameters and effects 58 18 1 Starting to look at the source code a
19. 59 18 2 Procedures containing definitions of the effects o o 61 19 Statistical Monte Carlo Studies 63 20 Constants 64 21 References 65 1 General information SIENA shorthand for Simulation Investigation for Empirical Network Analysis is a computer pro gram that carries out the statistical estimation of models for repeated measures of social networks according to the dynamic actor oriented model of Snijders and van Duijn 1997 Snijders 2001 and Steglich Snijders and Pearson 2004 The model is explained for network evolution only also in Snijders 2005 Some examples are presented e g in van de Bunt 1999 van de Bunt van Duijn and Snijders 1999 and van Duijn Zeggelink Stokman and Wasseur 2003 A website for SIENA is maintained at http stat gamma rug nl snijders siena html The program also carries out MCMC estimation for the exponential random graph model ERGM also called p model of Frank and Strauss 1986 Frank 1991 and Wasserman and Pattison 1996 This procedure is described in Snijders 2002 The model specification is discussed in Snijders Pattison Robins and Handcock 2004 This manual is about SIENA version 2 1 Further minor improvements of the version 2 1 manual are expected in the near future The program and this manual can be downloaded from the web site http stat gamma rug nl stocnet One way to run SIENA is as part of the StOCNET program collection Boe
20. 7 v4 Ui next is the v related activity effect i vi finally the v related dissimilarity effect gt Tij v vj d where d is the mean of all v v values 45 14 Limitations and time use The estimation algorithm being based on iterative simulation is time consuming The time needed is approximately proportional to p n 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 and 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 20 indicates the constants in the program that define limitations for the data sets used 46 Part II Programmers 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 SIENA program consists of a basic computation part programmed by the authors of this manual in Turbo Pascal and Delphi associated with the StOCNET windows shell programmed by Peter Boer and R
21. 7 4 0 2 Leaving in per 2 0 6 and joining in per 3 0 8 3 0 8 2 0 6 Note that for joining 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 4 7 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 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 an
22. Manual for SIENA version 2 1 Tom A B Snijders Christian Steglich Michael Schweinberger Mark Huisman ICS Department of Sociology Grote Rozenstraat 31 9712 TG Groningen The Netherlands February 14 2005 Abstract SIENA for Simulation Investigation for Empirical Network Analysis is a computer program 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 and Steglich Snijders and Pear son 2004 It also carries out MCMC estimation for the exponential random graph model according to the procedures described in Snijders 2002 and Snijders Pattison Robins and Handcock 2004 This manual gives information about SIENA version 2 1 Contents 1 General information I User s manual 2 Changes compared to earlier versions 3 Program parts 4 Input data 41 Digrapiidatallles o sicer 44 2 pa A AA ee Ee A AA a ak 4 1 1 Structurally determined values e 42 Dyadic Covariates NN 4 3 Individual covariates 24 oie o es o a a e a A as 4 4 Dependent action variables ee 4 5 Missing data ws ra e a tale ec eh a y AG Composition change card ie ees oe a PE Se ee as Ean A es ie Sk Avi Gentine e a a puke wR A GR ee A AE ES Be oe oe Ea Ae t 5 Model specification 5 1 Effects associated with covariates ee 5 2 Model Type wiry tentar e ta a A fee o eS 5 2 1 Model Type directed netwo
23. Model Type 1 which is the default Model Type as a product net ynet ynet ynet A p a x Mm A Aja Ais 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 net _ net Aji Pm for m 1 M 1 If there are only M 2 observations the basic rate parameter is called pret 2 The effect of actor covariates with values vp can be represented by the factor Aust exp an vhi h 3 The dependence on the position of the actor can be modeled as a function of the actor s outdegree indegree and number of reciprocated relations Define these by Ti gt Zij Tpi gt Uji Cir gt TijUlgi j j j recalling that xi 0 for all i Denoting the corresponding parameter by amp the dependence on the outdegree is represented by n 1 Ti Ti nist HE exp an 1 eo ba This formula is motivated in Snijders and Van Duijn 1997 This defines a linear function of the outdegree parametrized in such a way that it is necessarily positive For a general dependence on the outdegree indegree and number of reciprocated relations one can use an average of such terms the second and third one depending in the analogous way on 4 and 2x respectively Also a reciprocal dependence on outdegrees can
24. al E g if there are three networks with 12 20 and 15 actors respectively then these can be integrated into one network of 12 20 15 47 actors by specifying that ties between actors in different networks are structurally impossible This means that the three adjacency matrices are combined in one 47 x 47 data file with values 10 for all entries that refer to the tie from an actor in one network to an actor in a different network In other words the adjacency matrices will be composed of three diagonal blocks and the off diagonal blocks will have all entries equal to 10 In this example the number of actors per network 12 to 20 is rather small to obtain good parameter estimates but if the additional assumption of identical parameter values for the three networks is reasonable then the combined analysis may give good estimates In such a case where K networks in the preceding paragraph the example had K 3 are combined artificially into one bigger network it will often be helpful to define K 1 dummy variables at the actor level to distinguish between the K components These dummy variables can be given effects in the rate function and in the utility function for ego which then will represent that the rate of change and the outdegree effect are different between the components while all other parameters are the same 4 2 Dyadic covariates Each dyadic covariate also must be contained in a separate input file with a square
25. alls the procedure TestStatistic in the unit S_TEST 5 Unit S SIM is used for simulations and calls the function FRAN in S_BASE 6 The unit S ERGM_EST and the file S ERGM PAS which is an include file used in S BASE contain procedures used only for the ERGM 1 observation case 18 2 Procedures containing definitions of the effects If new effects are added to the model these additions must be made to each of the following procedures in a coherent way of course e For each kind of effect 1 Procedure DefineFunctionNames in unit S_BASE which contains the names of all the statistics calculated from each simulation 2 Function NetworkFunctions or ActionFunctions in unit S_DAT giving the total number of statistics calculated NetworkFunctions is the number of statistics calculated if there are no dependent behavior variables and ActionFunctions is the number of statistics that can be used additionally to these in case that there are one or more dependent behavior variables 3 Procedure Statistics in unit S_BASE which calculates these statistics e For an effect in the rate function for network change 1 Function NetworkEffects_l in unit S_DAT the total number of possible effects in the network change rate function 2 Procedure DefineModel_Inames in unit S BASE which contains the names of all effects in the network change rate function and the numbers of the corresponding statistics used for fitting the parameters 3 F
26. ameter estimation 6 2 to under stand the output file which is meant to be as self explanatory as possible and 11 for the basis of getting started We are grateful to Peter Boer Rob de Negro and Evelien Zeggelink for their cooperation in the development of the StOCNET program and its alignment with SIENA We also are grateful to NWO Netherlands Organisation for Scientific Research for their support to the integrated research program The dynamics of networks and behavior project number 401 01 550 the project Statistical methods for the joint development of individual behavior and peer networks project number 575 28 012 and the project An open software system for the statistical analysis of social networks project number 405 20 20 which all contributed to the work on SIENA and StOCNET lThis program was first presented at the International Conference for Computer Simulation and the Social Sciences Cortona Italy September 1997 which originally was scheduled to be held in Siena See Snijders amp van Duijn 1997 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 2 Changes compared to earlier versions The main changes in version 2 1 compared to version 1 98 are 1 10 11 extension by dependent actor variables inclusion of effects related to group position
27. and an update of the similarity effects implementing methods in Steglich Snijders and Pearson 2004 see Section 4 4 the addition of Neyman Rao goodness of fit tests according to Schweinberger 2005 see Section 7 the possibility to analyse dynamics of non directed networks according to Snijders 2005b statistical Monte Carlo studies see Section 19 extension of the specifications of the exponential random graph p model in line with Snijders et al 2004 and slight modifications of the algorithm for this case to increase efficiency missing data handling is extended to covariates and dependent actor variables addition of the program SIENAO8 for the multilevel analysis of multiple network evolution processes implementing methods in Snijders and Baerveldt 2003 analysing the dynamics of non directed networks not yet documented possibility to specify structural i e non random zeros and structural ones in the adjacency matrices see Section 4 1 1 a new format for the project definition file pname IN and the replacement of the internal project files pname mol through pname mo4 by files pname MO for model definition and pname Sl for simulation directives old project files still can be read correction of various errors The main changes in version 1 98 compared to version 1 95 are l 2 the advanced option modeltype is added implementing methods in Snijders 2003 maximum number o
28. andard error Do not confuse this t test with 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 outdegree 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 outdegree effect is difficult to interpret by itself 20 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 this parameter fixed at some large value see section 11 1 whether the value is large posit
29. are accessible in StOCNET e g through the model options mentioned in Section 10 The consecutive options are the following 1 Estimation method code 0 for unconditional estimation code 1 or code 21 for estimation conditional on observed changes in the network codes codes 21 for estimation conditional on observed changes on the dependent action variable k For exponential random graphs another available option is to include incidental vertex parameters code 10 for unconditional estimation with incidental vertex parameters code 11 for conditional estimation with incidental vertex parameters 53 2 A code for the type of model For longitudinal data this is the Model Code described in the section on model options For exponential random graph models this code defines the steps used in the one observation case for simulating a random di graph see also the description above code 1 Gibbs steps for single relations code 2 Gibbs steps for dyads code 3 Gibbs steps for triplets code 4 Metropolis Hastings steps for single relations code 5 Metropolis Hastings steps for dyads in which symmetric dyads remain symmetric and asymmetric dyads remain asymmetric appropriate for undirected graphs and for tournaments i e antisymmetric graphs code 6 Metropolis Hastings steps conditional on indegrees and outdegrees To each of these values the number 10 may be added so the val
30. atistics are available The selection of statistics is discussed extensively in Snijders et al 2004 with attention especially to statistics 16 19 Note that SIENA will note whether the observed graph is symmetric or not and choose accordingly between the statistics for undirected and directed graphs 1 For undirected graphs the number of edges gt 5 Pig for directed graphs the number of arcs gt gt 4j Tij 2 The number of reciprocated relations gt TijUji The number of out twostars Y 7 Py y Tin Vik The number of in twostars gt pp Thi Tki SI AeA o The number of two paths mixed twostars given for undirected graphs by gt gt gt Lk Chi Lik and for directed graphs by 9 Pp 4 Thi Vik 6 For undirected graphs the number of transitive triads 5 y jh Lig Cin Uh for directed graphs the number of transitive triplets gt gt jh Lig Lih Ljh 7 The number of three cycles given for undirected graphs by igh Tij Ejh hi and for directed graphs by 3 Dijn Lij Ejh Chi 8 The number of out threestars gt 3 9 The number of in threestars gt Fe f 10 The number of out fourstars gt i 11 The number of in fourstars gt 7 12 The sum of reciprocal outdegrees gt 1 x 4 c for some constant c 13 The sum of transformed outdegrees gt gt 1 xj4 c i c 1 for some constant c 14 The number of pairs directly and indirectly connected i
31. be specified this can be meaningful because the rate effect of the outdegree becoming a value 1 higher might become smaller and smaller as the outdegree increases Denoting the corresponding parameter by ag this effect multiplies the factor A 3 by a2 LA 2 aD indies This function was chosen so that for a parameter a2 0 there is no effect multiplication by a factor 1 and no problems division by 0 occur when x 0 41 13 1 4 Network rate function for Model Type 2 For Model Type 2 see Section 5 2 the network rate function is defined according to Snijders 2003 by PmAi s pm ee where Pm Ai s and pm Ai s represent respectively the rate at which an actor of current out degree s increases or decreases his outdegree by 1 The parameter pm is a multiplicative effect of the observation period Function xi is called the distributional tendency function and is represented according to Snijders 2003 formula 17 by s exp a aglog s 1 where the names given in SIENA are e a outdegrees effect e ag logarithmic outdegree effect e a3 factorial outdegree 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 v s 1 01 Also to this exponent effects of actor covariates can be added 13 2 Behavioral evo
32. berg ed Contributions to Social Network Analysis Information Theory and Other Topics in Statistics A Festschrift in honour of Ove Frank University of Stockholm Department of Statistics Steglich Ch T A B Snijders and M Pearson M 2004 Dynamic Networks and Behavior Separating Selection from Influence Submitted Van de Bunt G G 1999 Friends by choice An actor oriented statistical network model for friendship networks through time Amsterdam Thesis Publishers 65 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 Organization Theory 5 167 192 van Duijn M A J E P H Zeggelink M Huisman F N Stokman and F W Wasseur 2003 Evolution of Sociology Freshmen into a Friendship Network Journal of Mathematical Sociology 27 153 191 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 66
33. ble current value yn i j is the tie variable from i to j b ya is the vector of dependent individual variables current value ya i h is the h th individual variable for actor i c ynm gives the adjacency matrices of the dependent network variable all values ynm i j m is the tie variable from i to j at observation moment m d mis is the indicator matrix for missing values mis i j m 0 if ynm i j m is an observed value and 1 if it is missing Note that yn and ya change dynamically during the simulation process the variables con taining the data from which ynm and mis are calculated are read in the input phase and then are left unaltered For the sake of flexibility the variables in the list above are implemented as functions not as arrays ii Variables starting with z represent individual variables a Array z contains the constant actor variables the number of such variables is nz b Array zz contains the dyadic variables their number is nzz 59 c Array zc contains the changing actor variables their number is nzc d The number of dependent actor variables is nza these variables are the first nza among the nzc changing actor variables 2 Unit S_DAT contains the defining ingredients for the network models The intended demar cation between S_DAT and S_BASE is that the former contains the model definition and the latter the operation of the model dynamics This is not realized completely beca
34. bservation moments They can have the role of de pendent variables changing dynamically in mutual dependence with the changing network or of independent variables in the latter case they are also called changing individual covariates Dependent variables are treated in the section below this section is about individual variables in the role of independent variables then they are also called individual covariates When changing individual variables have the role of independent variables they are assumed to have constant values from one observation moment to the next If observation moments for the network are t to t then the changing covariates should refer to the M 1 moments t through ty 1 and the m th value of the changing covariates is assumed to be valid for the period from moment tm to moment t 1 The value at ty the last moment does not play a role Changing covariates as independent variables are meaningful only if there are 3 or more observation moments because for 2 observation moments the distinction between constant and changing covariates is not meaningful Each changing individual covariate must be given in one file containing k M 1 columns that correspond to the M 1 periods between observations It is not a problem if there is an M th column in the file but it will not be read The mean is always subtracted from the covariates See the section on Centering 4 4 Dependent action variables
35. c 0 1797 d f 1 p value 0 6716 2 apart c 7 0165 d f 1 p value 0 0081 3 apart c 13 3151 d f 1 p value 0 0003 In the example output three parameters are restricted reciprocity at value 1 transitivity and number of actors at distance 2 both at value 0 The p value corresponding to the omnibus test indicates that the restricted model is not tenable Looking at the separate tests it seems that the misfit is in the first place due to transitivity and actors at distance 2 Since both parameters imply clustering in social networks it seems that the assumptions of the baseline model with respect to the clustering of ties are incredible in the light of the observed data Thus it is sensible to improve the goodness of fit of the baseline model by including these clustering parameters either one of them or both and estimate them 7 2 2 Testing homogeneity assumptions SIENA by default assumes that the parameter values are constant across actors and periods It may be the case that these assumptions are hardly credible in the light of substantive insight and empirical data Consider the assumption that all actors share the same value of some parameter such as outdegree Inspecting the number of ties that actors added between observation points will show variation across actors Such variation is natural and does not necessarily imply that the actors do not share the same value of the outdegree parameter However some actor
36. c 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 including missing data identification 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 The basic information file contains up to eight sections each starting with a row containing the section number 01 through 08 These sections must have the following contents 1 Section 1 contains basic information about type and amount of data This section is required for all SIENA projects It must contain nine rows each starting with an integer number number of observations of the network 1 for exponential random graph modeling 2 or more for modeling network evolution over time denoted by M number of actors denoted further by n number of dependent network variables must be equal to one in the current version of SIENA The network data are further specified in Section 2 number of dependent actor variables Possible dependent actor variables are further specified in Section 3 number of files with constant actor covariates further specified in Section 4 number of files with changing actor variables further specified in Section 5 number of constant dyadic covariates further specified in Section 6 number o
37. changes values of dyads x u and Ehk Zn with i j 4 h k 29 keeping vj Uji Uhr Tk constant and option 3 changes the value of one triplet Lij Tn Lin or Zij Ejh Zhi keeping the sum Tij Lih Tip OF Lij Ejn Thi constant The number of steps for generating one exponential random graph is r n 2d 1 d where r is a constant which can be changed in the model options and called Run length in the model and estimation 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 5 This value can be increased when it is doubted that the run length is sufficient to achieve convergence of the MCMC algorithm The algorithm uses by default a continuous chain to make successive draws from the ERGM even for different parameter values This is in order to improve convergence speed For this purpose the possibilities 1 6 mentioned above should be communicated in the model options see p 54 by the values 11 16 When convergence as evidenced by all t statistics for convergence being less than 0 1 in absolute value is not easy to obtain then one can try to improve convergence in repeated runs of SIENA with the following options When some autocorrelations are markedly higher than 0 1 then it can help to increase the number of steps runlength When the provisional parameter estimate used as initial value for the estimation algorithm seems
38. code there are two kinds of parameters alpha and theta The alpha parameters 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 MO file which also indicates by 0 1 codes whether these variables are included in the model and whether they are fixed at their current value in the estimation process The theta parameters are the statistical parameters that correspond to the effects in the current model specification 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 effects for the evolution model are distinguished between effects for the network dynamics and effects for the behavior dynamics The effects are defined in several procedures which of course must correspond To each effect corresponds one statistic used for estimating the parameter for this effect This is spelled out in Section 18 2 In unit S_DAT the numbers of the various types of effects are defined 1 NetworkEffects_f the number of effects in the utility function for the network dynamics NetworkEffects_g the number of effects in the endowment function for the net
39. cts in the network utility function u called objective function and denoted f in Snijders 2001 are the following Note that in all effects where a constants c occurs this constant can be chosen and changed by the user Also note that the utility effects which are a function only of the outdegree of actor are excluded for Model Type 2 For non directed networks the same formulae are used unless a different formula is given explicitly 1 outdegree effect or density effect defined by the outdegree sii x ig D Tij where x 1 indicates presence of a tie from i to j while xi 0 indicates absence of this tie 2 reciprocity effect defined by the number of reciprocated ties sis 2 JD Tij Ty 3 transitivity effect defined by the number of transitive patterns in s relations ordered pairs of actors j h to both of whom 7 is tied while also j is tied to h for directed networks s x Nin EAS and for non directed networks s x ich Liz Tip Tin 4 balance defined by the similarity between the outgoing ties of actor and the outgoing ties of the other actors j to whom 27 is tied n n sa a Y ay Y bo ain zjn j 1 are ij where bg is a constant included to reduce the correlation between this effect and the outdegree effect defined by M 1 n n 1 w a Daa 2 YY Y I in tm ayn tm m 1i j l h 1 h i j 5 number of distances two effect or indirect relations effect
40. d the similarity variables derived from the individual covariates 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 13 The dependent network variable and the dependent action variables are not centered 12 5 Model specification After defining the data the next step is to specify a model In the StOCNET environment this is done by clicking the Model specification button that is activated after a successful Data specification in StOCNET s Model menu provided that SIENA was selected from the list of available models The model specification consists of a selection of effects for the evolution of each dependent variable network or behavior A list of all available effects for a given SIENA project is given in the secondary output file pname log Three types of effects are distinguished see Snijders 2001 Steglich Snijders and Pearson 2004 e rate function effects The rate function models the speed by which the dependent variable changes more precisely the speed by
41. defined by the number of actors to whom is indirectly tied through one intermediary i e at sociometric distance 2 sis 2 j vig 0 maxn zin hj gt O 38 10 11 12 13 14 15 16 popularity alter effect defined by 1 n times the sum of the indegrees of the others to whom 1 is tied sele i oy Vij 45 Dj Vig Dn Chg activity alter effect defined by 1 n times the sum of the outdegrees of the others to whom i is tied ste a 0 Bij j DO Lig Dy Lin outdegree up to c where c is some constant defined by sig 1 max ai c square root outdegree cx o d where c is some constant defined by sig 2 Tit CLi4 where c is chosen to diminish the collinearity between this and the outdegree effect squared outdegree c where c is some constant defined by stig 0 i e where c is chosen to diminish the collinearity between this and the outdegree effect sum of 1 outdegree c where c is some constant defined by sito 1 zi 0 sum of 1 outdegree c outdegree c 1 where c is some constant defined by shel a 1 2i 0 z c 1 number of 3 cycles S113 Y jp Vij Ejh This betweenness count net Sita Y jp Thi Tij 1 Ehi number of dense triads defined as triads containing at least c ties siis T Xj Hli tye in Ehi Tin Ung 2 ch where the indicator function I A is 1 if th
42. e tied pairs i j for which there exists at least one h such that in hj 1 i e tied pairs for which there is at least one twopath from i to j for undirected graphs this is eee Zij MAXn4i j Lin Un for directed graphs it is Da Lij MAXhZi j Lih Uhj t 15 The number of indirectly connected pairs i e pairs i j for which there is at least one twopath from i to j for undirected graphs this is pares maxn i j Lin nj for directed graphs it is iss maxp4i j Lih Lhj 16 The alternating k out stars combination n 1 Li T 2 1 ES a _ 1 o ae for some value c 44 17 18 19 20 21 22 23 24 The alternating k in stars combination n 1 Ea E Fae cea a es for some value c For undirected graphs the related k triangles statistic 1 Loi i lt j E for some value c where La is the number of two paths from 7 to j Lai ya LinXnj for directed graphs the formula is 1 Looij Zefi 1 1 k ij with the same definition of Lo For undirected graphs the k parallel two paths statistic nee c 3 f 5 which formula is replaced for directed graphs by El Ay For each dyadic covariate w j the sum ee j Tij Wij For each dyadic covariate wij the associated reciprocity effect defined by D j Tij ji 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
43. e carried out 1 for the outdegree effect 2 for the reciprocity effect if this is selected a list of actors also has to be supplied 31 10 A random number seed If the value 0 is chosen the program will randomly select a seed This is advised to obtain truly random results If results from an earlier run are to be exactly replicated the random number seed from this earlier run can be used Options about the simulation runs can be accessed in the StOCNET environment via the simu lation specification button on the SIENA model s main screen This button only is activated when simulation is chosen as the Run model There is one option for simulations that can be chosen here 1 The number of runs in the straight simulations Advice the default of 1000 will usually be adequate Depending on the choice for conditional or unconditional estimation in the estimation options also the simulations are run conditionally or unconditionally 32 11 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 van de Bunt van Duijn and Snijders 1999 and used as example also in Snijders 2001 and Snijders 2005 The data files are provided with the program The digraph data 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
44. e condition A is fulfilled and 0 otherwise and where c is either 5 or 6 this effect is superfluous and undefined for symmetric networks number of unilateral peripheral relations to dense triads ea yng Lig 1 25 1 En 1 ri LEG Eng 25x Ej Ene Ten 2 C where c is the same constant as in the dense triads effect for symmetric networks the uni lateral condition is dropped and the definition is sto 2 Doane ijl Cri 0 wea I Ejn Eng Ejk 2ej Che Len gt ch The effects for a dyadic covariate wij are 17 18 covariate centered main effect Sir gt viz wiz 0 where w is the mean value of wij covariate centered x reciprocity Sits 2 Do wig yi Wig 00 39 For actor dependent covariates vj recall that these are centered internally by SIENA as well as for dependent behavior variables for notational simplicity here also denoted v there are 10 possible effects 19 20 21 22 4 effects of covariate related similarity defined by the sum of centered similarity scores sim between and the other actors j to whom he is tied The main effect of this type is this one sio X ci sio sim where sim is the mean of all similarity scores which are defined as sim a with A max v v being the observed range of the covariate v The first two of these effects are interactions of covariate related similar
45. e containing the effect name the other containing sequences of numbers These have the following meaning x a 0 1 entry denoting whether the effect is included x a 0 1 entry denoting whether a corresponding random effect effect is included a 0 1 entry denoting whether the effect is fixed x a 0 1 entry indicating whether a fixed effect is included in goodness of fit calcula tions the starting value of the parameter for the estimation procedure x an effect specific parameter Of the three rows that follow this pattern the first row corresponds to the utility function the second row corresponds to the endowment function and the third row is reserved for future model extensions that allow the modeling of adaptive learning behavior In the current version of SIENA but one dependent network variable can be analyzed at a time so there will only be sections 2 1 y Sections starting 3 x contain the model specification for dependent action variables again indexed by x as for the network variables there are two subsections Subsections 3 x 1 contain the specification of the behavioral rate function Subsections 3 x 2 contain the specification of the behavioral decision rule including the utility endowment functions These subsections have the same format as the corresponding subsections for the network evolution model The final Section 4 contains specifications of various estimation options Most of these
46. e is called it may be necessary to close the DOS window after the program is ready 4 or a shortcut to the executable file can be made where the project name is indicated in the target in the properties of the shortcut 47 The third and fourth ways are the most straightforward in Windows Note that a shortcut is made by opening Windows Explorer giving a right mouse click on the executable file and then giving a left mouse click on Create Shortcut When the shortcut has been made the project name of the SIENA project must be added to the shortcut as follows give a right mouse click on the shortcut then give a left mouse click on properties and in the Target field add a space and the project name after the path plus filename of the executable file To run SIENA outside of StOCNET the steps taken are the following 1 Write the basic information file pname IN which describes the data files and variable names according to Section 16 1 This file must be in ASCII text format 2 Make shortcuts or batch files as indicated above for each of the programs SIENAO1 and SIENAO7 and if desired also for SIENA02 SIENA04 and SIENAO5 3 Give the session name indicated here as pname as the command line parameter in the shortcuts or batch files 4 Click on the shortcut or batch file for SIENAO1 This should be done only once to create the project because calling SIENAO1 for an existing project will overwri
47. e is simulate false Set the global variable simulate to true SIENA will then simulate data sets according to the probability model specified in the pname MO file Then manipulate the global constant sequences declared in unit Siena_7 by setting it to some positive integer value k the default is 1 The constant sequences gives the number of runs sequences The result is that running Siena will generate k data sets according to the probability model specified pname MO file From each data set the parameters are estimated and test statistics are evaluated Some Matlab source files are by default generated by SIENA The source code when inter preted by Matlab produces histograms of some statistics in particular histograms of the parameter estimates and the test statistics It should be noted that SIENA generates networks with desired properties but by default no covariates If covariates are desired suitable code must be added at the beginning of the procedure SimulateData in the unit S_EST Please note that both internal and external storage see Section 16 3 of generated covariates is required Internal storage is difficult unless one knows SIENA it is advisable to contact the authors in such cases 63 20 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
48. ego with other actor covariates or dependent actor variables is interpreted as an interaction of covariate ego with the score of alter on this variable The selection of effects with which covariate ego is to interact works the same way as sketched above for the interactions of covariate based similarity covariate alter or covariate related popularity defined by the sum of the covariate over all actors to whom i has a tie sizi 0 oy Vig Vj between covariate dissimilars defined by the sum of dissimilarity of all pairs of actors that are connected by a shortest 2 path via actor i 8153 D jp Tritij 1 Zpj sim sim Additional possible effects are documented in Steglich Snijders and Pearson 2004 and for Model Type 2 in Snijders 2003 13 1 2 Network endowment function The network endowment function e called gratification function and 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 and their formulae are the same 40 as in the utility function However the endowment function contributes to the probabilities of making changes only for dissolution of ties and not for formation of ties For further explication consult Snijders 2001 2005 and Steglich Snijders and Pearson 2004 13 1 3 Network rate function The network rate function t lambda is defined for
49. er 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 number 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 11 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 Example of file with times of composition change Present at all five observation times 0 10 5 00 Joining in period 2 at fraction 0 6 of length of period 2 0 6 5 0 0 Leaving in period 3 at fraction 0 4 of length of period 0 1 0 3 0 4 Joining in per 1 0 7 and leaving in per 4 0 2 1 0
50. er of ties 1 Number of reciprocated ties 0 Esad As can be seen for each effect there are two rows a row containing the statistic s name a row contining an indicator whether the statistic shall be simulated e Section 2 contains options for simulation Currently there is but one option the default number of simulations for straight simulation advice 1000 The file pname Sl by and large contains the same information as the screen opening up in StOCNET when clicking the Statistics specification button which is possible as soon as Simulation is selected as the Run model 55 16 3 Data files After the initial project definition the original data files are not used any more but the project data files are used These are the following e pname d01 Network data file time 1 e pname d02 etc Network data file time 2 etc e pname m01 etc Network missings file time 1 etc e pname s0l etc Fixed part of network structure period 1 etc e pname dav Data file constant actor dependent variables centered e pname mav Missings file constant actor dependent variables centered e pname dac Data file with changing actor dependent variables e pname mac Missings file changing actor dependent variables centered e pname z01 etc Data files dyadic covariates e pnamen0l etc Missings files dyadic covariates pname dex Data file times of composition change The user does not need to care about these da
51. f actors increased to 500 The main changes in version 1 95 compared to version 1 90 are 1 2 for the exponential random graph model some extra simulation options were added and inversion steps were added to the algorithm some effects 3 star and 4 star counts added to the exponential random graph model 3 4 for changing covariates the global rather than the periodwise mean is subtracted the program SIENAO2 for data description was added The main changes in version 1 90 compared to version 1 70 are I 2 possibility to use more than two observation moments inclusion of the exponential random graph p model corresponding to one observation moment possibility to have changes of composition of the network actors leaving and or entering changing actor covariates 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 small improvements in the user interface 3 Parts of the program The operation of the SIENA program is comprised of four main parts 1 input of basic data description 2 model specification 3 estimation of parameter values using stochastic simulation 4 simulation of the model with given and fixed parameter values The normal operation is to start with data input then specify a model and estimate its pa rameters and then continue with new model specifications
52. f exogenous changing dyadic covariates must be equal to zero in the current version of SIENA Section 7 is reserved for the specification of this type of covariate data indicator of file with times of composition change 0 means no change of network com position 1 means composition changes Possible composition change data are further specified in Section 8 2 Section 2 contains information about the network data as follows 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 a line with the codes that are regarded as missing data a line with the name of the network variable All codes should be in the range from 0 to 9 3 Section 3 contains information about the dependent actor variables in this format for each dependent actor variable the following three lines 49 a line with the name of the data file a line with the code that is regarded as missing data a line with the name of the variable 4 Section 4 contains information about constant actor covariates as follows e For each file containing such covariates 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 for each variable a line with the code for missing data x a line with the name of the variable Note that t
53. firm is and in addition the outdegree parameter In general the goodness of fit of some baseline model is tested with respect to some critical part of the model Critical parts may be identified by substantive insight and or explanatory analyses It is important to realise that carrying out too many tests may result in an inflation of the type I error probability In other words goodness of fit tests are recommended only for the most critical parts of the model In the present example Pahor 2003 expected on the basis of substantive reasons that firms tend to reciprocate ownership ties to ensure that the firms are on the same boat interest align ment That is it was desired to test whether the goodness of fit of the baseline model with respect to reciprocity was acceptable Hence the reciprocity parameter was added to the baseline model but restricted to the value 0 that is it is postulated that reciprocated ties do not have any added value given the other parameters in the model control parameters and outdegree in terms of estimating the model it means that the other parameters are estimated while reciprocity is kept constant at 0 throughout the estimation process as can be seen on the SIENA interface which is appealing in terms of computation time Estimating the model and evaluating the generalized score test statistic the following output is obtained 24 2 Generalized score test c Testing the goodness of fit
54. from targets 1 0 236 7 006 0 034 2 0 204 7 059 0 029 3 1 592 22 242 0 072 Good convergence is indicated by the t statistics being close to zero 19 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 in themselves not at all a reason for concern 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 estimation results are of doubtful value 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 03 Estimates and standard errors O Rate parameter 5 4292 0 6920 Other parameters 1 f outdeg
55. h run are also written to the file pname sdt sdt for 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 written to the file pname log 8 1 Conditional and unconditional simulation The distinction between conditional and unconditional simulation is the same for the simulation as for the estimation option of SIENA described in Section 6 3 3 If the conditional simulation option was chosen which is the default and the simulations do not succeed in achieving the condition required by its stopping rule see Section 6 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 unconditional simulation 28 9 One observation exponential random graph models By choosing only one observation moment the user specifies that not a model for network evolution is studied but an exponential random graph model ERGM also called a 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 This algorithm com putes a Monte Carlo approximation of the maximum likelihood estimate However if the model specification is not well in accordance with the data set then the algorithm will
56. his format differs from the one used in Sections 03 and 05 through 07 because here data files can potentially contain more than one covariate while in these other sections only one variable is given per file 5 Section 5 contains information about changing actor covariates in the same format as the dependent actor variables are given e for each changing actor covariate the following three lines a line with the name of the data file a line with the code that is regarded as missing data a line with the name of the covariate 6 Section 6 contains information about constant dyadic covariates in the same format e for each constant dyadic covariate the following three lines a line with the name of the data file a line with the code that is regarded as missing data a line with the name of the covariate 7 Section 7 refers to changing dyadic covariates which cannot be handled by SIENA yet 8 Section 8 contains information about network composition change namely e a line with the name of the file containing times of network composition change Whenever a certain type of data is not present leave out the entire section in the file pname IN corresponding to this type For example if you do not have any files containing changing actor covariates leave out Section 5 If there are problems in reading the basic input file try deleting superfluous blanks and or empty rows See to it that the basic inp
57. ired change of the adjacency matrix and the associated updates of various statistics Procedure ChangeBehavior is called at the end of procedure RunStep if a change in behavior is made and carries out the required change of the dependent action variable and the associated updates of various statistics g Function NetworkLambda which is the rate function for the network changes made by each actor and is used in procedure Runstep For Model Type 2 it uses functions and v h Function ActionLambda which is the rate function for the behavior changes made by each actor and is used in procedure Runstep i Function contr_fn which defines the contribution sX x see Section 13 1 1 of each given effect h to the utility function for the network and is used in procedure Runstep j Function contr_gn which defines the contribution of each given effect to the endowment function for the network and is also used in procedure Runstep k Function contr_fa which defines the contribution s4 x of each given effect h to the utility function for the behavior and is used in procedure Runstep 1 Function contr_gn which defines the contribution of each given effect to the endowment function for the behavior and is used in procedure Runstep 60 4 In unit S_EST the Robbins Monro algorithm is contained in the procedure POLRUP for Polyak Ruppert see Snijders 2001 When parameters are to be tested by Neyman Rao tests S EST c
58. irst project in the list here project A so in file A mo and applies this model definition to all projects To get started try this out with a small data set e g the data set included in the zip file with project CB and the subprojects CB1 CB3 CB4 Then these three projects must be initialised first that can be done by using StOCNET but another option is a batch file with the commands start w siena01 cb1 start w siena01 cb3 start w siena01 cb4 The batchfile must have extension bat it must be in a directory containing the Siena01 exe file as well as the data files and you can run it as usual by double clicking on it 37 13 Mathematical definition of effects Here the mathematical formulae for the definition of the effects are given In Snijders 2001 and Steglich Snijders and Pearson 2004 further background to these formulae can be found The effects are grouped into effects for modelling network evolution and effects for modelling behavioral evolution i e the dynamics of dependent actor variables Within each group of effects the effects are listed in the order in which they appear in SIENA 13 1 Network evolution The model of network evolution consists of the model of actors decisions to establish new ties or dissolve existing ties according to utility and endowment functions and the model of the timing of these decisions according to the rate function 13 1 1 Network utility function The potential effe
59. 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 network effects reciprocity transitivity etc to get an impression of what the network dynamics looks like and later add effects of covariates 11 1 1 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 t2 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 hard
60. ity with network effects the desired network effect s number needs to be given in the parameter column on the advanced model specification screen E g the main effect above figures as an interaction of covariate related similarity with the outdegree effect the corresponding effect parameter would be 1 for indicating interaction with the outdegree effect which has number 1 see above Possible parameters here are 1 through 7 outdegree through activity alter and 16 peripheral status The next two effects are interactions of covariate related similarity with other covariates or behavioral variables The desired covariate s number needs to be given in the parameter column on the advanced model specification screen The numbering is as follows first come the constant actor covariates followed by the dependent action variables and the changing actor covariates and at the end come the dyadic covariates If number 0 zero is given as parameter then the main effect of covariate related similarity is included 4 effects of covariate ego The main effect of this type would be the interaction of covariate ego with the outdegree effect covariate related activity defined by 7 s outdegree weighted by his covariate value sigo x Vi Ti Also here the first two effects are interactions of covariate ego with network effects while the next two effects are interactions of covariate ego with covariates Note that interaction of covariate
61. ive 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 The indicative sizes of 2 and 5 result from experience with network effects and with effects of covariates on usual scales with standard deviations ranging between say 0 4 and 2 These numbers have to be modified for covariates with different standard errors 3 Collinearity check After the parameter estimates the covariance matrix of the estimates is presented 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 outdegree 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 different combinations of parameter values could represent the same data pat tern 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 I
62. led 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 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 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 outdegree 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 oth
63. lues Values of effects not included in the 13 model are not changed by the estimation process 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 5 1 Effects associated with covariates For each individual covariate there are several effects which can be included in a model specifi cation both in the network evolution part and in the behavioral evolution part should there be dependent behavioral variables in the data While the possible effects on behavioral evolution are still limited to a main effect of the covariate on the behavioral utility function there is more choice concerning the possible effects on network evolution e network rate function 1 the covariate s effect on the rate of network change of the actor e network utility function 1 the covariate similarity effect a positive parameter implies that actors prefer ties to oth ers with similar values on this variable thus contributing to the network autocorrelation of this variable not by changing the variable but by changing the network 2 the effect on the actor s activity covariate ego a positive parameter will imply the tendency that actors with higher values on this covariate increase their outdegrees more rapidly 3 the effect on the actor s popularity to other actors covariate alter a positive parameter will imply the tendency that the indeg
64. lution The model of the dynamics of a dependent actor variable consists of a model of actors decisions according to utility and endowment functions and a model of the timing of these decisions ac cording to a rate function just like the model for the network dynamics The decisions now do not concern the creation or dissolution of network ties but whether an actor increases or decreases his score on the dependent actor variable by one or keeps it as it is 13 2 1 Behavioral utility function beh Effects for the behavioral utility function u can be selected from the following 1 behavioral tendency effect seh a Xi where z denotes the value of the dependent behavioral variable of actor i 2 similarity effect defined by the sum of centered similarity scores simf between i and the other actors 7 to whom he is tied siz 2 sim sim 42 3 indegree effect sh z 24 ji 4 outdegree effect spr a Xi 2 Tij 5 indegree up to c effect where cis a constant between 1 and n 1 sa zil lt 6 where again JA denotes the indicator function of the condition A 6 similarity x reciprocity effect defined by the sum of centered similarity scores simf between i and the other actors j to whom he is reciprocally tied sie 2 ey Lig sims sim 7 dense triads effect defined by the number of dense triads in which actor i is located sip x zistis 2 8 periphe
65. ly any change from 1 to 0 then it is possible that the outdegree parameter must be fixed at some high positive value 11 1 2 Exploring which effects to include The present section describes an exploratory approach to model specification A more advanced approach to testing model specifications is described in Section 7 For an exploration 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 among the simulated 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 capitalization 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
66. n and reconsider whether a tie will exist between them a new tie is formed if at least one wishes this Pairwise compensatory additive model a pair of actors is chosen and reconsider whether a tie will exist between them this is based on the sum of their utilities for the existence of this tie In Models 1 2 where the initiative is one sided the rate function is comparable to the rate function in directed models In Models 3 5 however the pair of actors is chosen at a rate which is the product of the rate functions A and A for the two actors This means that opportunities for change of the single tie variable x occur at the rate A x Aj The numerical interpretation is different from that in Models 1 2 17 6 Estimation The model parameters are estimated under the specification given during the model specification 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 repeated simulation of the evolution process of the network These repetitions are called runs in the following The estimation algorithm is based on comparing the observed network obtained from the data files to the hypothetical networks generated in the simulations Note that the estimation algorithm is of a stochastic nature so the results can vary This is of course not what you would like For well fitting combinations of data set and model
67. nction e B For the utility function 58 1 Procedure DefineModel_fnames defines the names of the effects and the index numbers of the corresponding statistics 2 function Contr_fn gives for each effect for the network dynamics the contribution to the difference between the value of the utility function after a change will be made and its current value 3 function Contr_fa gives for each effect for the behavior dynamics the contribution to the difference between the value of the utility function after a change will be made and its current value e C For the endowment function 1 Procedure DefineModel_gnames defines the names of the effects and the index numbers of the corresponding statistics 2 function Contr_gn gives the contribution of each effect to the endowment function for the network dynamics 3 function Contr_ga gives the contribution of each effect to the endowment function for the behavior dynamics e D For the statistics 1 Procedure DefineFunctionnames defines the names of the statistics 2 procedure Statistics calculates the statistics 18 1 Starting to look at the source code If you wish to start with understanding the structure of the source code it may be helpful to take the following tour of some essential ingredients 1 Unit EIGHT contains the fundamental data structures i Functions starting with y represent dependent variables a yn is the adjacency matrix of the dependent network varia
68. nditioning is possible for each of the dependent variables network or behavior where conditional means conditional on the observed number of changes on this dependent variable Conditioning on the network variable means running simulations 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 Conditioning on a behavioral variable means running simulations until the sum of absolute score differences on the behavioral variable between the initially observed behavior of this period and the simulated behavior is equal to the sum of absolute score differences between the initially and the finally observed behavior of this period Conditional estimation is slightly more stable and efficient because the corresponding rate parameters are not estimated by the Robbins Monro algorithm so this method decreases the number of parameters estimated by this algorithm Therefore it is the default for models that do not include any dependent behavioral variables For models including dependent behavioral variables the default estimation type is unconditional because in most applications there will be no straightforward choice for the conditioning variable The possibility to choose between unconditional and the different types of conditional estimati
69. ng individual variables can be dependent variables changing dynamically in mu tual dependence with the changing network or independent variables exogenously changing variables then they are also called individual covariates 2 dyadic covariates which can be symbolized as w for each ordered pair of actors i 7 they are allowed only to have integer values ranging from 0 to 255 In the current version of SIENA dyadic covariates are not allowed to change over time All variables must be available in ASCII data files described in detail below These files the names of the corresponding variables and the coding of missing data must be made available to SIENA In the StOCNET environment files and variable names are entered in the Data dialog window while missing data are identified in the Transformation dialog window In the Model dialog window network data and additional variables subsequently can be selected for SIENA analyses This is done by first choosing SIENA from the list of available statistical methods and then pushing the Data specification button Names of variables must be composed of at most 12 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 The use of the default variable and file names proposed by StOCNET is not recommended 4 1 Digraph data files Each digraph must be contained in a separate input file in the fo
70. nk 2003 StOCNET An open soft ware system for the advanced statistical analysis of social networks Version 1 4 Groningen ProGAMMA ICS 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 Association 81 832 842 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 Handcock Mark S 2002 Statistical Models for Social Networks Inference and Degeneracy Pp 229 240 in Dynamic Social Network Modeling and Analysis Workshop Summary and Papers edited by Ronald Breiger Kathleen Carley and Philippa E Pattison National Research Council of the National Academies Washington DC The National Academies Press Huisman M E and T A B Snijders 2003 Statistical analysis of longitudinal network data with changing composition Sociological Methods amp Research 32 253 287 Pahor M 2003 Causes and Consequences of Companies Activity in Ownership Network Ph D Thesis University of Ljubljana Slovenia Schweinberger M 2005 Statistical Modeling of Network Dynamics Given Panel Data Goodness of fit Tests Submitted for publication Snijders T A B 2001 The statistical evaluation of social network dynamics Pp 361 395 in Soci ological Methodolog
71. not converge properly This is discussed in Snijders 2002 and Handcock 2002 How to specify the model is discussed in Snijders Pattison Robins and Handcock 2005 focusing on how to specify transi tivity To model this concept more complicated effects are required than the traditional transitive triplet count Also when the model specification is good however it may require repeated SIENA runs each using the previously obtained estimate as the new starting value to obtain satisfactory convergence of the algorithm This means in practice that 1 great care is required for the model specification 2 the user may have to tune two constants for the algorithm called rstep and the initial gain parameter which are discussed below 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 For unconditional estimation the total number of ties is a random variable The choice between these two is made in the advanced options If there are structural zeros see Section 4 1 1 and the elements of the adjacency matrix that are not structurally determined split the network into two or more components which will happen in the case where several smaller networks are artificially combined into one network with structural zeros between the original smaller networks then the conditional estimation option keeps the total number of ties constant within each componen
72. ns which are not yet 51 available through StOCNET whether such options exist will depend on the versions of SIENA and StOCNET When looking at the pname MO file you can see that this file by and large contains the same information as the screen opening up in StOCNET when clicking the Model specification button More precisely the pname MO file consists of several sections marked by O symbols as follows e Section 1 contains general information about the project such as data format numbers and names of variables The information given in this section must be compatible to the information provided in the file pname lN e Sections starting 2 x contain the model specification for dependent network variables in dexed by x There are two subsections Subsections 2 x 1 contain the specification of the network rate function which looks like this 2 1 1 rate function effects for dependent network variable 1 11 number of these effects each effect is given in two rows first row contains label of the effect second row contains flags for inclusion fixing and testing the starting value and potential extra parameters for effect calculation basic network rate parameter 000 5 851107 O outdegrees effect on rate 000 0 000000 O Esc The section must contain first a row with the number of effects further down for each of these effects two rows one containing the effect name the other containing a sequence
73. ob de Negro in Delphi with first Evelien Zeggelink then Mark Huisman and later Christian Steglich as the project leader The computational part can be used both directly and from the windows shell The StOCNET windows shell is much easier for data specification and model definition 15 Running SIENA outside of StOCNET The present computational part is composed of six executable programs These programs are 1 SIENAO1 EXE for the basic data input using an existing basic information file see below 2 SIENAO2 EXE for data description SIENAO4 EXE for confirmation of the model specification SIENAO5 EXE for simulations with fixed parameter values SIENAO7 EXE for parameter estimation O oh FF WwW SIENAO8 EXE for multilevel analysis These programs can be used also independently of StOCNET To run them the project name must be given in a command line e g 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 four ways to specify a command with a command line parameter in Windows 1 The command line can be given at the DOS prompt in a Windows environment 2 it can be given in the Windows Run command for Windows 98 and higher 3 a batch file with extension BAT can be created e g with filename SIE1 BAT containing the single line SIENAO1 bunt so that the program SIENAO1 will be executed when the batch fil
74. of the model restricted by 1 description f reciprocity c 22 6545 d f 1 p value lt 0 0000 To grasp the meaning of the output consider the case where the network is observed at two time points and let R be the number of reciprocated ties at the second time point Then it can be shown that the test statistic is some function of Expected R under the restricted model observed R Thus the test statistic has some appealing interpretation in terms of goodness of fit when recip rocated ties do have added value for the firms which means that the reciprocity parameter is not 0 other than the model assumes then the deviation of the observed R from the R that is expected under the model will be large large misfit and so will be the value of the test statistic Large values of the test statistic imply low p values which in turn suggests to abandon the model in favor of models incorporating reciprocity Under some conditions the distribution of the test statistic tends as the number of observations increases to the chi square distribution where the number of degrees of freedom is equal to the number of restricted parameters The corresponding p value is given in the output file In the present case one parameter is restricted reciprocity hence there is one degree of freedom d f 1 The value of the test statistic c 22 65 at one degree of freedom gives p value lt 0000 The fact that 22 65 is remarkably large compared
75. om subphase 2 2 onward for some parameters these may be the parameters that 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 35 11 3 Composition change Example data files for a network of changing composition are also provided with the program 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 artificially 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 4 6 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 10 7 3 0 0 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
76. on is one of the model options If there are changes in network composition see Section 4 6 only the unconditional estimation procedure is available 22 6 3 4 Automatic changes from conditional to unconditional estimation Even though conditional estimation is slightly more efficient than unconditional estimation there is one kind of problem that sometimes occurs with conditional estimation and which is not en countered by unconditional estimation It is possible but luckily rare that the initial parameter values were chosen in an unfortu nate way such that the conditional simulation does not succeed in ever attaining the condition required by its stopping rule see Section 6 3 3 This is detected by SIENA which then switches automatically to unconditional estimation after some time it switches back again to conditional estimation 23 7 Goodness of fit To compare competing models for network and behavior evolution goodness of fit tests are indis pensable A generalized Neyman Rao score test is implemented in SIENA which can be used for goodness of fit tests see Schweinberger 2005 In section 7 1 it is described how goodness of fit tests can be carried out and in section 7 2 an example is given including interpretation Section 7 3 considers an alternative application of the test which may be of interest when facing convergence problems 7 1 How to do Most goodness of fit tests will have the following form some model
77. one of the values 11 16 because these generate a continuous chain which yields much better convergence The number of subphases in phase 2 of the estimation algorithm This determines the precision of the estimate Advice 3 for quick preliminary investigations 4 or 5 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 for serious investigations 1000 for estimations of which results are to be reported A constant used in other estimation procedures In the ERGM non longitudinal case this is the multiplication factor r for the run length used in the MCMC algorithm The initial gain value which is the step size in the starting steps of the Robbins Monro procedure indicated in Snijders 2001 by a The choice between standard initial values suitable estimates for the outdegree and reci procity parameters and zero values for all other parameters or the current parameter values as initial values for estimating new parameter values The selection of the period for which a goodness of fit on period homogeneity is to be carried out The selection of the effect for which a goodness of fit on actor homogeneity is to b
78. r Huisman Snijders amp Zeggelink 2003 which can be downloaded from the same website For the operation of StOCNET the reader is referred to the corresponding manual If desired SIENA can be operated also independently of StOCNET as is explained in Section 15 This manual consists of two parts the user s manual and the programmer s manual There are two parallel pdf versions s_manx_s pdf for screen viewing and s_manx_p pdf for printing where the x stands for a version number They were made with the TEX pdfscreen sty package of C V Radhakrishnan which made it possible e g to insert various hyperlinks within the manual Both versions can be viewed and printed with the Adobe Acrobat reader This is the print version Section numbering may differ between the two versions The manual focuses on the use of SIENA for analysing the dynamics of directed networks The case of non directed networks is very similar and at various points this case is described more in particular Sections on data requirements general operation etc apply as well to parameter estimation in the ERGM non longitudinal model Some specific sections are devoted to the specification of that particular model For getting started one excellent option is to read the User s Manual from start to finish leav ing aside the Programmer s Manual Another option is to focus on Sections 5 for the model specification 6 to get a basic insight in what happens in the par
79. ral effect defined by the number of dense triads to which actor 7 stands in a unilateral peripheral relation sig x zisti x For each actor dependent covariate vj recall that these are centered internally by SIENA as well as for each of the other dependent behavior variables for notational simplicity here also denoted vj there is one main effect 9 covariate effect gbeh z BY Additional possible effects are documented in Steglich Snijders and Pearson 2004 13 2 2 Behavioral endowment function Also the behavioral model knows the distinction between utility and endowment effects The formulae of the effects that can be included in the behavioral endowment function eP are the same as those given for the behavioral utility function However they enter calculation of the endowment function only when the actor considers decreasing his behavioral score by one unit downward steps not when upward steps or no change are considered For more details consult Steglich Snijders and Pearson 2004 13 2 3 Behavioral rate function The behavioral rate function AP consists of a constant term per period beh _ beh for m 1 M 1 13 3 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 x exp 6 u x p 0 43 where u x is a vector of statistics The following st
80. rates is once again equivalent to the tables shown above and the interpretation of a low p value would be that the value of the specified parameter in the specified period seems to deviate from the value of the parameter in other periods 7 3 Alternative application convergence problems An alternative use of the test statistic is as follows When convergence of the estimation algorithm is doubtful it is sensible to restrict the model to be estimated Either problematic or non problematic parameters can be kept constant at preliminary estimates estimated parameters values Though such strategies may be doubtful in at least some cases it may be in other cases the only viable option besides simply abandoning problematic models The test statistic can be exploited as a guide in the process of restricting and estimating models as small values of the test statistic indicate that the imposed restriction on the parameters is not problematic 27 8 Simulation The simulation option simulates the network evolution for fixed parameter values This is meaning ful mainly at the point that you have already estimated parameters 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
81. re included Use a smaller number of effects delete non significant ones and increase complexity step by step Retain parameter estimates from the last sim pler model as the initial values for the new estimation procedure provided for this model the algorithm converged without difficulties 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 In this case it may be better to exclude one of these effects from the model e An effect is included that is large but of which the precise value is not well determined see above section on fixing parameters This will be seen in estimates and standard errors both being large and often in divergence of the algorithm Fix this parameter to some large value Note large here means e g more than 5 or less than 5 depending on the effect of course If there are problems you don t understand but you do know something about the operation of SIENA 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 If this happens fr
82. ree density 0 7648 0 2957 2 f reciprocity 2 3071 0 5319 3 f number of distances 2 0 5923 0 1407 The rate parameter is the parameter called p in section 13 1 3 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 utility function The terms in the utility function in this model specification are the outdegree effect defined as s in Section 13 1 1 the reciprocity effect si2 and the number of distances 2 indirect relations effect defined as sis Therefore the estimated utility function here is 0 76 si x 2 31 siz x 0 59 sis 5 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 positive The weights in the utility function can be tested by t statistics defined as estimate divided by its st
83. rees of actors with higher values on this covariate increase more rapidly 4 the interaction effect of covariate similarity with reciprocity 5 several other interaction effects of the covariate or covariate similarity with endogenous network effects and other covariates or behavioral variables e network endowment function 1 the covariate similarity effect a positive parameter indicates that being tied to similar network neighbors is preferred to both being tied to dissimilar network neighbors and creating new ties to similar others The usual order of importance of these covariate effects on network evolution is utility effects are most important followed by endowment and rate effects Inside the group of utility effects it is the covariate similarity effect that is most important follwed by the effects of covariate ego and covariate alter Note that while in principle there is one endowment effect corresponding to each utility effect in the current version of SIENA the effects listed here are the only covariate related network endowment effects implemented For each dyadic covariate the following network utility effects can be included in the model for network evolution e network utility function 1 main effect of the dyadic covariate 2 the interaction effect of the dyadic covariate with reciprocity 14 e network endowment function 1 main effect of the dyadic covariate The main utility effect is usually the mos
84. rks e e e 5 2 2 Model Type non directed networks o e 6 Estimation 6 17 Algorta o a A A A A AA a 6 2 Output a ES ee Seb A A A iE E A LI A ENS 6 3 Other remarks about the estimation algorithm e e 6 3 1 Changing initial parameter values for estimation 6 3 2 Automatic fixing of parameters 6 3 3 Conditional and unconditional estimation o a e 6 3 4 Automatic changes from conditional to unconditional estimation 7 Goodness of fit Yel HOW de data Oe ee ae at te ee ee Ee ee a ee et T2 Examples 42 2 Sop ed A oe BOER oe oe ep ee Abd be eee Lhe BPS eee 7 2 1 Omnibus tests with more than one restriction e 7 2 2 Testing homogeneity assumptions 02 0000 000000 7 3 Alternative application convergence problems o o 8 Simulation 8 1 Conditional and unconditional simulation 0 200000000005 9 Exponential random graphs 10 Options for model type estimation and simulation 11 Getting started 111 Model choice 2 cs Ab ah dr Oe a EE eB doe AA tc a det Ad ds Fixing parameters ii e Ge ek Se e e Ge A EE 11 1 2 Exploring which effects to include e e 11 2 Convergence problems rt ca sled Wotan ery nies asa tale ate a ale tga a eg ae gE a 11 3 Composition change 00 00 o 10 10 11 12 13 14 15 15 17 18 18 19 21 21 21 22 2
85. rm 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 Although this section talks only about digraphs directed graphs it is also possible that all observed adjacency matrices are symmetric This will be automatically detected by SIENA and the program will then utilize methods for non directed networks 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 number All code numbers must be in the range from 0 to 9 except for structurally determined values see below 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 codes must of course be different from the code numbers representing present arcs 4 1 1 Structurally determined values
86. s 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 check that your data were entered correctly and the coding was given correctly and then re specify 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 model 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 11 1 6 3 3 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 and the co evolution of the behavioral dimensions if any are included carry on until the predetermined time length chosen as 1 0 for each time period between consecutive observation moments has elapsed In conditional estimation in each period the simulations run on until a stopping criterion is reached that is calculated from the observed data Co
87. s may deviate so strongly from the bulk of actors that the question may rise whether those actors have the same outdegree parameter value as the remaining actors Therefore SIENA admits to test homogeneity assumptions with respect to actors and periods An outlier test can be carried out as described in Section 7 1 by specifying one actor as outlier candidate with respect to e g outdegree When such outlier tests are desired SIENA generates a goodness of fit table which is equivalent to the tables above If the p value that is found is low it would seem that the specified actor indeed seems to deviate from the remaining actors with respect to the specified parameter such as outdegree 26 Consider now the assumption that the value of some parameter such as outdegree is constant across periods Sometimes such assumptions are not defensible For instance due to exogenous changes in the environment actors may have uniformly changed strategies corresponding to parameter values as a response As an example in the above example with ownership ties between firms governmental laws may have been introduced at some point in time which make it much less attractive to have lots of ownership ties As a result the outdegree parameter can be expected to be deviate from the value in previous periods When it is tested whether the value of some parameter in some specified period is the same as in the other periods the goodness of fit table that SIENA gene
88. s well as missing entries on dependent action variables are replaced by the variable s average score at this observation moment In the course of the simulations however the adjusted values of the dependent action variables and of the network variables are allowed to change In order to ensure a minimal impact of missing data treatment on the results of parameter estimation method of moments estimation and or simulation runs the calculation of the target statistics used for these procedures is restricted to non missing data When for an actor in a given period any variable is missing that is required for calculating a contribution to such a statistic this actor in this period does not contribute to the statistic in question For network and dependent action variables an actor must provide valid data both at the beginning and at the end of a period for being counted in the respective target statistics 4 6 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 This is described more extensively in Huisman and Snijders 2003 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 hand
89. screen you can specify rate function effects At first leave the specification of the rate function as it is see Section 5 in which it was advised to start modeling with a constant rate function Then let the program estimate the parameters You will see a screen with intermediate results current parameter values the differences deviation values between simulated and observed sta tistics these should average out to 0 if the current parameters are close to the correct estimated value and the quasi autocorrelations discussed in Section 6 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 In most cases this is not necessary Some patience is needed to let the machine complete its three phases How this depends on the data set and the number of parameters in the model is indicated in Section 14 After having obtained 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 outdegree and the reciprocity effects and other effects may be included 33 11 1 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
90. t The program recognizes automatically if the data set is symmetric an non directed graph with zij x for all i j or anti symmetric a tournament with xij 4 xj for all i 4 j In such cases this is respected by the Metropolis Hastings algorithm number 5 in the list below chosen by SIENA for the MCMC estimation and the exponential random graph model is considered only 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 cf Snijders 2002 1 Gibbs steps for single relations xij 2 Gibbs steps for dyads 2 1 Gibbs steps for triplets ij Th Tin and Zij Ejh Zhi Metropolis Hastings steps for single relations zij E ee Metropolis Hastings steps for dyads z j ji in which symmetric dyads remain symmetric and asymmetric dyads remain asymmetric This is appropriate for symmetric and antisym metric graphs 6 Metropolis Hastings steps keeping the indegrees and outdegrees fixed see Snijders and van Duijn 2002 The choice between these types of steps is made in the model options Some other options are available by modifying the pname MO file as indicated in Section 16 2 1 below In the conditional option where the number of arcs is fixed options 1 and 4 exchange values of arcs xij and Zak with i j 4 h k with probabilities defined by the Gibbs and Metropolis Hastings rules respectively option 2
91. t important In the current version of SIENA there are no effects of dyadic covariates on behavioral evolution 5 2 Model Type 5 2 1 Model Type directed networks For directed networks the Model Type distinguishes between the model of Snijders 2001 Model Type 1 and that of Snijders 2003 Model Type 2 Model Type 1 is the default model and is described in the basic publications on Stochastic Actor Oriented Models for network dynamics In Model Type 2 the decisions by the actors consist of two steps first a step to increase or decrease their outdegree when this step has been taken the selection of the other actor towards whom a new tie is extended if the outdegree rises or from a an existing tie is withdrawn if the outdegree drops The decision by an actor to increase or decrease the number of outgoing ties is determined on the basis of only the current degree the probabilities of increasing or decreasing the outdegree 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 utility and endowment 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 observed degrees on the conclusions about the s
92. t is then advisable to omit one of the corresponding effects from the model because it may be redundant given the 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 significance to significance 6 3 Other remarks about the estimation algorithm 6 3 1 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 one of the model options It can also be done by breaking in into the SIENA program 6 3 2 Automatic fixing of parameters If the algorithm encounters computational problems sometimes it tries to solve them automatically 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 21 problem is not in the parameter that is being fixed but is caused by an incorrect starting value of this parameter or one of the other parameter
93. ta files but should not delete them either 16 4 Output files The output for the user goes to pname out Extra output is written to pname log which in the first place is a log file of what the program did The estimation procedure also writes a file pname chk containing a more detailed report of the estimation algorithm The latter two files are for diagnostic purposes only The pname chk file is overwritten with each new estimation procedure 56 17 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 2 S_BASE contains the basic model definition S_SIM contains the procedure for straight simulation S_EST contains the procedure for estimation S_TEST contains procedures for goodness of fit tests O oOo A WwW S_DESC contains procedures for data description Then there is an intermediate unit 7 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 Procedure ReadWriteData from S_START must be followed always by procedure BeforeFirst ModelDefinition from S_BASE Further there are three units containing specific kinds of utilities 8 SLIB is a library of various computational and input output utilities 9 RANGEN is a library for generation of random variables
94. te the output file 5 Open the file pname MO in a text editor edit it to obtain the desired model specification see section 16 2 1 and save it as a text ASCIT file 6 Click on the shortcut or batch file for SIENAO7 The last two steps modifying the pname MO file and running SIENAO7 can be repeated as much as one likes Some of the model defining statistics in the SIENA model contain numbers or fixed parameters that can be set at other values by the user Examples are the value 3 in outdegree up to 3 for the longitudinal version of SIENA and the value 2 in the linear combination of k out stars in the non longitudinal p version of SIENA These numbers should not be confused with the statistical parameters that are estimated by SIENAO7 These values are represented in the pname MO file as the last of the 6 values in the line for this effect When these values are modified the change must be put into effect by calling SIENA04 Other possibilities are 7 Get some basic descriptive statistics by running SIENAO2 8 Simulate the model for fixed parameter values by running SIENAO5 The statistics to be simulated are indicated in the file pname si which can be modified to add to or delete from the list of simulated statistics 48 16 SIENA files Internally the following files are used Recall that pname is the name of the project which the user can choose at will 16 1 Basic information file The basi
95. ted are rather unreliable 18 The number of subphases in phase 2 and the number of runs in phase 3 can be changed in the model options 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 process 6 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 The latter file also contains some supplementary output that usually is disregarded but sometimes is helpful Some diagnostic output containing a history of the estimation algorithm which may be informative when there are convergence problems is written to the file pname 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
96. 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 normally is the current value that is the value that the parameters have immediately before you start the estimation process as an alternative it is possible to start instead with a standard initial value Usually a sequence of models can be fitted without problems each using the previously obtained estimate as the starting point for the new estimation procedure Sometimes however problems may occur during the estimation process which will be indicated by some kind of warning in the output file or by parameter estimates being outside a reasonably expected range In such cases the current parameter estimates may be unsatisfactory and using them as initial values for the new estimation process might again lead to difficulties in estimation Therefore when the current parameter values are unlikely and also when they were obtained after a divergent estimation algorithm it is advisable to start the estimation algorithm with a standard initial value The use of standard initial values is one of the model options 6 1 Algorithm During the estimation process StOCNET transfers control to the SIENA program The estimation algorithm has three phases
97. the first actor joins the network and then stays in during the whole period being analyzed 36 12 Multilevel network analysis The program Siena08 exe is a relatively simple multilevel extension to SIENA This program must be run independently i e not through StOCNET It runs several SIENA estimations subsequently and combines the estimates in a meta analysis or multilevel analysis according to the methods of Snijders and Baerveldt 2003 All Siena projects to be used must already exist i e each project data set must have gone through SIENAO1 or through StOCNET SIENA at least once This is for making the mo files and transformed data files which are essentially used by Siena08 An easy way to operate Siena08 is to make a shortcut in Windows right click on the shortcut and open the properties tab and in the Target which already contains the path and filename of the Siena08 exe file add the projectname after the filename separated by a space E g suppose the projectname is ABC Then there must be a project file with the name ABC mli the root name ABC can be chosen by the user the extension name mli is prescribed If the number of network evolution projects combined in this Siena08 run is given by K e g the K 3 projects with names A B and C then the file ABC mli must consist of K lines each with the project name e g A B Cc Siena08 considers the model definition in the mo file of the f
98. to account for the observed network density For directed networks it mostly is also advisable to include the reciprocity effect this being one of the most fundamental network effects Likewise behavior utility functions should normally always contain the tendency parameter to account for the observed prevalence of the behavior e endowment function effects The endowment function similar to the gratification function in Snijders 2001 is an exten sion of the utility function that allows to distinguish between new and old network ties when evaluating possible network changes and between increasing or decreasing behavioral scores when evaluating possible behavioral changes The function models the loss of satisfaction incurred when existing network ties are dissolved or when behavioral scores are decreased to a lower value hence the label endowment Advice start modeling without any endowment effects The estimation and simulation procedures of SIENA operate on the basis of the model specifi cation which comprises the set of effects included in the model as described above together with the current parameter values and the Model Type see Section 5 2 After data input the constant rate parameters and the outdegree effect in the network utility function have default initial values depending on the data All other parameter values initially are 0 The estimation process changes the current value of the parameters to the estimated va
99. to the usual standard 3 84 corresponding to significance level 05 indicates that the discrepancy between the degree of reci procity expected by the model and the degree of reciprocity that indeed was observed must be huge That is it seems that the model which assumes that reciprocated ties have no added value is not tenable and hence reciprocity should be included into the model and estimated as the other parameters 7 2 1 Omnibus tests with more than one restriction In the case where K gt 1 model parameters are restricted SIENA evaluates the test statistic with K degrees of freedom A low p value of the omnibus test would indicate that the goodness of fit of the model is intolerable However the omnibus test with K degrees of freedom gives no clue as to what parameters should be included into the model the poor goodness of fit could be due to only one of the K restricted parameters it could be due to two of the K restricted parameters or due to all of them Hence SIENA carries out in addition to the omnibus test with K degrees of freedom additional tests with one degree of freedom that test the single parameters one by one The goodness of fit table looks as follows 25 02 Generalized score test c Testing the goodness of fit of the model restricted by 1 description f reciprocity 2 description f transitivity 3 description f number of actors at distance 2 c 32 1155 d f 3 p value lt 0 0000 1 apart
100. tructural 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 and v are included On the other hand effects in the utility function that depend only on the outdegrees 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 outdegrees and the fitted distribution of the outdegrees as exhibited by the simulated outdegrees For Model Type 2 this comparison is always given For Model Type 1 this comparison is given by adding 10 to the Model Code in the advanced options For TAT X users the log file contains code that can be used to make a graph of the type given in Snijders 2003 For using Model Type 2 it is advised to first estimate some model according to Model Type 1 this may be a simple model containing a reciprocity effect only but it could also include more effects and then using the parameters estimated under Model Type 1 change the specification to Model Type 2 and use the unconditional estimation method see Section 6 3 3 instead of the conditional method which is the default It is likely that the very first model estimated under Model Type 2 will have results with poor convergence properties but in such cases it is advised just to
101. ues 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 For practical purposes one should always use a continuous chain 3 The number of subphases in phase 2 of the estimation algorithm advice 4 4 The number of phase 3 iterations for the estimation algorithm advice 500 for longitu dinal data 1000 for modeling one observation data by an exponential random graph 5 A number r proportional to the number of steps used for generating one graph in the one observation case The number of steps is rn 2d 1 d where n is the number 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 6 The initial value of the gain parameter in the estimation algorithm advice 0 1 7 An indicator for the initial value used in the estimation algorithm code 0 current value as specified in the preceding sections code 1 standardized starting value meaning that a good starting value is chosen for the outdegree effect and in the one observation exponential random graph case also for the reciprocity effect For still other configurations also starting values for the rate parameters and the tendency effect for dependent action variables are internally
102. unction NetworkLambda in unit S_BASE the network change rate function itself e For an effect in the utility function for the network 1 Function NetworkEffects_f in unit S_DAT the total number of possible effects in the network utility function 2 Procedure DefineModel_fnames in unit S_BASE which contains the names of all effects in the network utility function and the numbers of the corresponding statistics 3 Function Contr_fn in unit S_BASE the contribution of a given effect to the difference between the value of the utility function after the change will be made and its current value e For an effect in the endowment function for the network 1 Function NetworkEffects_g in unit S_DAT the total number of possible effects in the network endowment function 2 Procedure DefineModel_gnames in unit S_BASE which contains the names of all effects in the network endowment function and the numbers of the corresponding statistics 61 3 Function Contr_gn in unit S_BASE the contribution of a given effect to the endowment function e For effects in the rate function for behavior change the analogous procedures have to be changed as those for the rate function for network change function ActionEffects_I in unit S DAT procedure DefineModel_Inames in unit S BASE and function ActionLambda in unit S_BASE e For effects in the utility function for behavior change the analogous procedures have to be changed as those for the utility
103. use of various conflicting constraints 3 Unit S_BASE contains the simulation procedures The main procedures in this unit are the following a Function FRAN generates the required statistics and is called by procedure Simulate in S_SIM and by Estimate in S_EST The procedure FRAN first simulates the network and behavior by the procedure Runepoch and then calculates statistics by the procedure Statistics the values of these statistics are output arguments of FRAN b Procedure Statistics calculates the statistics from the generated network or adjacency matrix and behavior variables and is called by FRAN c Procedure Runepoch generates a random network and action variables for given parame ter 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 If there are M observations M gt 2 Runepoch is called M 1 times d Procedure Runstep makes one stochastic step according to the actor oriented evolution model i e it either changes one entry i j of the adjacency matrix to be changed or it changes the value of one action variable for one The time variable time is also increased by an amount depending stochastically on the rate functions This procedure is called by procedure Runepoch e Procedure ChangeTie is called at the end of procedure RunStep if a change in the network is made and carries out the requ
104. ut file is an ASCII text file with numbers separated by blanks lines separated by hard returns The variable names given in the input file will be used in the output files If no names are provided and SIENA is run in the StOCNET environment SIENA uses the default variable names generated by StOCNET in the StOCNET Data menu This is not recommendable because it can lead to identical names for different variables If no names are provided and SIENA is run outside of the StOCNET environment SIENA uses its own default variable names and this problem does not occur An example for the basic input file is the following file bunt IN 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 50 1 general information about SIENA project bunt 2 number of waves 32 number of actors number of dependent network variables number of dependent actor variables number of files with constant actor covariates number of exogenous changing actor covariates number of constant dyadic covariates number of exogenous changing dyadic covariates indicator for file with composition change directives O0Oo0O0OOo0ROrRr 2 network files in temporal order names follow vrnd32t2 dat 1 2 3 code for tie 6 9 code for missing vrnd32t4 dat 1 2 3 code for
105. value of 1 000 and can be changed in the simulation 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 estimate 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 algorithm 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 effects corresponding to the statistics with large t values are candidates for now being added to the model One should be aware however that such a data driven approach leads to capitalization on chance Since the selected effects were chosen on the basis of the large deviation between observed and expected values the t tests based on the same data set will tend to give significant results too easily The generated statistics for eac
106. which each network actor gets an opportunity for changing her score on the dependent variable Advice in most cases start modeling with a constant rate function without additional rate function effects Constant rate functions are selected by exclusively checking the basic rate parameter for network evolution and the main rate effects for behavioral evolution on the model specification screen When there are important size or activity differences between actors it is possible that different advice must be given and it may be necessary to let the rate function depend on the individual covariate that indicates this size or on the outdegree e utility function effects The utility function called objective function in Snijders 2001 models the network actors satisfaction with their local network neighborhood configuration It is assumed that actors change their scores on the dependent variable such that they improve their total satisfaction with a random element to represent the limited predictability of behavior In contrast to the endowment function described below the utility function evaluates only the local network neighborhood configuration that results from the change under consideration hence the reference to the utility concept In most applications the utility function will be the main focus of model selection The network utility function normally should always contain the outdegree or density effect
107. work dynamics NetworkEffects_l the number of effects in the rate function for the network dynamics ActionEffects_f the number of effects in the utility function for the behavior dynamics 2 3 4 5 ActionEffects_g the number of effects in the endowment function for the behavior dynamics 6 ActionEffects_l the number of effects in the rate function for the behavior dynamics 7 NetworkFunctions the number of statistics that can be calculated and which can be used if there are no dependent behavior variables this number must be at least NetworkEffects_f NetworkEffects_g NetworkEffects_l it is allowed to be larger then there are some statistics that are superfluous for parameter estimation by the method of moments 8 ActionFunctions the number of statistics that can be used additionally to the statistics men tioned before in case that there are dependent behavior variables In unit S_BASE the definitions of the effects and statistics are given e A For the rate function 1 Procedure DefineModel_Inames defines the names of the effects and the index numbers of the corresponding statistics 2 function NetworkLambda defines the network change rate function 3 procedure Transform_l calculates some variables for more efficient calculations in Net workLambda 4 for Model Type 2 the rate function for network change also depends on the functions and v 5 function ActionLambda defines the behavior change rate fu
108. y 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 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 Dynam ics Proceedings of the National Academy of Sciences USA to be published Available from http stat gamma rug nl snijders siena html Snijders T A B 2004 Explained Variation in Dynamic Network Models Math matiques Informa tique et Sciences Humaines Mathematics and Social Sciences 168 4 Snijders T A B 2005 Models for Longitudinal Network Data Chapter 11 in P Carrington J Scott and S Wasserman Eds Models and methods in social network analysis New York Cambridge University Press Snijders T A B P E Pattison G L Robins and M S Handcock 2004 New specifications for exponential random graph models Submitted for publication Snijders T A B and M A J Van Duijn 1997 Simulation for statistical inference in dynamic network models Pp 493 512 in Simulating Social Phenomena edited by R Conte R Hegselmann and P Terna Berlin Springer Snijders T A B and M A J Van Duijn 2002 Conditional maximum likelihood estimation under various specifications of exponential random graph models Pp 117 134 in Jan Hag

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