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1. 7 quo Help Figure 32 ULTRAS specifications for Maximum Likelihood Estimation a Number of Ultrametrics The observed network might have been generated from two or more ultrametrics corresponding to two or more interaction contexts such as work place and neighborhood If two actors are close friends either at the work place or in the neighborhood then this will probably give rise to an observed tie between them b Number of iterations A conservative rule of thumb is to carry out n x 100 iterations where n is the number of actors c Temperature The temperature is an essential ingredient to the Simulated Annealing algorithm used by ULTRAS This algorithm sometimes makes downhill steps to escape from local maxima of the likelihood function The probability of making downhill steps depends on the temperature It is sensible to choose a value of the temperature which allows the algorithm in the initial stages of the estimation process to explore the parameter space It is advised to experiment with the temperature and try out several possible values Some indication can be obtained by running the program with the default temperature and then looking i The probability model underlying ULTRAS assigns to every possible network a probability of occurrence when a particular network is observed the ML method asks what value of the parameter makes the probability of observing this particular ne
2. X Cancel A car 7 Help Figure 27 Specification for simulation After specification of the simulation options clicking the OK button will make the initial specifications active and the module can be executed by clicking the Run button This results in opening the SIENA window which shows the progress of the estimation or simulation process The SIENA estimation window is presented in Figure 28 It also gives the opportunity to stop the module Stop Estimation button restart the estimation from the current parameter value button Set N 0 terminate phase 2 of the estimation process button End Phase 2 or change the parameter values and start again button Change parameters When the execution of the module is finished the results appear in the output box of the result step see figure 29 32 Figure 28 SIENA executing StOCNET StOCNET sessions SIENA example sns Initial data description E Simulations Bl Initial data description For the following statistics missing values if any are not counted Network density indicators observation time 1 2 3 density 0 046 0 047 0 050 average degree 2 306 2 367 2 490 a missing fraction 0 000 0 000 0 000 E Tie changes between subsequent observations periods D gt 0 0 gt 1 l gt 0 l gt 1 Distance Missi l1 gt 2 2278 59 56 57 115 Oo A 2 gt 3 2278 56 50 66 106 DI Dyad counts Figure 29 SIENA results
3. Model fit measures E Convergence info Ba Specific covariate effects B3 Sender covariates Attribute2 Receiver covariates Attribute2 Bs Density covariates standard error 0 0000 parameter estimate 0 0181 quantiles from sam OSS 2 5 225 0 01 0 01 0 01 quantiles from sam 0 5 2 5 25 0 02 0 02 0 02 quantiles from sam y Figure 21 p2 results 26 4 3 SIENA The module SIENA Simulation Investigation for Empirical Network Analysis carries out the statistical estimation of models for the evolution of social networks according to the dynamic actor oriented model of Snijders 2001 2003 2005 This section gives information about executing SIENA within StOCNET For more detailed information about the program SIENA or stochastic actor oriented models the reader is referred to the manual Snijders et al 2006 and the articles Snijders 2001 2005 Steglich Snijders and Pearson 2004 and Snijders Steglich and Schweinberger 2006 SIENA can also carry out MCMC estimation of the parameters of an exponential random graph model this is documented in the next section Stochastic actor oriented models are used to model longitudinal network data The dependent variable is the evolving relation network represented by repeated measurements of a directed graph The network evolution is modeled as the consequence of actors initiating new relations or withdrawing existing relations such
4. Figure 1 shows how to get access to definitions and specifications made earlier When selecting Open previously used session an earlier session created by StOCNET with extension SNS can be opened which contains the desired definitions and specifications In every session step in StOCNET the main window contains the buttons Notes Examine View Apply Cancel and Help They have the following functions the functions Notes View and Help are also accessible via the main menu Notes Opens an edit window to make notes on a session This function is the same as the Notes function in the Session menu Note that details of the history of this session can also be found in the session tree on the left side of every window Examine Gives results of simple mostly descriptive analyses of the data The data used in these analyses are those that are available at the specific step in the StOCNET session in which the button is clicked For example simple variable counts for network data in STEP 1 or network characteristics like degree of reciprocity or transitivity for a selection of the actors in STEP 3 of a session The Examine function will be described in more detail in Section 4 View Opens a viewing window in which a specified file can be viewed that is either the values of the relations in the network or the values of the attributes in the attribute file are displayed Like Examine this function is step specific which means that only th
5. 33 4 4 SIENA p The module SIENA can also be used to estimate the parameters of the exponential random graph model ERGM also called the p model Frank and Strauss 1986 Frank 1991 Wasserman amp Pattison 1996 using Markov Chain Monte Carlo MCMC methods described in Snijders 2002a and Snijders Pattison Robins and Handcock 2006 In this section information is given about operation of SIENA p in StOCNET as far as this differs from what is mentioned in the preceding section For more detailed information about the program SIENA or the p model the reader is referred to the manual Snijders Steglich Schweinberger amp Huisman 2006 and the articles Snijders 2002a Snijders Pattison Robins and Handcock 2006 Robins Pattison Kalish and Lusher 2006 Robins Snijders Wang Handcock and Pattison 2006 or the further literature An exponential random graph model is estimated when only one observation moment in the SIENA module is chosen i e when only one digraph is selected in the Digraphs in sequential order window If the MCMC estimation algorithm converges properly the computed estimate is an approximation of the maximum likelihood estimate However the literature mentioned discusses that for many data sets convergence of the estimation algorithm can be obtained only for adequate specifications of the model It is advisable to consult the recent 2006 literature concerning the model specification before emb
6. transitive T xj Xx Xx 1 or other O This can be helpful for investigating dynamics in transitivity 50 In Output box 7 the results for the three observations of the freshmen data are presented From the results it follows that between observation 1 and 2 many new relations were initiated shown by the large value of the distance Hardly any mutual dyads and no transitive triplets exist at the first observation time because most students don t know each other yet Between observations 1 and 2 many mutual and asymmetric dyads emerge and also many transitive triplets Between observations 2 and 3 the mutual dyads and the transitive triplets generally remain mutual or transitive respectively 3 Arcs Numbers of changes between subsequent observations obs times 0 gt 0 0 gt 1 1 gt 0 1 gt 1 Distance Missing It 2 369 523 0 7 523 93 9 2 to 3 220 66 15 412 81 279 285 3 Dyads Number of dyad tween subsequent observations obs times M A M gt N M gt any to 2 2 to 3 125 times A BOL 2 to 3 times N tO 2 to 3 3 Triplets Changes from intransitive triplets i e changes for triplets starting with i gt j j gt h not i gt h obs times I gt T I gt I I gt O I gt any lto 2 1 0 0 1 2 64 3 478 1028 140 1646 Changes from transitive triplets i e changes for triplets starting with i gt 3 j gt h i gt h obs times T gt
7. 5 Sequences per model lt is advised to let the module generate several independent Gibbs sequences which approximate samples from the posterior distribution of the classification to check if the results are stable The default number of Gibbs sequences is 3 6 Advanced options This button activates a new window with advanced options for improving convergence The default is that these options are on usually their influence is small For more detailed information the user is referred to the BLOCKS manual Snijders amp Nowicki 2004 After specification of the options clicking the Apply button will make the initial specifications active and the module can be executed by clicking the Run button Executing the module results in the appearance of the BLOCKS window that shows the progress of the estimation process This window is given in Figure 14 It also gives the opportunity to stop the module by clicking the Stop button When the execution of the module is 20 finished the results appear in the output box that is shown in the result step see Figure 15 A secondary output file containing extra details of the estimation process can be viewed by clicking the Details button BLOCKS sessi StOCNET BLOCKS session sess1 Gibbs sampling non identified model 3 colors 2 3 Gibbs sequence fr 1 3 number of iteration 7500 1 10000 Convergence is assumed Figure 14 BLOCKS executing StOCNET G Stocnet se
8. Di lt lt Network3 f Filet Dyadic covariates lt l gt Network2 Y OK X Cancel 7 Help Figure 17 p data specification Model specification Clicking the Model specification button activates the window presented in Figure 18 For the pz model only Covariate selection and here Kappa and Tau can be ignored and Options are relevant For more information about other options in this window the reader is referred to the 2 manual Zijlstra 8 Van Duijn 2005 23 P2 model specification E xj Covariate selection Random effects Separate estimates Advanced multivariate model Options Fixed parameter valt_4 gt Kappa Attribute diff O File1 Attribute1 abs di M Attribute abs diff O File1 Attripute3 abs diff M Network2 el Attributel abs diff O File1 Attribute2 diff M Filel Attribute abs diff O File1 Attribute3 diff O Filel Attribute3 abs diff CO Network2 Sender Receiver Tau O Filel Attributel O Filel Attributel Y File Attribute2 File Attribute O Filel Attribute3 O Filet Attribute3 Y OK X Cancel Help Figure 18 p2 model specification Covariate selection Covariate selection Here covariate effects to be included in the model are specified Covariates for the Density Reciprocity Sender and Receiver effects can be included In all four lists the effects are based on covariates
9. FP TP square root outdegree 0 o d I effect Attribute3 on rate FP E squared outdegree 0 I not implemented FP E sum 1 outdegrees 1 FT not implemented TP sum 1 0 deg 1 o deg 2 FT notimplemented DD 3 cycles D I betweenness status FE dense triads gt 6 ties FT peripheral to dense triads D O Attribute similarity centered FO Attribute similarity x reciprocity FP Attribute sim x Attribute alter TP Attribute sim x Attributel alter TDT Attihutet aan zi Advanced Help Figure 24 Model specification objective and rate function effects 29 iii Options By clicking the Options button in the model specification screen the window in Figure 25 appears Here the estimation method the model code the number of phase 2 subphases the number of phase 3 iterations the multiplication factor and the initial value of gain parameter can be chosen In addition an actor homogeneity test can be done for all actors or a selection of actors In Figure 25 the default options are depicted See the SIENA manual for further information about these options SIENA model specification x network variable 1 Options Options Estimation method 1 Number of phase 3 iterations 500 Model code 1 Si Multiplication factor 2 Number of phase 2 subphases 4 3 Initial value of gain parameter 0 2 T tandardized starting value Actor homogeneity test IT Standardized starting val ce
10. gt X Cancel Help Figure 23 SIENA data specification Specify actor attribute files Under Available attrib files all attribute files are listed that are available in the analysis From this list the attribute files have to be selected into one of four categories of covariates the files contain Missing data are not allowed in the covariate data There are four categories of attributes that are distinguished by SIENA one or more attribute files can be used as dependent variables constant covariates changing covariates and one attribute can be a file with times of composition change Constant covariates do not change over time e g gender Files with varying attributes contain only one variable which changes over time Such a variable can be used as a dependent variable or as a changing covariate The files must consist of n lines giving for each actor the values of the covariate in each observation period separated by blanks For each actor the number of observed values of the changing covariate must be as large as the number of selected digraphs minus one i e the covariates are assumed to be constant between two observation moments For each varying covariate a separate file has to be selected The last type of attribute file contains the times at which the composition of the network changes i e the times at which some actors join or leave the network This file consists of n lines with four numbers The first
11. nr 7 Toeval zit overal programmatuur voor random co ffici nt modellen pp 113 131 Groningen ProGAMMA Van Duijn M A J Snijders T A B amp Zijlstra B H 2004 p2 a random effects model with covariates for directed graphs Statistica Neerlandica 58 234 254 Wasserman S 8 Faust K 1994 Social network analysis Methods and applications Cambridge Cambridge University Press Wasserman S amp Pattison P 1996 Logit models and logistic regressions for social networks An introduction to Markov graphs and p Psychometrika 61 401 425 Zeggelink E P H 1993 Strangers into friends The evolution of friendship networks using an individual oriented modeling approach Amsterdam Thesis Publishers 1993 Zijlstra B J H 8 Van Duijn M A J 2003 Manual p2 version 2 0 0 7 Groningen ICS University of Groningen Zijlstra B J H Duijn M A J van amp Snijders T A B 2005 MCMC estimation of the p2 model a multinomial model with cross nested random effects and covariates for the analysis of directed graphs Submitted The manuals of the statistical programs can be downloaded from the StOCNET website http stat gamma rug nl stocnet 55
12. 0 780 0 609 smoking 32 2 2 00 139 1 00 0 499 0 249 3 Correlations Correlations above the diagonal covariances below the diagonal gender 0 511 0 492 program j 0 633 smoking Output box 6 Some examine results of STEP 2 3 attributes SIENA The module SIENA treats the selected files as repeated observations of one network It models the evolutionary process as the consequence of actors initiating and or withdrawing relations The following change statistics are calculated when clicking the Examine button Note that all observed networks must have dichotomous relations Changes in arcs between subsequent observations The number of tie variables that remain O that change from 0 to 1 from 1 to 0 and that remain 1 The distance i e the total number of changes from 0 to 1 and 1 to O between the two observations and the number of missing tie variables missing at only one observation time or at both time points Changes in dyads between subsequent observations The number of dyads that change from one class to another mutual M asymmetric A null N Note that if a dyad is asymmetric at both moments the tie variables can have remained the same indicated by A gt A or the tie variables can have switched e g with the dyad changing from 0 1 to 1 0 indicated A gt A Changes in triplets between subsequent observations Changes between triplets Xj Xik Xx being intransitive l xj Xx 1 Xx 0
13. 4000 Size of Simulation Sample eooo E Interval 1 Si X Cancel Help Figure 19 p gt model specification Options After specification of the data and the model the module can be executed by clicking the Run button This results in the appearance of the pz window showing the progress of the estimation process see Figure 20 The window contains some extra functionalities as pausing the estimation process by clicking the Pause button and aborting the estimation process by clicking the Abort iteration button Because updating both screens with random effects and the parameter estimates for each new iteration is a rather demanding task with the button Hide Estimates these screens can be closed This will increase the speed of the MCMC simulation process When the execution of the module is finished the results appear in the output box of the result step see Figure 21 A P2 About P2 MCMC Burn In model parameters 2f hz 1 o 2 144 E 2 24 T 0 50 100 150 200 5 0 5 10 sender effect sender variance mu receiver variance rho sender receiver covariance Hide Estimates Pause Figure 20 p2 executing 25 StOCNET X StOCNET sessions p2 test 2 1 12 05 sns Er StOCNET Session fa Data ta Transformation Selection Model P2 E Results General Inforrnation General Information Descriptives Random effects Fixed effects
14. C By prior probabilities 1 Selected Network Select one data set from the set of available networks The values of the network relation must be integers ranging from 9 to 9 This allows to analyze relations in more detail than the usual dichotomous relations Missing values can be specified All dyads with one or two of the arc variables missing are disregarded The diagonal values of the network matrix are also disregarded by the program 2 Number of latent classes The number of latent classes groups of equivalent actors has to be chosen in advance This number is fixed at one value or at a sequence of values by specifying the values for Minimum and Maximum see Figure 12 If only one value is desired the Minimum and Maximum should be equal 3 Default number of iterations The estimation procedure is based on Gibbs sampling which needs a start up period Iterations before convergence and a number of iterations after the start up to estimate the parameters of the posterior distribution terations after convergence 4 Identification of latent classes When there is no a priori information about the classes the classes are called unidentified that is one cannot say actor fis in class j If prior information is available the model can be identified in two ways by vertex numbers or by prior probabilities After selecting one of these options the Specify button activates a new window Identification of l
15. Cancel Transpose Hel 7e Figure 6 Available symmetry transformations 12 After clicking the Recode button the window in the left panel of Figure 7 appears In this window current values of relations in case of networks or attributes can be specified in the edit boxes From and To and new values can be defined the box New value Clicking the Add button adds the recoding to the list of current recodings and with the Remove button a selected recoding can be removed from the list For the networks only integer values can be used in the recode function for attributes also non integer values are allowed e g from 4 5 to 6 5 gt new value 1 x ees 1 pn fe ry Missings Hi ma E 5 a sj 0 EN AE la xi New missing value new il El Add Remove Current missing values cancel _Bemove x corca O Kca Cancel Help quo quo Figure 7 STEP 2 recoding networks or attributes left and defining missing values in network data right Current Apo pera For network data missing value codes can be defined by clicking the Missing values button The missings window presented in the right panel of Figure 7 is opened and new values can be added to the list of current missing values This list may contain more than one value and values may also be removed By clicking the OK button the current recodings list and current missing values list become active and the transformat
16. a posteriori how many different latent classes of actors can be distinguished and what is the class to which each actor belongs by estimating the posterior probability distribution of the configuration of the class structure given the network data The parameter estimates are obtained with Gibbs sampling In Figure 12 the model specific user interface for BLOCKS is presented Six options have to be specified by the user Figure 12 shows the default values StOCNET G Stocnet sessions sessi sns ol xj Session Files Step Options Help a ig a E Back Forward Data Transformation Selection Model Results StOCNET S 3 ession Model Data Transformation Model choice Selection BLocks o BLOCKS y EE Model BLOCKS StOCNET Model 2 w Selected Network Nr of latent classes Model Specific User Interface Nr of iterations Latent classes identificat Selected Network Number of latent classes Minimum 2 3 Maximum 2 Sequences per model New Results Network1 X Default number of iterations Iterations before convergence 10000 Iterations after convergence 10000 Sequences per model Nr of Gibbs sequences E S Advanced Bun E STOCNET Session info Notes Examine View Y Apply X Cancel 7 Help J e E 7 Figure 12 BLOCKS Model specific user interface rldentification of latent classes No identification C By vertex numbers
17. actors the p parameter indicates the tendency towards reciprocity in the network is a general parameter for the network density and the A parameters are normalizing constants insuring that the probabilities sum to 1 for each dyad Estimation of pl model for network 3 C StOCNET Vrnd32t4 dat 3 Parameter estimates Actor Alpha Rho Theta 2 964 2 194 0 334 237 862 lt Not all estimates are presented here 579 43 Model fit and expected values G 2 statistic 524 67 Degrees of freedom 596 Output box 8 Examine results of STEP 4 01 model It should be noted that in case of large networks many actors the estimation procedure may take a little time In Output box 8 the results for the third observation of the freshmen data are presented Because the p model is fitted only to completely observed data the actors with missing relations were removed from the data first STEP 2 selection The results show a large reciprocity parameter and also large sender and receiver effects for some actors In addition the G goodness of fit value with the corresponding degrees of freedom is given The model would be more useful if the distribution of G squared were known as it is the model fit cannot be assessed very well Other information indicates that the fit is not excellent analyzing these data with SIENA p shows that there is a large transitivity effect not accounted for by p Expected values are n
18. diagonal are disregarded that is self relations are not considered Missing values are allowed multiple missing value codes can be specified The module treats them by simply ignoring the tie variables for which values are missing see the p2 manual for more details ii Specify actor attribute files Actor attribute files that are available for analysis are listed under Available attrib file s From this list files can be added to the list Selected attrib file s by using the select buttons lt lt and gt gt and the actor attributes contained in these files are available in the analysis Missing values in the attribute files are allowed If an actor has a missing value for an attribute that is selected to be included in the model this actor will be removed from the data both in network and attribute files After specification of the data types clicking the Ok button will make the specifications active In Figure 17 one digraph is selected to be analyzed with the 2 model Network 3 One of the other networks Network 2 the same network observed at an earlier time point is selected as dyadic covariate There is one attribute file File 1 of which the actor attributes can be used as covariates P2 data specification z x Nr of groups fi Covariates for all groups Group 1 ee network types Specify actor attribute files Digraphs Available attrib files Selected attrib file s Available network s
19. either dyadic attributes upper half of the screen or actor attributes lower half of the screen To identify the attributes first the file that contains the attribute is mentioned next the attribute name and finally in the case of density or reciprocity effects the kind of effect For density effects each attribute can be included as a dissimilarity effect based on differences i e the direction of the difference is important and or as a dissimilarity effect based on absolute differences i e the direction is unimportant Reciprocity effects can only be included as dissimilarities based on absolute differences Note that one should only include a covariate as reciprocity effect if the corresponding density effect based on absolute dissimilarities is also included When a reciprocity effect is selected without its corresponding density effect p2 will produce an error message Options The screen displayed in Figure 19 shows the default options In most cases these options are convenient More details about the options in the model specification can be found in the pz manual Pressing OK brings the main screen pz screen under the Model step to the front again 24 P2 model specification E x Covariate selection Random effects Separate estimates Advanced multivariate model Options Fixed parameter vali 4 gt Options Estimation method fo 3 Number of Batches 25 i Batch Size 100 i Number of Burn in Iterations
20. j gt h and i h non missing Network 2 Total 4 9357 Transitive 1 7032 Transitivity T 0 250 0 752 Triad census Network 1 Network 2 Network 3 Triad 003 012 102 Num Prop 4754 0 958 115 0 023 88 18 o o Num 116 269 376 Pr 0 op 032 074 103 Num 54 161 185 FU K O ge 021 062 071 021D 021U 021C 111D 111U 030T 030 201 120D 120U o 000 55 000 65 000 52 000 193 000 259 000 118 000 11 000 222 000 248 000 172 120 000 132 210 0 000 819 224 204 300 0 0 000 547 150 162 Tot non missing 4960 3654 2600 015 39 018 121 014 0 053 0 071 032 35 003 43 061 068 30 047 036 015 047 000 000 170 013 017 067 012 052 087 00000000000o 1 0 0 1 0 0 0 0 1 0 0 o0o0o00O0000000000000o Ea ao E ER o A ak 3 Segmentation and components Segmentation index S3 number of isolated vertices and number of weak components of 2 or more vertices Networ 1 2 3 Segmentation S3 1 000 0 647 0 600 Num isolates 22 0 0 Num components 4 1 1 Output box 5 Examine results of STEP 2 3 triplets and triads segmentation and components 5 Segmentation and components For both graphs and digraphs networks with valued relations are dichotomized Missing tie variables are regarded as absent arcs edges e Degree of segmentation S3 Measure of segmentation based on the distribut
21. of some descriptive analyses of the network and attribute data see also Section 2 2 The Examine button is active in the steps Data definition Transformation Selection and Model Specification in the last step Results this button is not active In every step clicking the Examine button gives descriptives of all available network and attribute data i e all network files and all attributes in all attribute files The only exception is STEP 4 specification of a statistical model where only the specified data sets are used in the descriptive analyses Each time the specifications are changed in some session step e g when the data are recoded or when a different set of actors is selected descriptives of these new data sets are presented After clicking the button the program Examine is executed and the results of the examination of the data are presented in the Examination Result window shown in Figure 39 Like the main windows of each step specific interface the window is divided in two parts one shows the results of the analysis right and one presents a history tree that contains an overview of the calculated descriptives left The history tree can be used for navigating through the results clicking the corresponding gives details of the output and double clicking the names of the descriptives gives the corresponding output in the right part of the window The Examination Results window further contains the three but
22. relations are defined and the missing value code is specified Therefore more elaborate descriptive analyses can be performed In STEP 3 of the session a sub set of actors is selected that will be used in the statistical analysis For this selection of actors descriptive network statistics and attribute statistics are calculated The subset of actors on which the descriptives are based is mentioned in the results Note that in the case of selecting all actors examination of the data in STEP 2 and STEP 3 gives the same results Because StOCNET is a program for the analysis of social networks the emphasis is on network statistics descriptives References to definitions of and information on some specific statistics are provided The statistics for which no reference is given are described in Wasserman amp Faust 1994 providing a detailed overview of a large number of network statistics A distinction is made between undirected graphs and directed graphs digraphs and between nonvalued relations i e dichotomous relations absent or present and valued relations numerically coded polytomous relations e g best friend friend acquaintance known by face name unknown In case of networks with valued relations the relation values will sometimes be dichotomized The dichotomization that is used is always the same and is mentioned in the output the value O remains 0 the values 1 and larger are given the value 1 Networks For each specif
23. tendency 0 03661 Model Type 1 Standard actor oriented model Simulations for a specified time Time duration for simulations in each period is 1 0 ia 4 _ seo em Deels Eulrpor gt STOCNET Session info Notes Examine View apl X Cancel 7 Help y Figure 11 STEP 5 view results of the analysis e Print opens a window to print a selection of the output e Details which opens an additional information file in the Notepad editor if such a file is available e Full report which opens the output file in the Notepad editor In the left part of the StOCNET window the session tree shows the history of the session and an overview of the results This allows for a structured view through the output file in the right part of the StOCNET window by selecting certain output items The items are indicated in the output file by the symbol 1 for chapters 2 for sections 3 for subsections and so on see Figure 11 These items are presented in the session tree on the left and the user can select an item by double clicking it The corresponding part of the output file is presented in the output box on the right After viewing the results one may decide to alter some of the options specified in earlier steps in the StOCNET session By clicking on the appropriate button in the StOCNET toolbar by using the step menu in the main menu or by double clicking on the appropriate step name in the sessi
24. that a more rewarding configuration for the actor in the network emerges to which is added a random influence This goal is modeled in a so called objective function the actors try to maximize The models are continuous time Markov chain models that are implemented as simulation models In Figure 22 the model specific user interface for SIENA is presented Specifications of data and model can be made and the specified model can be run One can choose to estimate or simulate the model StOCNET X StOCNET sessions session1 1 sns El ol xj Session Files Step Options Help gt E Back Forward Data Transformation Selection Model Results El StOCNET Session ES Model Data H Transformation Model choice E Selection siena SIENA Model SIENA StOCNET Model y 2 w Results Model Specific User Interface Specifications Data specification Model specification Run model Estimation 2 Si Bun Statistics specification Appl X Cancel Help E O Figure 22 SIENA model specific user interface 1 Data specification Clicking the button Data specification activates a window in which the different network files left and actor attribute files right can be specified see Figure 23 i Specify network types Under Available network types the set of all available networks is listed From this set one or more networks can
25. the directory of the temporary files is the same as the directory of the session files When the specified directories do not exist StOCNET gives an error message The user has to specify existing directories before the program can be used Online help on the working of the program and the implemented statistical models The online help function is based on the StOCNET manual For most users the sequential process of five steps in a StOCNET session will soon become a cyclic process possibly even with skipping certain steps The interactive features of StOCNET imply that any revised analysis can easily be undertaken in the current or in a new session The sequential steps in a session are the following STEP 1 STEP 2 STEP 3 Data definition Specification and description of the network s and the actor attributes in separate ASCII data files Transformation Recoding and symmetrizing of network data and actor attributes and specification of missing values Selection Selection of actors by specifying a range of actors by calculating simple network statistics or by specifying attribute values STEP 4 Model specification and analysis Choice of the statistical model i e module for data analysis Subsequently specification of which data is to be used the model parameters and options in the model specific user interface and running the module STEP 5 View results Inspection of the output and results of the analyses
26. the output file generated during the statistical estimation procedure is shown This always is an ASCII file In Figure 11 an example is given of the output of SIENA The output window contains four buttons e Save opens a Save as window to save the output under a new name Note that adjusting model definitions and specifications in STEP 4 and estimating the same model again usually results in appending the new results to the output file However when a new statistical model is selected new data specifications are given or changes are made in STEP 1 through STEP 3 a new output file may be made that overwrites the old one and previous results are lost StOCNET G Stocnet sessions sessi sns _ 10 x Session Files Step Options Help gt E 15 Bach Forward Data Transformation Selection Model Results Er StOCNET Session Results Data H Transformation Model SIENA E i a Selection el E Simulations E Results E Data input Reading network vari Simulated values of statistics written to file sessl sdt R Reading dependent Parameter values are Initial data description l constant network rate period 1 1 61044 E Simulations l constant network rate period 2 0 24864 Simulation Results l rate Filel period 1 0 77126 Estimated means l rate Filel period 2 0 59815 Cova ianca mati ES outdegree density 1 94591 g u reciprocity 0 00000 tstatistics for obse u behavior Filel
27. two concern joining the last two leaving 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 between two observations 3 the last observation moment at which the actor is observed and 4 the time of leaving also expressed as a fraction of the length of the period Only one such file can be selected The requirements for this file as well as some examples are given in the SIENA manual In Figure 23 File 1 is selected as a constant covariate 28 2 Model specification By clicking the button Model specification the window of Figure 24 appears in which for each network variable the desired effects can be included in the objective and rate function By clicking on Options extra options can be chosen Objective function f Specification of the effects to be included in the objective function These effects can be specified as an evaluation u effect or an endowment e effect The endowment function represents parts of the value of a tie that are lost when the tie is broken but that have no cost or loss when the tie is created It is advisable to start modeling with the evaluation effects only and include endownment effects only if some experience with fitting simpler models has been obtained Further it is almost always a bad idea to specify an endowment effect without the corresponding evaluation effect The effects to be included in the obje
28. 32t2 dat and Vrnd32t4 dat available with the program and actor attribute file Vars dat are added to the list of data sets available for analysis This selection will become active once the Apply button has been clicked The actor attribute file contains three variables that are shown in the attribute list attribute 1 gender attribute 2 program and attribute 3 smoking The names of the attribute have been changed in Figure 4 attribute 1 is changed into gender etc in the attribute list Also descriptions of the variables are added in the description list The maximum number of attributes that can be included within one file is 10 If there are any dyadic covariates these should be included as separate network files In STEP 4 where the model for data analysis is chosen the distinction between dyadic covariate files and network data files is made The session tree in the left part of the window shows the history of the session so far three networks and one actor attribute file containing three variables are specified StOCNET G Stocnet sessions sessi sns x i 01 xj Session Files Step Options Help gt f E Back Forward Data Transformation Selection Model Results tee cana Data Definition E Network s Network s oat VRND32T2 DAT VRND32T4 DAT Network GAStocnet Networks VRND32TO DAT Actor attributes GAStocnet Networks RND32T2 DAT E YARS DAT GAStocnetiNetworksiYRAND32T4 DA
29. 50 Huisman M amp Snijders T A B 2003 Statistical analysis of longitudinal network data with changing composition Sociological Methods amp Research 32 253 287 Huisman M amp van Duijn M A J 2003 StOCNET Software for the statistical analysis of social networks Connections 25 1 7 26 Huisman M amp van Duijn M A J 2004 Software for statistical analysis of social networks Paper presented at the 6 International Conference on Logic and Methodology RC33 Amsterdam August 16 20 2004 Lazega E amp van Duijn M A J 1997 Position in formal structure personal characteristics and choices of advisors in a law firm a logistic regression model for dyadic network data Social Networks 19 375 397 Molloy M amp Reed B 1995 A critical point for random graphs with a given degree sequence Random Structures and Algorithms 6 161 179 Nowicki K amp Snijders T A B 2001 Estimation and prediction for stochastic block models Journal of the American Statistical Association 96 1077 1087 Pattison P Wasserman S Robins G amp Kanfer A 2000 Statistical evaluation of algebraic constraints for social networks Journal of Mathematical Psychology 44 536 568 Schweinberger M 2003 Manual for ULTRAS version 1 1 Groningen ICS University of Groningen Schweinberger M 2005 Statistical Modeling of Network Dynamics Given Panel Data Goodness of fit Tests Submitted for publication Schw
30. CNET Session d Data p Model Transformation Model choice Selection H Model ULTRAS SIOCNET Model JULTRAS 2 H Results B Model Specific User Interface Selected Network Number of ultrametric levels zl ae 2 Maximum 2 Labels Nr of Sequences Probability model Load from file y E Bernoulli C Poisson gt Method C Gaussian Bun L STOCNET Session info Notes Examine View X Cancel Help L Figure 31 ULTRAS model specific user interface Maximum Likelihood Estimation C Bayesian Inference Specify 1 Selected Network Select from the list of networks one network to which the model is to be applied 2 Labels Load from file t can be handy to denote the actors not by integers 1 2 n but instead by labels such as the actors names The labels have to be stored in a ASCII file with one label on each line and in the same order as the adjacency matrix in the network file Loading a labels file will force ULTRAS to represent any matrix in the output file using the inputted labels instead of integers 3 Number of ultrametric levels The number of ultrametric levels is the number of values that the ultrametric distance between two distinct actors can take To the experience of the authors a sensible choice is 3 or 4 which works reasonably well in most applications Howeve
31. ODME Session T w Data H Transformation Model choice E Selection i Ga a Model P2 gt 2 Results Model Specific User Interface Specifications Data specification Model specification STOCNET Session info Notes Examine View ply 36 Cancel Help ZA Figure 16 pz model specific user interface 1 Data specification Clicking the button Data specification opens the window presented in Figure 17 Dependent networks and actor attributes can be specified for one group p2 model or for several groups multilevel pz model In addition covariates can be included 22 For other options in this window the reader is referred to the pz manual Zijlstra amp Van Duijn 2005 i Specify network types In the list Available network s the set of networks available for analysis is presented From this set of networks at least one network univariate p2 model or more than one network multivariate 2model has to be selected and assigned to the list Digraphs by using the select buttons lt lt and gt gt Networks in this box are networks of which the dyadic ties are the dependent variables in the pz model Other available data in the set networks can be used as dyadic covariates by assigning them to the Dyadic covariates box this also can be more than one network The network relations must be dichotomous on off relations coded as 1 0 and the values on the
32. StOCNET An open software system for the advanced statistical analysis of social networks User s Manual version 1 7 February 2006 Groningen ICS Science Plus http stat gamma rug nl stocnet Peter Boer Mark Huisman Tom A B Snijders Christian E G Steglich Lotte H Y Wichers Evelien P H Zeggelink Contents Content et et UN ai ie 2 O SORW ANE e T E E A E E E E E A E E A E E 3 Ti VAEFOGUCTION POE AE EOT EA EEN ida 4 2 TOO PO AM castes ii A EA 5 21 OPENING WIN Wicca A See ee 5 2 2 Main Menu ANd WINKOW aa a a a EE aa aaa E a a Eaa a aoran 6 A STOCNET AOS t s 8 3 1 Export to other data fm als menaa a AAA aa EAA ARANEA rra rca 9 3 2 STEP 2 Data delicia ll did 9 33 STEP 22 Transformations PERE EEEE EE T A E lindaa cda 11 34 N ci ae Seleccion al di ddr 14 3 5 STEP 4 Model specification and analysis ooonnccnnnnidinnccnnncccnnccnnnrnnonrncnancncnnnn conca ronca 16 3067 STEPS Resulta ad di ca 17 A Statistical MOS atras 19 4 1 BI OG KS a ar da dt a aos 19 LA E AE ca vate nett shinies ENAT sass land ster Tis obs sitet sive caste T EANA AT E everett 22 AS SIENA ot a A E A AEE AT 27 e T a S SE E EE EEEE AAT EE ATE T EAE A ET E 34 deb UETRAS ETE EEE ETE ATE E EA A E A E AE TA 35 A O EE A TEA N E E A E T A T eR 39 5 Descriptive statistics Examine cccceseecceseeeeeeeseeeeeeeseneeeeeneneeeeeseneeeeeseneeeeeseneeeeeneneeneetes 43 5 1 EXAMINGHINS EP A E es EE EE lla E EAA EEES 44 52 gt l
33. T ad Add Bemove Edit smoking 7 amp Transformation p Actor attribute file s Selection F GAStocnet Actiles WARS DAT y Model SIENA Ba F Results Add Remove Edit gende Gender of the students Study program followed regular short Smoking behavior of students yes no X Cancel Help Ai Figure 4 STEP 1 specification of network data and actor attribute data STOCNET Session info 3 3 STEP 2 Transformation Once the data have been defined they can be transformed if necessary For instance some modules require dichotomous network data while others are able to handle all kinds of network data Also in case of missing values codes indicating the missing values have to be defined Transformations are performed in STEP 2 of a StOCNET session Clicking the button Transformation opens up a new window as presented in Figure 5 All files defined in the previous step are presented either in the list Network s or the list Actor attribute file s and for each attribute file the list of attributes it contains is presented Each network or attribute can be transformed separately and differently by selecting it and performing the transformation or a selection of networks or attributes can be transformed simultaneously by selecting all appropriate files with the usual mouse click and drag operations 11 StOCNET G Stocnet sessio
34. T T gt I T gt 0 T gt any 1 to 2 0 0 0 2 to 3 4082 99 304 4485 Output box 7 Examine results of STEP 4 SIENA change statistics P2 As was mentioned in Section 4 2 the 2 model can be regarded as an extension of the p model of Holland amp Leinhardt 1981 where actor parameters are replaced by random effects and attribute effects can be included Therefore pre analyzing the data with the p model may be informative Clicking the Examine button results in fitting the p model for the networks selected in the p user interface The procedure requires that the network relations are dichotomous and that there are no missing values in the data sets 51 The p probability distribution of an adjacency matrix X is expressed in terms of probabilities of the three types of dyads that can be found in a network my the probability that the dyad x x j is mutual i e Xj Xj 1 aj the probability that the dyad is asymmetric i e xj X and nj the probability that the dyad is null i e x X 0 The probabilities of each type of dyad are modeled as a function of three sets of parameters the expansiveness of each actor the popularity of each actor and the reciprocity The probabilities m aj and nj are modeled as mj 2 exp p 20 0 0 B B ay i exp o a B and where the a parameters indicate the expansiveness productivity of the actors the B parameters indicate the popularity attractiveness of the
35. TEP 3 selection of set of actors for subsequent analyses Select all The first way is to select all n actors that are available in the specified network files This is the default option Selection by range of actors The most straightforward way to select a set of actors is to specify the range of actors that are needed A range of actors can be specified in two ways The first way is by entering the numbers of the actors in the edit box i e the row numbers of the adjacency matrix see Figure 8 The entered numbers have to be separated by commas or by dashes for groups of successive actors The second way of specifying a range of actors is by clicking the Specify button The window presented in Figure 9 will appear and a range of actors can be selected by clicking the appropriate columns or rows Clicking on a row or column a second time cancels the selection of that actor The selections hold for all adjacency matrices and attribute files It is possible however to inspect visually the selection by selecting a network of which the adjacency matrix is shown After clicking the OK button the program will automatically take the corresponding rows and columns of the network and attribute data Select Range lol B x Select network Network1 h Network X Cancel P Help Figure 9 STEP 3 selecti
36. a Neve Interval homogeneity test 0 S C Default actors C Specified list of actors Figure 25 Model specification Options iv Advanced Clicking the Advanced button opens the window presented in Figure 26 In this window evaluation u and endowment e effects can be specified The effect can be specified as a random effect r which means that the parameter has an actor dependent component The parameter can be fixed f without estimating it or the value of a fixed parameter can be tested by a score test t described in Schweinberger 2005 St value is the starting value for estimation or a fixed value in case the parameter is fixed Par is a constant parameter which is indicated by c in the Siena manual section 15 30 Advanced model specifications xj Advanced settings E QA Advanced objective function Advanced rate function letet Mrde fe stvaue par L t stvatue outdegree density u O O m 1 94591 constant network rate period 1 7 M 0 575 0 polo 00 constant network rate period 2 M m 0 95 0 reciprocity 000o outdegrees effect on rate Onjo D 0000 in degrees effect on rate DOI D transitive triplets pop Ojo reciprocity effect on rate milwi D oomo effect 1 outdegree on rate Onjo 0 balance 0000 effect gender on rate DOI D polo 00 effect program on rate mimi 0 number of actors at distance 2 u D O 0 effect smoking on rate Onjo D 0000 not implemented Oojo 0 popularity of alter polo ojo no
37. anual for BLOCKS version 1 6 Groningen ICS Dept of Statistics amp Measurement Theory University of Groningen Snijders T A B Steglich C Schweinberger M amp Huisman M 2006 Manual for SIENA version 2 4 Groningen ICS University of Groningen Snijders T A B Pattison P E Robins G L and Handcock M S 2006 New specifications for exponential random graph models Sociological Methodology In press Snijders Tom A B and van Duijn Marijtje A J 2002 Conditional maximum likelihood estimation under various specifications of exponential random graph models Pp 117 134 in Jan Hagberg 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 C E G Snijders T A B amp Pearson M 2004 Dynamic Networks and Behavior Separating Selection from Influence Submitted for publication 54 Schweinberger M 2005 Statistical Modeling of Network Dynamics Given Panel Data Goodness of fit Tests Submitted for publication Van de Bunt G G Van Duijn M A J amp Snijders T A B 1999 Friendship networks through time An actor oriented statistical network model Computational and Mathematical Organization Theory 5 167 192 Van Duijn M A J 1995 Estimation of a random effects model for directed graphs In T A B Snijders Ed SSS 95 Symposium Statistische Software
38. arking upon the use of SIENA p In the case of one observation moment the conditional option keeps the total number of ties constant If only one observation moment that is only one observed network file is selected in the model specific user interface of SIENA clicking the Specify button for estimation and simulation will open specification screens that are different from the ones presented in the previous section The model specification window is presented in Figure 30 In this window the user can specify the network effects and covariates that are included in the model These effects are listed under Objective function the rate function and gratification function are not included in the model for one observation moment SIENA model specification x network variable 1 Options objective function effects for network variable 1 Effect number of arcs W reciprocity D out 2 stars D in 2 stars FP 2 paths I transitive triplets D 3 cycles D out 3 stars D in 3 stars E out 4 stars D in 4 stars I sum 1 outdegrees 1 I sum 1 o deg 1 0 deg 2 I ord pairs direct ind connectd FP ordered pairs indirectly connectd M alternating out k stars parameter 2 I alternating in k stars parameter 2 P alternating k triangles parameter 2 P alternating independent 2 paths par 2 Advanced Y OK X Cancel 7 Help Figure 30 STENA p specifications for estimation Clicking the Adva
39. at gamma rug nl stocnet Here new versions of the program and the corresponding documentation will be presented and made available for downloading In addition a brief history of the project is given and of its goals and team members The list of programs models that are implemented StOCNET is planned to be extended in future versions of the program depending on proposed new programs and the availability of the required resources The StOCNET team hopes to continue collaboration with the developers of new methods to include new statistical procedures and models 53 7 References Baerveldt C amp Snijders T A B 1994 Influences on and from the segmentation of networks hypotheses and tests Social Networks 16 213 232 Frank O 1991 Statistical analysis of change in networks Statistica Neerlandica 45 283 293 Frank O amp Harary F 1982 Cluster inference by using transitivity indices in empirical graphs Journal of the American Statistical Association 77 835 840 Frank O amp Strauss D 1986 Markov graphs Journal of the American Statistical Association 81 832 842 Holland P W amp Leinhardt S 1975 Local structure in social networks In D Heise ed Sociological Methodology 1976 San Francisco Jossey Bass Holland P W amp Leinhardt S 1981 An exponential family of probability distributions for directed graphs with discussion Journal of the American Statistical Association 76 33
40. atent classes For both ways of identification this window is given in Figure 13 In the case of vertex numbers for each class one vertex actor with a high prior probability to be in that class must be specified If there are c classes c 1 or c different vertices must be specified In the case of prior probabilities a matrix of prior probabilities that an identifying vertex belongs to a certain class must be specified The number of columns i e classes of this matrix equals c the number of rows i e identifying actors equals c 1 or c as before The rows of the matrix must sum to one and by default the diagonal probability is fixed at 0 9 and the others proportional such that the sum equals one This option is only available if one value for the number of classes is specified i e Minimum Maximum In both cases the identifying vertices and the prior probabilities can be saved and used in later sessions Identification of latent classes xi Identification of latent classes x dentificatiorr Identification Number of vertices to identify 2 i Number of vertices to identify 25 m Vertices m Probabilities Class nr Wertex nr 1 0 9 0 1000 2 0 1000 0 9 Y 0K Cancel Load Save f Help Y DK Cancel Load Save Ano L Z Help Figure 13 BLOCKS identification of latent classes by vertex numbers left and prior probabilities right
41. be selected and assigned to the list Digraphs in sequential order by using the select buttons lt lt and gt gt These data sets contain the digraphs that are 27 modeled as dependent variables in the SIENA model They are treated as repeated measures of a network where the digraph selected first represents the first measurement the second digraph the second observation of the network and so on If additional network data to be used as dyadic covariates are available these should be assigned to the box Dyadic covariates The network relations must be dichotomous i e present or absent coded as 1 0 and self relations are disregarded Missing values are allowed in the network data see the SIENA manual for details about missing data treatment and must be indicated by one or more missing data codes In Figure 23 three digraphs Network 1 Network 2 and Network 3 are selected and used as observations of the same network at three observation times SIENA data specification r Specify network types Available network s Digraphs in seq order Specify actor attribute files Available attrib files E xl Dependentvariables Network a lt lt gt gt lt lt gt gt keka Network2 ele Network3 Constant covariates Name lt lt gt gt File Dyadic covariates 3 Changing covariates lt lt gt gt lt lt gt gt File with times of composition change lt lt gt
42. bed above These different types of attribute files are described in the sections on the statistical models Section 4 More than one attribute file can be added but every additional file can only be seen by using the small box on the right with an arrow pointing downwards Once an actor attribute file is selected the number of variables covariates in this file is automatically specified Each variable has a default name Attribute1 Attribute2 and so on The names can be modified by selecting the variable and clicking on the name The number of characters that can be used to compose the names of variables must not be larger than 14 However a more extended description can be given for each variable In Figure 4 an example is presented of STEP 1 of a StOCNET session named sess7 in which network and attribute files are defined The data consist of three observations at consecutive time points of a network of freshmen students following a common study program in a Dutch university The relation studied is friendship ranging from 1 best friend to 5 unfriendly relationship see Van de Bunt Van Duijn amp Snijders 1999 In addition an actor attribute file is included which contains the attributes gender program the study program followed regular or short and smoking behavior dichotomous smoking not smoking For a longitudinal analysis of these data with the SIENA module see Snijders 2001 The networks Vrnd32t0 dat Vrnd
43. c and O EP Seite tse cisco als a aaa aaa ia See eaten 45 A AS o AEA AE E AE EA E ARET EE EEE E AA TEE REA E NA 49 6 Contributions to StOCNET connnccccconnnccccanananonananaconanan ono canan arranco rara arrancar arar rra 53 A UE ple E Ae OOO E sek deen ca ewe sensei ede a ce veetcawaioentl S cosdenvecedneuscucudecue duswemeesssec 54 0 Software StOCNET is an open software system to perform statistical analysis of social network data The system consists of several statistical modules and provides a platform for easy access and execution of the various models and inclusion of new models The following hardware and software specifications are required for installing StOCNET e atleast a Pentium processor with a minimum of 16MB RAM better is 32 MB e Microsoft Windows version 95 98 or NT and e aminimum of 5 MB free disk space to install and run the program StOCNET is a 32 bits program and it will not run under Windows 3 x or Windows 3 x with Win32s To install StOCNET on your hard disk download the corresponding files from the website http stat gamma rug nl stocnet Unzip the file using WinZip or PKunzip and run SETUP EXE The installation itself is self explanatory The program is distributed also in another form which does not need to be installed with the Install Wizard for which some Windows XP users may not have permission Just unzip this file and put the files in the directory where you wish StOCNET to be In both installa
44. ctive function may be network effects e g reciprocity transitivity actor covariate effects e g gender popularity gender similarity or dyadic covariate effects The actor covariates are available in three ways as covariate related popularity activity and dissimilarity If no attribute file is specified attribute effects will not appear in the specification window The dyadic covariates are available as covariate related preference and in interaction with reciprocity By default the network effect density outdegree is included because all other network effects should be controlled for this effect Rate function lambda By default constant or basic change rates between two consecutive observation times are included Non constant rate functions may be specified depending on network effects outdegrees indegrees reciprocity and or actor covariates x network variable 1 Options objective function effects for network variable 1 rate function effects for network variable 1 ul eleffect 5 effect E outdegree density constant network rate period 1 M O reciprocity E constant network rate period 2 F E transitive triplets E outdegrees effect on rate PE balance I in degrees effect on rate FT E number of actors at distance 2 I reciprocity effect on rate FP E popularity of alter I effect 1 outdegree on rate FP activity of alter I effect Attributel on rate TF outdegree up to 0 O effect Attribute on rate
45. data and actor data see Figure 2 It consists of two groups Network s and Actor Attribute file s Both groups contain the same buttons Add to add a data file to the set of available data sets for that session Remove to remove a file from the set of available data sets and Edit to edit the contents of a selected file by opening the data file in the program Notepad In the first group a file with network data can be added to the list of available data with the Add button Once Add has been selected an Open window pops up with the possibility to browse through different directories in order to finally select one or more data files of a specific type The network must be presented as an adjacency matrix saved in ASCII format This means that each network is presented by n lines with n integer numbers separated by blanks and each line is ended by a hard return Therefore only data files DAT text files TXT and all files are distinguished to select from in the Open window Once a file has been selected the network in that file is added to the set of available networks for that session Each network has a name that can be modified by the user by clicking on it The default names are Network1 Network2 and so on in sequential order The program determines the number of actors in the network by counting the number of rows and columns in the adjacency matrix Networks that contain different numbers of actors can be included but
46. ed and will be created again when re opening the same session By using the View button in the step specific interfaces or via the File menu the data files can be saved under different names and used in other sessions and or programs A report of the transformations applied is contained in the StOCNET session info treated at the beginning of Section 3 3 4 STEP 3 Selection In the third step of a StOCNET session the set of actors to be used in subsequent statistical analysis is selected Clicking the Selection button on the toolbar or using the Step menu opens the step specific interface of this step presented in Figure 8 The figure shows that there are four different ways to select a set of actors which will be discussed below StOCNET G Stocnet sessions sessi sns oj xj Session Files Step Options Help gt EE Back Forward Data Transformation Selection Model Results E StOCNET Session w Data Selection amp Transformation C SelectAll B by Calculated variable Network Network Variable outdegree C Select by range of actors Criterion gt 5 AND lt 15 Model SIENA Results Select by calculated variable Network file Newor2 y Calculated variable outdegree Criterion 75 AND lt 15 C Select by attribute Actor attribute file File z Actor attribute Criterion 2 X Cancel Help o dh STOCNET Session info Figure 8 S
47. eggelink 1993 e Degree of reciprocity R the ratio of the maximum number of reciprocated ties Some results for the freshmen data are presented in Output box 4 It shows that the number of complete dyads decreases over the three observations due to nonresponse But the number of mutual dyads increases proportionally and the number of null dyads decreases indicating a preference for reciprocated relations This is also shown by the degree of reciprocity Note that the program reports the standard dichotomization of the relations even though the networks were already recoded into dichotomous data sets in STEP 2 of the StOCNET session 46 3 Dyad count Dyad census lt M A N gt In network 1 relations are dichotomized 0 In network 2 relations are dichotomized 0 network 3 relations are dichotomized 0 degr of reciprocity 2M 2M A Network 1 Complete dyads Mutual M Asymmetric A Null N Reciprocity Output box 4 Examine results of STEP 2 3 dyad count Triplets and triads In these calculations triads and triplets with at least one missing tie variable are not counted For both graphs and digraphs networks with valued relations are dichotomized Triad count The number of null neutral intransitive In and transitive triads Tr for graphs The total number of triplets xj Xk Xx with xj 1 Xx 1 and X non missing and the number of transitive triads i e non missing triplet
48. einberger M amp Snijders T A B 2003 Settings in social networks Represented by latent transitive structures Submitted Snijders T A B 1981 The degree variance An index of heterogeneity Social Networks 3 163 174 Snijders T A B 1991 Enumeration and simulation methods for 0 1 matrices with given marginals Psychometrika 56 397 417 Snijders T A B 2001 The statistical evaluation of social network dynamics In M E Sobel amp M P Becker Eds Sociological Methodology pp 361 395 London Basil Blackwell Snijders T A B 2002a Markov Chain Monte Carlo estimation of exponential random graph models Journal of Social Structure 3 2 Internet address http www2 heinz cmu edu project INSNA joss index1 html Snijders T A B 2002b Manual for ZO version 2 3 Groningen ICS Dept of Statistics amp Measurement Theory University of Groningen Snijders T A B 2003 Accounting for Degree Distributions in Empirical Analysis of Network Dynamics Pp 146 161 in R Breiger K Carley and P Pattison eds Dynamic Social Network Modeling and Analysis Workshop Summary and Papers National Research Council National Academy of Sciences USA Washington DC The National Academies Press 2003 Snijders Tom A B and Baerveldt Chris 2003 A Multilevel Network Study of the Effects of Delinquent Behavior on Friendship Evolution Journal of Mathematical Sociology 27 123 151 Snijders T A B amp Nowicki K 2004 M
49. elected the corresponding model specific user interface appears in the lower part of the model specification window In Figure 10 the model specific user interface of the module SIENA is shown this interface will be explained in detail in Section 4 4 and the choice can be made for an other module here p2 The interface requires detailed input specifications that can involve depending on the model an assignment of data or selections of data for specific functionalities e g dependent or independent variables specification of actor attributes included model effects and parameters and estimation options The model specific user interfaces of the currently available statistical modules are discussed in Section 4 As usual the selection of a model and the specifications must be confirmed by clicking the Apply button Apart from specific buttons and choice options every model specific user interface contains the button Run This button is clicked to carry out the estimation of the model after the model specification is completed The progress of the analysis is shown in a new module window that appears during the data analysis 3 6 STEP 5 Results When the execution of the selected model is finished or interrupted the program automatically jumps to the final step of the session view the results In STEP 5 the results of the analysis or any messages generated during the data analysis appears in the output window In this window the content of
50. error messages will appear when network files with different numbers of actors are selected in STEP 4 to be analyzed simultaneously The procedure for adding files with actor attributes covariates is similar to that of adding network files Again the actor attributes must be in files saved in ASCII format The general form of an attribute file is a file that contains k covariates the file must consist of n lines with on each line k numbers that are read as real numbers i e a decimal point is allowed The numbers in Some problems may arise when using long file names or file names that contain spaces To prevent errors from occurring use short file names and no spaces old DOS conventions for file names i e maximum of 8 characters the file must be separated by blanks and each line must be ended by a hard return The maximum number of attributes per file is 10 Identification numbers are not needed to identify the different actors The program assumes that the order of the actors in the network and attribute data is the same and implicitly uses the row number of the adjacency matrices and attribute matrices as identification This means that errors occur when different networks possibly with different numbers of actors and different attribute files are analyzed simultaneously Some statistical programs e g SIENA distinguish different types of attribute files some of which can have a different form than the general form descri
51. ession When you start or open StOCNET the main menu and opening window presented in Figure 1 appear From the opening window a StOCNET session can be started by starting a new session open the last used session or open an arbitrary session that was used earlier with a browse option After selecting one of these options the Apply button must be activated to continue the session Always when the Apply button is active and shows the green check mark the program is waiting for you to confirm the choice made the confirmation is given by clicking this button 2 StOCNET Session Files Step Options Help 2 Data Transformation Selection Model Results a OENE T Seeieh Welcome to StOCNET e StOCNET 1 7 An open software system for the advanced statistical analysis of social networks Applicants ICS Frans Stokman Marijtje van Duijn Tom Snijders Project managers Evelien Zeqgelink Programmers Peter Boer Science Plus Mark Huisman Rob de Negro Science Plus Christian Steglich Bert Straatman Science Plus Start StOCNET C Start with new session C Open last used session CAStOCNET1 Asessionsibuntsns Open previously used session STOCNET Session info X Cancel Help Figure 1 StOCNET opening window and main menu toolbar activated 2 2 Main menu and window Figure 1 also shows the main menu of the StOCNET program The menu bar consists of five menu items that refer to standard Windows functionalities e
52. for the analysis of binary undirected network data using ultrametric i e hierarchical clustering measurement models Schweinberger and Snijders 2003 and e ZO version 2 3 for simulation and or enumeration of graphs with given degrees Snijders 1991 There are separate manuals for StOCNET and for the analysis modules that it contains The StOCNET manual provides general information on the modules focusing on how to use the models within the StOCNET environment For more detailed information on the implemented models and theoretical background and for the operation of the separate programs the reader is referred to the corresponding manuals which can also be downloaded from the StOCNET website In this manual the reader is guided through the five main steps of StOCNET data definition transformation selection model specification and analysis and viewing results The manual starts with a general description of the program in Section 2 followed by detailed information on the five steps in a StOCNET analysis session in Section 3 Section 4 focuses on the procedures required to run the available modules BLOCKS p2 SIENA ULTRAS and ZO within StOCNET 1 7 In five of the four main StOCNET steps descriptive analyses can be performed which are described in Section 5 The manual ends with a short description of the guidelines for new contributions to StOCNET When reporting results obtained with the help of StOCNET please give the fo
53. ied network the following descriptives are calculated 1 Descriptives per observed network e Density The proportion of potential edges arcs that are actually present nonvalued relations or the average numerical value of the relations valued relations e Average degree The average number of relations per actor nonvalued relations or the average value of the relations per actor valued relations e Fraction of missing relations Some results for the freshmen data are presented in Output box 2 Self relations are assumed not to exist and are therefore not counted Symmetric networks are treated as undirected graphs networks that are not symmetric as directed graphs Network 1 Density 0 035 Average degree 1 094 Missing fraction 0 000 Symmetric no Dichotomous no Output box 2 Examine results of STEP 2 3 network descriptives 2 Degrees and degree variances Missing tie variables are regarded as absent arcs edges for these calculations e Degrees the degree per actor that is the number of ties per actor for graphs The indegree and outdegree per actor that is the number of incoming and outgoing relations per actor for digraphs No distinction is made between valued and nonvalued relations e Degree standard deviation the degree standard deviation graphs or in outdegree standard deviation digraphs indicating the variability in the in out degrees Only for nonvalued relations 45 e Index of heteroge
54. in the network Again n x 100 iterations provide a crude guess Heat posterior To make large steps in the state space it is sensible to heat the posterior distribution during the burn in phase 2 O 37 Pressing Run will start ULTRAS When the estimation process starts an interface appears on the screen see Figure 34 The interface shows the current sequence and the current iteration PRULTRAS A ES Help ULTRAS A Program to Uncover Latent Transitive Structures Using Ultrametrics Programmed by A Schweinberger Figure 34 Ultras executing The interface provides a Cancel button to stop the estimations When this button is pressed the computations stop and only the most important results are printed to the output file When the estimations are done an informative interface Figure 35 appears on the screen Pressing the OK button on this interface will terminate the program and make the interface disappear FR ULTRAS version 1 2 LO xj Help Figure 35 Ultras calculations ready 38 4 6 ZO The module ZO Zero One is used to determine probability distributions of statistics of random graphs with given degrees and random digraphs with given in and out degrees In addition it is possible to request a given number of mutual dyads and or a connected graph ZO carries out simulation and or enumeration analysis of the graphs according to the algorithms of Snijders 1991 and Molloy amp Reed 1995 Th
55. inear combinations with each row consisting of 16 the weights or 17 the weights and a critical value numbers decimal points allowed separated by blanks 20 Specify Oj x Number of simulation runs fioo Simulation algorithm Snijders Number of linear combinations of triad counts fi M Read weights for linear combinations from file fT ssi Selec ject X Cancel Help Figure 37 ZO Simulations Specify After specification of the options clicking the_Ok button brings back the model specific interface of ZO Here clicking the Apply button will make the specifications active and the module can be executed by clicking the Run button This results in opening one of two ZO windows showing the progress of the simulation or enumeration process The ZO simulation window is presented in Figure 38 It gives the opportunity to stop the simulations When the execution is finished results appear in the output box of the result step 41 20 Simulation 20 example Number of simulated matrices 4910 1 Number of attempts 4910 Figure 38 ZO executing 10000 42 5 Descriptive statistics Examine In four of the five steps of a StOCNET session the user has the opportunity to examine the data that are available up to and including the functionalities of the current step After specification of the relevant options in each step specific interface clicking the Examine button gives the result
56. ion of distances in the network indicating the fraction of actors that are distant from each other among those who are not directly related see Baerveldt amp Snijders 1994 e Number of isolates The number of vertices actors that have no ties with other vertices e Number of components The number of maximal subgraphs consisting of two or more vertices actors that have no ties to other vertices Some results for segmentation and components in the freshmen data are presented in Output box 5 At the first time point the segmentation of the digraph is maximal because at the start of the study only a few freshmen knew each other After some time friendship relations emerge and the segmentation of the graph decreases Attributes For each attribute the following descriptives are calculated e Frequency tables Frequency of specific categories percentages valid percentages without missing values and cumulative valid percentages Continuous variables are categorized into seven categories based on the minimum and maximum value found e Descriptive statistics Tne number of actors the mode only for categorical variables the median the mean the minimum value the maximum value the standard deviation and the variance Categorical variables with more than ten categories are treated as continuous variables e Correlations Pairwise product moment correlations between the attributes All variables are treated as continuous and missing
57. ion window in Figure 5 reappears Note that the symmetry transformations recoding variables and specifying missing value codes must be done for each network separately For attribute data missing value codes can be defined in the Missing value box in the step specific interface of STEP 2 Figure 5 An attribute has to be selected from the Attribute list after which a missing value code for this attribute has to be entered This means that for each attribute only one missing value code can be defined Recall that for networks it is possible to specify more than one missing value code How missing values are treated depends on the module chosen in the Model step The only thing that StOCNET does in this respect is to pass on the code to the module if the module accepts a missing value code In Figure 7 the values of the relations in the networks are recoded such that only dichotomous 0 or 1 relations remain 0 remains 0 1 to 4 get value 1 and 5 to 6 get value 0 and the missing value codes are 6 and 9 After clicking the OK button the values become active Then they are shown in the session tree see Figure 5 All recodings can be inspected by clicking the View button and examining the network and or attribute files The recoded data is saved in a temporary data file that has the same name as the old file preceded by For example Vrnd32t2 dat is saved as Vrnd32t2 dat After closing a StOCNET session these temporary data files are delet
58. is section gives information about executing ZO within StOCNET For more detailed information about the program ZO or probability distributions of statistics of random graphs and digraphs the reader is referred to the manual Snijders 2002b and the articles of Snijders 1991 and Molloy amp Reed 1995 ZO can determine the distribution of statistics for general rectangular random 0 1 matrices with given row and column sums including matrices with structural zeros i e the restriction that a given set of entries is equal to 0 For graphs and digraphs the adjacency matrix is square the set of structural zeros is the diagonal of the matrix the row sums are the outdegrees and the column sums are the indegrees In all cases the distribution of the random 0 1 matrices is uniform that is each matrix satisfying the restrictions has the same probability The results include p values that can be used for testing reciprocity or transitivity while controlling for the in and outdegrees For very small matrix sizes up to 8 12 rows and columns this can be done by enumerating all matrices satisfying these constraints the simulation method is more generally applicable In Figure 36 the model specific user interface of ZO is presented The various model specifications will be discussed below StOCNET X StOCNET sessions 20 example sns A oj xj Session Files Step Options Help e E a Back Forward Data Transformation Selection Model Result
59. llowing reference Boer P Huisman M Snijders T A B Steglich C E G Wichers L H Y and Zeggelink E P H 2006 StOCNET An open software system for the advanced statistical analysis of social networks Version 1 7 Groningen ICS Science Plus http stat gamma rug nl stocnet 1 The main goals and developments of StOCNET are explained in detail on the StOCNET website http stat gamma rug nl stocnet or see Huisman amp Van Duijn 2003 2004 2 The program 2 1 Opening window An analysis within StOCNET takes place within a so called session which consists of five sequential steps The steps start with the data definition and result in specified output after which all or some steps can be repeated Within a session the user generally uses the same selection of data sets After defining the data transformations can be performed and the user may select those actors on which the analysis should be based Next a statistical method is chosen to analyze the network s and the model specifications for the data are defined Finally the module is run and the output can be viewed All definitions specifications and results are saved when saving the session and can easily be activated again when opening the same session a second time StOCNET can be started by double clicking on its icon or by double clicking on existing sessions created by StOCNET saved with extension SNS such that you immediately return to the requested s
60. me session By using the View button in the step specific interfaces or via the File menu the data files can be saved under different names and used in other sessions and or programs A report of the selections applied is contained in the StOCNET session info 3 5 STEP 4 Model specification and analysis The fourth step involves selecting the desired method to analyze the data A statistical model has to be selected and the corresponding options have to be specified to analyze the network data accordingly The model specification window consists of two parts as shown in Figure 10 In the upper part named Model choice a model for the statistical analysis has to be selected The models that are currently implemented in StOCNET are e BLOCKS version 1 6 manual Snijders amp Nowicki 2004 for a posteriori blockmodeling of relational data that is latent class analysis for dichotomous or valued graphs and digraphs according to Nowicki amp Snijders 2001 e p2 version 4 manual Zijlstra amp Van Duijn 2005 for the analysis of binary network data with actor and or dyadic covariates and random effects according to Van Duijn 1995 e PACNET for constructing a partial algebraic model for observed multiple complete networks using a statistical approach e SIENA version 2 4 manual Snijders Steglich Schweinberger amp Huisman 2006 for the analysis of longitudinal network data according to the dynamic actor oriented models of S
61. nced button opens the Advanced options screen presented earlier in Figure 26 With the option Code for model specification the type of step in the MCMC procedure is defined with the multiplication factor the user can specify the number of steps for generating one exponential random graph See the SIENA manual for more information about these advanced options 34 4 5 ULTRAS The module ULTRAS aims at estimating latent transitive structures in social networks Such structures can be used to identify close knit subsets of actors in social networks Latent transitive structures can be expressed by ultrametrics The module ULTRAS estimates ultrametrics given one observed network ULTRAS can handle binary integer valued and continuous network data Maximum Likelihood Estimation is implemented by a Simulated Annealing algorithm a non greedy optimization algorithm and Bayesian inference with uniform priors is implemented using hybrid MCMC methods This section concentrates on running ULTRAS within StOCNET Details about the program and the underlying class of models can be found in the ULTRAS manual Schweinberger 2003 and in the article Schweinberger amp Snijders 2003 In the model specific interface presented in Figure 31 the model can be specified as follows StOCNET X StOCNET sessions ULTRAS example sns 15 x Session Files Step Options Help gt a Back Forward Data Transformation Selection Model Results Er StO
62. neity The index of heterogeneity is computed from the observed degree variance standardized based on the density of the graph It is the heterogeneity index J defined in Snijders 1981 with the value O if the observed degree variance is equal to its expected value for a random graph and 1 if it is the maximum possible value Only for nonvalued relations Some results for the freshmen data are presented in Output box 3 The network analyzed in this box is network 2 of which the relations are dichotomized 0 0 1 3 1 4 5 0 6 and 9 missing The density now gives the proportion of observed relations to all possible relations In Output box 3 only indegrees are presented It shows an indegree standard deviation of 3 60 and an index of heterogeneity of 0 21 which indicates that the variance is larger than would be expected under the null model of randomly distributed arcs Network 1 Density 0 145 Average degree 4 483 Missing fraction 0 094 Symmetric no Dichotomous yes 3 Degrees and degree variances Indegree network 1 Actor lt _ Notall indegrees are presented here Degree st dev Heterogeneity Output box 3 Examine results of STEP 2 3 degrees Dyad count Networks with valued relations are dichotomized Missing tie variables are regarded as absent arcs edges e Dyad census The number of complete mutual M asymmetric A and null dyads N in the network 2M 2M A to the total number of ties see Z
63. ng a range of actors Selection by calculated variable The third selection method is the most complex one It involves an examination of the network s and computation of some network statistics The list Calculated variable contains the different network statistics that can be used to select the actors see Figure 8 In the current version of StOCNET only two simple statistics can be used in the selection procedure indegree number of incoming relations and outdegree number of outgoing relations After selecting a statistic variable a criterion value for that statistic has to be specified The following operators can be used in the definition of the criterion equals gt larger than gt larger than or equal to lt smaller than lt smaller than or equal to OR A or B means that A B or both expressions have to be true for the whole statement to be true AND A and B means that both expressions have to be true for the whole statement to be true The operator has to be followed by a value of the selected statistic to complete the criterion A criterion can only consist of statements with at most two operators In the calculation of the variable missing values are ignored Actors for whom the variable is missing because all relations are missing for that actor are automatically not selected For example the outdegree of the actors is chosen as statistic and only actors with a medium outdegree say more than 5 but le
64. nijders 2001 and MCMC estimation of exponential random graphs according to Snijders 2002a e ULTRAS version 2 manual Schweinberger 2003 for the analysis of symmetric network data according to ultrametric measurement models proposed in Schweinberger and Snijders 2003 which can be regarded as stochastic hierarchical clustering models e ZO version 2 3 manual Snijders 2002b for determining of probability distributions of statistics of random graphs and digraphs with given in out degrees by simulation and or enumeration analysis according to the algorithms of Snijders 1991 and Molloy amp Reed 1995 StOCNET G Stocnet sessions sessi sns o x Session Files Step Options Help gt amp Back Forward Data Transformation Selection Model Results StOCNET Session Data Model Network s Model choice Actor attributes E Transformation StOCNET Model SIENA al 2 w Network s _ BLOCKS Actor attributes Model Specific User Inte B Selection Select all Specifications 7 n Model SIENA Digraphs in seq order t Dependent actor covarie Data specification Model specification w Results pRun model Estimation C Simulation Bun X Cancel 7 Help A gt STOCNET Session info Notes Examine View 4 Apply Figure 10 STEP 4 model selection and model specific user interface After a model has been s
65. ns sessi sns oj xj Session Files Step Options Help a 5 Back Forward Data Transformation Selection Model Results E StOCNET Session Transf ii Data ransformations fee Transformation gt Network s Network s Network WAND32T0 DAT A tri ol nonias Network WAND32T2 DAT Symmetry transf Model SIENA Network3 VRND32T4 DAT Results Recode Missing values Actor attributes Actor attribute file s Attribute smoking Recode Missing value STOCNET Session info Notes Examine View SF Apply X Conca 7 Help Y Figure 5 STEP 2 transformation of network and attribute data In the transformation step three functionalities are available which can be applied for each network separately symmetry transformations recoding variables and specifying missing value codes After clicking the Symmetry transf button the window in Figure 6 appears The symmetry transformations operate on the symmetrically located pairs of elements Yj and Yj in the adjacency matrix The choices are between doing nothing symmetrizing to the maximum i e replacing both values by their maximum summarizing to the minimum i e replacing both values by their minimum and transposing i e interchanging these two values Symmetry Transformations k l x Current Symmetry Transformation C None C Symmetrize to minimum x
66. on tree the program jumps to the step in which the alterations can be made After the alterations have been made click the Apply button and subsequently the Run button in STEP 4 If a new analysis is performed with the same model and only new model specifications are defined the results of the analysis are appended to the existing output file and shown in the session tree If a new model is selected or specifications in earlier steps of the session data definition transformation or selection are changed the existing output file will be overwritten In this case the user will be presented an option to save the output file with a new name Save as option 4 Statistical models 4 1 BLOCKS The module BLOCKS is designed for stochastic blockmodeling of relational data according to the methods described in Nowicki amp Snijders 2001 This section gives information about executing BLOCKS within StOCNET For more detailed information about the program BLOCKS or stochastic blockmodeling the reader is referred to the manual Snijders amp Nowicki 2004 and the article of Nowicki and Snijders 2001 Posterior blockmodeling searches for equivalent groups of actors with respect to relational patterns based on the observed relations between the actors When the observed data are assumed to have been generated by some stochastic mechanism this approach to blockmodeling is called stochastic blockmodeling The method implemented in BLOCKS searches
67. os The numbers of rows and columns of this matrix do not have to be equal The positions of the structural zeros have to be specified in a separate matrix Run model type The ZO program contains two types of run model Most important is the analysis by Monte Carlo simulation This is the default option When this option is selected the Specify button will become active and simulation options can be defined In addition analysis by enumeration can be performed This run model however is only available for very small graphs i e for data matrices which have at most 15 rows and columns for most combinations of row and column sums the number of matrices will be too large to enumerate already for about 10 rows and columns ZO options e Only connected graphs Requirement that the generated graphs should be connected or weakly connected for digraphs This option is only available for matrices of the types directed graph and undirected graph By default this option is turned off e Prescribe number of mutual dyads Requirement that the generated graphs should have a given number of mutual dyads This option is only available for matrices of the type directed graph By default it is turned off If this option is selected the required number of mutual dyads must be specified This must be a positive number between 0 and half the sum of the degrees e Write all produced matrices to file f this option is turned on all generated matrices are
68. ose data are displayed that are available in a specific step of the session In the viewing window two options are available Print to print the displayed file and Save as to save the file under a different name The view and save functions are also available in the File menu Note that in the View function the values of the displayed variables cannot be changed Apply Activates the newly defined or changed specifications in the current window Only after clicking the Apply button the new specifications will be active and the subsequent step in the session can be entered Cancel Cancels all unapplied specifications Help Gives online help based on the StOCNET manual Unlike the Help menu in the main menu the Help button only gives help on the specific step in which the button is clicked Clicking the Help button of other windows within the same step gives help on that specific window and its functionalities Clicking specific buttons in the main window of a particular step usually results in opening a new window These windows have their own specifications and functionalities but apart from that always contain the buttons OK Cancel and Help With the OK button the newly defined or changed specifications in that particular window are activated The Cancel button cancels the defined or changed specifications and closes the window The Help button gives help on the opened window The left part of the StOCNET window shows the so called se
69. ot presented because of the large number of actors 52 6 Contributions to StOCNET In order to provide a new platform to make statistical programs available to a wider audience the StOCNET system was set up in such a way that new programs can be implemented with as little effort as possible New contributions can be implemented as executables or as DLLs and their source codes are allowed to be written in a large variety of programming languages e g Delphi C and C The platform with its common data structure and user interface is provided by the StOCNET system and the programs containing the statistical methods are treated as black boxes All procedures will have globally similar interfaces and therefore contributors only need to provide information with respect to data input data representation data output parameter restrictions and so forth Moreover the procedures should have some general properties e proper documentation e definition of files and options used by the program in an ASCII file for which the extension name in is used that will be written by StOCNET from the information supplied by the user in the StOCNET interface the status of the calculations sent to a displayed window user break and or pause possibility proper error handling and error messages through error or log files and correct memory handling and allocation News about the StOCNET software can be found at the StOCNET website at http st
70. ov Chain Monte Carlo algorithm according to Zijlstra van Duijn and Snijders 2005 This section gives information about executing pz within StOCNET For more detailed information the reader is referred to the manual Zijlstra amp Van Duijn 2005 and the articles of Van Duijn 1995 and Lazega and van Duijn 1998 The examples used here are based on the pz model For more information on the multivariate p2model and the multilevel pzmodel see the pz manual Zijlstra amp Van Duijn 2005 The purpose of the pz model is to test the effects of actor and or dyadic attributes on the ties observed in a directed network controlling for reciprocity and for differences between actors in activity and popularity The 2 model is a type of logistic regression model for the ties in a network to which a reciprocity effect is added as well as random sender and receiver effects representing differential activity and popularity respectively In that respect it can be regarded as an extension of the well known p model Holland 8 Leinhardt 1981 in which the actor parameters are replaced by random effects and actor and dyadic attributes can be included In Figure 16 the model specific user interface for p2 is presented Two groups of model options have to be specified StOCNET X StOCNET2 sessions p2 test 1 12 05 sns 15 x Session Files Step Options Help gt amp Back Forward Data Transformation Selection Model Results E SI
71. owards the corresponding step in this session Clicking the button STOCNET Session info opens the Notepad editor and shows the contents of the history tree The contents are automatically saved in the file info txt The right part of the main window contains the step specific interfaces in which the user must make the appropriate choices to conduct a network analysis In the following sections the step specific interfaces of the five steps are described When opening an already existing session by double clicking on the file name with the extension SNS or opening a desired session in the opening window or via the Session menu the window belonging to STEP 1 data definition is opened and new analyses can be conducted 3 1 Export to other data formats It is possible to export data of a StOCNET session to the data formats used by the programs Multinet Netminer Pajek and Structure This is done by clicking on Session and selecting the desired export format see Figure 3 The default directory for the export file can be determined in the Options Directories menu item Session Files Step Options New Open session Save Session Save session As Notes Export to Multinet Export to Pajek Export to Netminer Export to Structure Exit Alt x Figure 3 Exporting to other formats 3 2 STEP 1 Data definition In STEP 1 the right part of the window contains the options for the specification of network
72. persed distribution The ultrametric that maximizes the profile log likelinood will be a reasonable starting point in many applications To check convergence however one is advised to execute in addition several runs using ultrametrics sampled at random from an overdispersed distribution as starting points and to compare the results b Use Order In large networks one can hardly see any structure in the matrices given in the output file For this reason it is sensible to re order all matrices in such a way that the structure can be seen more easily ULTRAS automatically re orders the set of actors during the Maximum Likelihood Estimation procedure and writes the order to a text file If you choose Yes then ULTRAS reads the order stored in this file and uses it to re order all matrices in the output so that parts of the output corresponding to MLE and Bayesian estimation will use the same order Length of Burn in lt is sensible to give MCMC algorithms time to explore the state space and therefore to choose some reasonably high number of burn in e iterations A conservative choice is n x 100 iterations Length of Markov chain This gives the number of iterations after the burn in phase During this post burn in phase the algorithm samples from the posterior distribution To obtain reasonable Bayes estimates the number of iterations needs to be sufficiently large where sufficiently large will depend on the number of actors
73. pletely finished The manual was written in various phases by Evelien Zeggelink Mark Huisman Tom Snijders and Lotte Wichers 1 Introduction StOCNET is an open and user friendly software system for the advanced statistical analysis of social networks focusing on probabilistic stochastic models This manual is a provisional description of the current version StOCNET 1 7 February 2006 but it is not yet completely updated from the 1 6 release of February 2005 You are advised to check the StOCNET website occasionally for updates and new versions of the program the address is htto stat gamma rug nl stocnet If after reading the manual you have any questions feel free to contact us via email at c e g steglich rug nl or t a b snijders rug nl StOCNET consists of several statistical models for network analysis In the present version six modules are implemented e BLOCKS version 1 6 for stochastic blockmodeling of relational data Nowicki amp Snijders 2001 e p2 version 4 for the analysis of binary network data with actor and or dyadic covariates Van Duijn 1995 e PACNET for constructing a partial algebraic model for observed multiple complete networks using a statistical approach Pattison Wasserman Robins and Kanfer 2000 e SIENA version 2 4 for the analysis of repeated measures on social networks Snijders 2001 and MCMC estimation of exponential random graphs Snijders 2002a e ULTRAS version 2
74. r one is advised to try out several values and to compare the results 35 Number of sequences Since running multiple sequences is convenient to check convergence ULTRAS offers the possibility to run more than one sequence with the same input values subsequently Probability model The tie variables can be considered to be Bernoulli distributed binary network data Poisson distributed non negative integer valued network data and Gaussian distributed continuous network data The contents within the parentheses indicate what probability model may be appropriate for what kind of network data If the option chosen requires different kinds of data e g the Bernoulli option is chosen but the ties in the data file take more than two values then ULTRAS may adjust the probability model option Method Maximum Likelihood ML estimation as well as Bayesian inference can be used to estimate models from observed network data A rule of thumb is to carry out some runs using the ML method first because ML estimation produces simple and readily interpretable results It is advisable to complement ML estimation with Bayesian inference which admits to study model uncertainty Specify This button depends on the method chosen i Maximum Likelihood Estimation Specifications for Maximum Likelihood Estimation x Number of ultrametrics 1 al v Number of Iterations i 00000 vr Temperature E e X Cancel
75. s E StOCNET Session qe Model w Data Transformation Model choice Selection oic 20 StOCNET Model 20 a Data file Network2 Model Specific User Interface Rows 50 P Files Type of matri Columns 50 Data file E om E Graphmode Newor 50 rows unrestricte directed graph hewoike _Select 50 columns directed graph fH Results File indicating positions of structural zeros C undirected graph Select C general I Only connected graphs IV Prescribe number of mutual dyads J Write all produced matrices to file gt Run model type ME NT HH Simulate Required nr of mutual dyads jo C Enumerate Version of statistics to be evaluated 1 Specify Bun te View Y Apply X Cancel Help ZA STOCNET Session info Figure 36 ZO model specific user interface 1 Files ZO can use a dichotomous adjacency matrix defined in STEP 1 of the StOCNET session as input However since the results depend only on the row and column sums it is 39 4 also allowed to have no network data file but only a file containing the row and column sums In the latter case the file must consist of one or two lines the first containing the required row sums the second the required column sums The file must contain non negative numbers separated by blanks Clicking the Select button opens a data selection window in which either a S
76. s standard deviations and the gt Save Print Eull report Figure 39 Examine output window 43 5 1 Examine in STEP 1 In STEP 1 the network and attribute data are defined Because missings are not defined yet only simple analyses are performed on the network data For the attributes no descriptives are calculated Networks For each specified network the following descriptives are calculated e Relation count the number of actors number of total possible relations number of relations with a specific value e Dyad count the number of dyads with a specific value Results for the freshmen data are presented in Output box 1 below The number of actors in the network is n 32 and the total number of relations is n n 1 992 Counts of relations and dyads with specific values are given Dyads are defined as a pair of relations Dj x xj For example in network 2 there is 1 dyad for which the relation xj 2 and x 1 3 Relation count Number of actors in the observed networks is 32 For digraphs the total number of relations is 992 Relations network 1 0 3 count 6 Relations ne count Relations ne count 43 Dyad count Cross tabulation of dyads network 2 xyi 0 92 0 0 3 81 3 36 m FPONOYFEDN ht N Ou JURA uw oowooorgyu WORDrRGDCOKRO Output box 1 Part of the examine results of STEP 1 44 5 2 Examine in STEP 2 and STEP 3 In STEP 2 all
77. s with xj 1 Xx 1 and Xx 1 for digraphs Degree of transitivity For graphs T ES UN the ratio of total number of transitive 3Tr 2 In triads to the total number of transitive and intransitive triads see Frank and Harary 1982 transitive triads and Zeggelink 1993 For digraphs T the ratio of potentially transitive triads the number of transitive triads to the number of potentially transitive triads The normalized degree of transitivity based on the expected degree of transitivity under a random distribution of the same number of relations in a network of the same size see Zeggelink 1993 Only for graphs The triad census The number and proportion of the triads that belong to one of the isomorphic triad classes defined by Holland and Leinhardt 1976 see Wasserman amp Faust 1994 Only for digraphs Some results for the digraphs of the freshmen data are presented in Output box 5 The increasing transitivity index shows there is a tendency for transitive relations This is also suggested by the triad census for instance the proportion of null triads class 003 see Wasserman amp Faust 1994 decreases from observation time 1 to 3 whereas the proportion of complete triads class 300 increases over time 47 3 Triplets and triads In network 1 relations are dichotomized In network 2 relations are dichotomized In network 3 relations are dichotomized Directed graphs triplets with i gt j
78. ss than 15 should be selected This results in the following criterion value gt 5 AND lt 15 Subsequently the set of actors that fulfills this network requirement is selected Selection by attribute The last possibility is the selection of actors based on the values of an attribute First the attribute file containing the desired variable has to be selected Next the specific attribute has to be specified and finally a criterion value has to be defined Definition of the criterion value proceeds in the same way as in the previous selection procedure For example using the attribute gender female actors can be selected see Figure 8 For this purpose the attribute file is specified in this case File1 the default name StOCNET uses for attribute files Next the attribute itself is specified here gender Finally the selection criterion 2 This definition selects all actors who have the value 2 for the variable gender that is all female actors Actors with missing values for the attribute used in the selection procedure are automatically not selected All selections can be inspected by clicking the View button and examining the network and or attribute files The selected data is saved in a temporary file that has the same name as the old file preceded by For example Vrnd32t2 dat is saved as Vrnd32t2 dat After closing a StOCNET session these temporary data files are deleted and will be created again when re opening the sa
79. ssion tree The use of the session tree is described in the next section 3 StOCNET sessions If in the opening window the option to start with a new session is selected or if the toolbar item Session is used to start a new session the window presented in Figure 2 appears This window pertains to the first step in a StOCNET session data definition When starting a new session the files containing the network data and the desired actor attribute files have to be specified Jax Session Files Step Options Help 3 m gt a E Back Forward Data Transformation Selection Model Results Data Definition Transformation Network s fa Selection Filename Model SIENA Results Add Remove Edit rActor attribute file s DA El Add Remove Edit Description STOCNET Session info Notes Examine View Figure 2 Starting a new session X Cancel 7 Help ZA In every step of a StOCNET session the structure of the main window stays the same The left part of this window shows the session tree that contains global information on the history of the present session The operation of this tree is similar to standard options in Windows Explorer with the difference that here an overview is given of actions taken together with details of these actions The details can be viewed by clicking the corresponding Double clicking the step name results in a move t
80. ssions sessi sns Session Files Step Options Help gt Sa Back Forward Data Transformation Selection Model Results E StOCNET Session Data Transformation Selection Results Model BLOCKS Bo New run of BLOCKS Secondary output is on file sessl PQR file sessl POR is overwritten in each run of BLOCKS with this project na The input file specifies that if there exists an earlier file named ses the folloving new output is appended to the earlier existing file New run of BLOCKS Input of project descri Input of data file E 2 colors Gibbs sequence n Iterations value Results Matrix of pai an Probabilities Input of project description file E Finding stric AERERERRENE NEAR ARRR RRE ENE SER RARAAA B Reducer Poste Reducec ani A ny ee ee Reducec Save Print m Reducec Notes Examine View Figure 15 BLOCKS results BLOCKS version 1 53 Random number generator seed is 69939 Details Eull report X Cancel 7 Help STOCNET Session info 21 4 2 P2 The module p2 is designed for the analysis of binary social network data with actor and or dyadic covariates The program carries out the estimation of a random effects model with the dyadic ties as the dependent variable according to the Iterative Generalized Least Squares algorithm for nonlinear multilevel models as described by Van Duijn 1995 or Mark
81. t implemented ooo D 000o not implemented onjo 0 miimi m 00o Opoo onoo 000o oO Ojo opoo 00m0 oO o po Ojo activity of alter outdegree up to 0 square root outdegree 0 0 d squared outdegree 0 sum 1 outdegrees 1 S M9 S 0 SC m S 0 S o 0 S oO c OS o c oO o2 200000000000000000000 X Cancel Help Figure 26 Model specification Advanced 3 Run model SIENA can be used for two types of analysis Estimation of the parameters of the stochastic actor oriented model or Simulation of the network evolution process for given fixed parameter values One of these options must be selected i Estimation This is the most fundamental option when using SIENA The estimation is used to obtain estimates of parameters ii Simulation With the Simulation option the network evolution is simulated with a model with fixed parameters This is only meaningful if the model parameters are already estimated Therefore it is advised to run Simulation after Estimation With the simulation procedure expected values of specified statistics are computed which can be compared with their observed values These statistics have to be selected using the Specifications for simulation window that appears after clicking the Statistics specification button This window is shown in Figure 27 The number of simulation runs default 1000 can be changed in the same window 31 Specifications for sim
82. tOCNET network file adjacency matrix or a file containing row and column sums can be selected The numbers of rows and columns which do not necessarily have to be equal are automatically detected by StOCNET and shown in the user interface see Figure 36 and used for determining the default type of matrix If the file contains only one line the undirected graph type of matrix is chosen If the network data contains structural zeros see the option Type of matrix general mentioned below the positions of the structural zeros have to be specified They have to be presented in a separate file ASCII which contains an adjacency matrix that has the same number of rows and columns as the selected network The matrix entries are either 0 absence of a structural zero or 1 presence of a structural zero Type of matrix There are four types of matrices that can be used in the ZO program By default in most cases the second matrix type is selected i e a digraph e Unrestricted matrix a matrix without structural zeros The numbers of rows and columns of this matrix do not have to be equal e Directed graph an adjacency matrix with directed relations The numbers of rows and columns are equal e Undirected graph a symmetric adjacency matrix with undirected relations without structural zeros The numbers of rows and columns are equal Row and column sums are identical e General matrix a matrix with an arbitrary set of structural zer
83. tion modes if the program is not put into a directory called C StOCNET then after installing first adapt the Options Directories to the directory and subdirectories where you did put the program The continuous development of the program and its statistical modules results in new versions which will be made available on the website New versions of the statistical modules can be downloaded and installed separately The updates of executables of the separate modules have to be copied to the folder where the StOCNET software is installed to replace the old executables The StOCNET system was developed by Peter Boer Mark Huisman Tom Snijders Christian Steglich and Evelien Zeggelink A histrocial account is given on the StOCNET website The following persons were involved in programming parts of the system StOCNET Peter Boer Rob de Negro and Bert Straatman A J Straatman scienceplus nl Examine functionality Mark Huisman J M E Huisman rug nl Module BLOCKS Tom Snijders and Peter Boer 1 A B Snijders rug nl Module p2 Bonne Zijlstra B J H Zijlstra rug nl Module SIENA Tom Snijders Christian Steglich Michael Schweinberger and Mark Huisman T A B Snijders rug nl Module ULTRAS Michael Schweinberger M Schweinberger rug nl e Module ZO Tom Snijders T A B Snijders rug nl e Module PACNET Pip Pattison pepatt unimelb edu au This manual was written with consecutive updates from the first version This version is not com
84. tons Save Print and Full report which have the same functionality as in the Result step Section 3 6 Figure 11 In the remainder of this section the descriptive statistics that are available in the four steps of a StOCNET session are presented In each step a distinction is made between network statistics and attribute statistics Some results are shown of descriptive analyses on the example data of the university freshmen described in Section 3 2 Examination Result Results E EXAMINE data in TRANSFC E Network descriptives Degrees and degree Dyad count Triplets and triads Segmentation and co E Attribute descriptives Frequency tables Descriptive statistics Correlations H EXAMINE data in TRANSFC H EXAMINE data in TRANSFC Self relations are assumed not to exist and are therefore not counted For the counts of arcs dyads triplets and triads missing values are not counted For the numbers of isolates components s d s and variances missing values are considered as absent arcs Network 1 2 3 Density 0 014 0 521 0 500 Average degree 0 111 4 167 4 000 Missing fraction 0 000 0 333 0 111 Symmetric no no no Dichotomous yes yes yes Symmetric networks are treated as undirected graphs networks that are not symmetric as directed graphs g3 Degrees and degree variances For undirected graphs only indegrees are presented For dichotomous network
85. twork a global maximum the global maximum of the probability is found by using algorithms that start with an initial guess of the parameter and approach the maximum by updating the guess in small steps iterations However on its way to the global maximum the algorithm may encounter local maxima and if the algorithm moved uphill only but not downhill it would get stuck at local maxima The temperature helps to rescue the algorithm from such local maxima by allowing downhill steps and thus helping the algorithm to get over local maxima 36 at the output The output tells what the largest difference between succeeding likelinoods has been during the estimations process A rule of thumb is to set the temperature equal to this value ii Bayesian inference xi mMlnitial Ultrametic 7 Use Order By HCS G No C MLE O Yes AtRandom L Length of Burin f Length of Markov Chain i 00000 E f 00000 v v Y DK Heat posterior C No Yes X Cancel Ee 7 Help Figure 33 ULTRAS Specifications for Bayesian inference a Initial ultrametric ULTRAS allows you to choose as initial ultrametric either an ultrametric obtained by constructing a Hierarchical Clustering Scheme HCS the ultrametric which maximizes the profile log likelihood which requires that you already carried out Maximum Likelihood Estimation an ultrametric sampled at random from an overdis
86. ulation xj r Statistics lt Amount of network change in period 1 Amount of network change in period 2 Number of ties Number of reciprocated ties Number of transitive triplets Amount of balance Number of directed distances equal to 2 Sum of squared indegrees O0OKKi Sum of outdegrees up to 0 Sum of square root outdegrees 0 o d Sum of squared outdegrees 0 Sum of 1 outdegrees 1 Sum of 1 out deg 1 out deg 2 Number of 3 cycles Number of isolates indegree up to 0 Number of dense triads Number of peripherals to dense triads 4 m p jm pm pam E p c pm 4 O Amount of similarity on gender C Sum of reciprocated ties x similarity on get O Sum of similarity on gender x gender O Sum of similarity on gender x gender O Sum of outdegrees x gender CO Sum of reciprocated ties x gender ego C Sum of crossproducts gender ego x gend C Sum of crossproducts gender ego x gend Sum of crossproducts indegree x outdegrel Sum of indegrees x gender L Amount of dissimilarity of bridged actors o C Amount of similarity on program C Sum of reciprocated ties x similarity on pre C Sum of similarity on program x gender C Sum of similarity on program x program CO Sum of outdegrees x program C Sum of reciprocated ties x program ego C Sum of crossproducts program ego x gen C Sum of crossproducts program ego x proc gt I Number of iterations for straight simulation 1000
87. values are handled by pairwise deletion Results for the freshmen data are presented in Output box 6 below only the frequency table for the variable program is shown From the descriptive statistics table it follows that there are no missing values for the attributes and that all three attributes are categorical the mode is calculated for all variables The correlations between the variables above the diagonal in the correlation covariance matrix are of moderate strength 5 3 Examine in STEP 4 For the different models that can be selected in STEP 4 of the session different descriptive analyses and statistics are important or of interest as pre analyses of the data Therefore the offered Examine functionality depends on the selected model In the current version of StOCNET descriptive statistics are available for the modules SIENA and p gt Note that also in the output of some of the programs important descriptive statistics can be presented According to the contributors of these programs these statistics are too important to miss even if the user does not click the Examine button 49 3 Frequency tables Attribute program freq 3 val perc cum perc 2 6 8 18 8 18 8 3 10 31 3 50 0 4 16 A 50 0 100 0 missing 0 32 3 Descriptive statistics The mode is only calculated for categorical variables n Mode Median Mean Min Stvdev Var gender 32 1 1 00 125 1 00 0 440 0 194 program 32 4 3 50 3231 2 00
88. written to a file This is usually undesirable it may produce a very large file by default it is turned off e Version of statistics to be evaluated See the ZO manual Snijders 2002b for more details on the versions of statistics of which the probability distribution is determined by the program By default the version equals 1 40 5 Specify simulation options Clicking the Specify button opens the ZO Specify window presented in Figure 34 In this window four simulation options can be defined For more details about these options see the ZO manual Snijders 2002b e Number of simulation runs By default the number of runs is 10 000 e Simulation algorithm Two algorithms can be selected the algorithm of Snijders 1991 this is the default and the algorithm of Molloy and Reed 1995 e Number of linear combinations of triad counts lt is possible to let ZO calculate the triad census and linear combinations of it as defined by Holland and Leinhardt 1976 This option defines the number of linear combinations of the triad census that are to be calculated as statistics default 0 The number of linear combinations can be at most 16 This option is only available for matrices of type directed graph and undirected graph and for statistics version 1 e Read weights for linear combinations from file Only available if the number of linear combinations is larger than 0 The file with the weights must contain as many lines as there are l
89. xcept for the Step menu the Session menu is typically a StOCNET menu but contains standard options Session Files Step Options Help Start open save and close sessions and export data In addition the option Notes is provided which opens an edit window to organize your thoughts and decisions for the analysis in this specific session The notes will be saved as an ASCII file with the same name as the session and the extension NTS and are available any time during a session View and save data files This menu is only available after data files network files and or attribute files are defined and opened The data files may be saved under a new name and or extension Enter the consecutive steps in a StOCNET session The steps are Data definition Transformation Selection Model and Results A global description of each step follows below and details are given in subsequent sections Activate a number of options Toolbar the StOCNET toolbar which contains speed buttons for fast entry of the different steps in a session It also contains the buttons Back and Forward to allow a fast switch between actions in previous and current steps defined by the step buttons Directories specify directories of session files network files actor attribute files export files and temporary files These specifications are automatically updated when a user opens a data set or saves a StOCNET session file in another directory By default

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