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1. When there are missings in constant or changing monadic covariates and centered FALSE for their creation by coCovar or varCovar the mean will be im puted used to be 0 which was an error For changing covariates this is the global mean In coCovar and varCovar there is a new argument imputationValues which are used if given for imputation of missing values Like all missings they are not used for the calculation of the target statistics in the Method of Moments New effects outOutActIntn toDist2 from w ind In the target statistic for the higher effect contributions for value ego value alter are now set appropriately at 0 5 was 0 New effectGroup tripleNetworkObjective allEffects csv effects r see earlier in this man ual for its characteristics Decent error message when there are almost all NA in the dependent behavioural variable effects r function getBehaviorStartingVals The centering within effects for similarity variables at distance 2 now is done by the same similarity means as for the simX effect attr mydata cCovars mycov simMean etc e 2015 04 02 Revision 284 Changes in RSiena and RSienaTest 181 New effects simEgoDist2 simEgoInDist2 simEgoDist2W simEgoInDist2W sameXOutAct diffXInPop diffXOutAct The centering for the similarity measure in effects such as simEgoDist2 and simDist2 is not yet clear this affects only the outdegree parameter Relevant for crea
2. ASTVA MOe sus BUI JO JS V WOT A NOIL BUAIS ssepo JO yoolqo ue SIJBILO Jys over dnoryeusls yst qo oyvorg dnoryeuols syeorgdnorneuors mo10eu rs Aq posn squstn3 e 0 UIS ureNIopour JoyjO 03 SI J I 7 otueu s joofoid 913 SI ureN pour TTQN wotssos moT0eu rs WO pojeo sr uorjounj y Jl uorssos yndut ASO UOISSOSG TTIQN oureusly a SI UOISS9S U uorss s oY SI TY Anois 10 JD9QOUPISSISUION 1989 88 qeus UCISsaGUIOLJo Vole VC eUdIS Bye LU Y S978919 PUR 9 Y Y WO UOISSIS V NHIS Y spe x gt qoAu UOISSOSUIO 9 89 1 eye Lurs e si sn Aq sn 10 30U suonmounj 8utoqut 10 UOLPeJU9UINIOP MOJE 09 Seg e st uoneyu um 00 7 08 poyeaxo ore squavIn31e oy UYM pariddns yagapou ay UY9JBUI 09 SOY H JONeUSIG SSET JO 3o qo IS1Y I UL SMOI JO 19QUINU oY 03 enb q33U9 YPM SIOJY poweu 398 SUIS Y SI JNMPJA SOS POU PUIG JO ISI Y SI SIOS opou ASUBYDUOLSOCUILOS 1eaogpedquea IBAO_ peAp ueyo pedqoo ITBAOQILA IBAOJOD JUSPpu9da PUAIS sse o esuoo SUOD TSUOD ASTVA UO01yequounoo 193 jo sp fqo ayy syuesaldar 7 syoofqo Inoraegoq pue uo yau ayea1 eye euars TIN N SIS9pou ISOdUIOD SOJBTIBAO SYIOMJOU VIOIJ 399 qo VUIS Y S L N gt VAAN cu jogeorgegeqeuor joyeorgeyeqeuotrs uoryjdraos qT s durexri xequrg oure N a3e1s ased snora ad uo panurquos v ede L 173 ponurguop ureu Y 07 Y US
3. Fix for short name for egoXaltX effect for undirected networks Now matches the name for directed networks 2011 06 04 R forge revision 153 Maximum likelihood this is still under development Correction for bipartite networks and networks with constraints Variable length of permutations will change results slightly compared with previous versions Creation effects not yet complete Requested time dummies should now appear on the effects object print Bayesian routine still very much under development has altered 2011 05 27 R forge revision 150 Removed effect for an absolutely constant covariate with two networks 2011 05 26 R forge revision 148 Improvements to sienaGOF added script to manual 2011 05 16 R forge revision 146 Documentation improvements Can read some undirected networkd from Pajek files 2011 04 19 R forge revision 144 New effects out trunc effect 195 Enhancements to siena08 2011 03 13 R forge revision 142 3 GWESP effects RSienaTest only 2011 02 24 R forge revision 140 adds functionality to sienaGOF for plotting image matrices of the simulations cumulative tests based on the Kolmogorov Smirnov test statistic and conforms to coding standards 2011 02 24 R forge revision 139 fixes for bipartite networks with ML ML is still incomplete and will not work correctly with missing data or endowment effects 2011 02 22 R forge revision 137 RSienaTest only A
4. changes to validation of bipartite networks should now be consistent 192 2012 01 17 R forge revision 192 minor but extensive changes to manual minor changes to scripts 2011 12 15 R forge revision 191 Some of these may alter results slightly Altered calculations of probabilities to avoid overflows Fixed bug in storage of MII in bayes Removed endowment effect for IndTies for symmetric networks Removed code for storing change contributions on ministeps not functioning Set random number type to default at start of siena07 2011 12 14 R forge revision 190 Fixed bug in Bayes left over from R 189 2011 12 14 R forge revision 189 Fixed minor bugs in reports and error messages 2011 12 04 R forge revision 186 Fixed some bugs in ML estimation procedure which will alter the results slightly Added algorithm functions to RSienaTest package 2011 11 27 R forge revision 185 Bayes and algorithm code now uses parallel package Fixed memory leaks in ML estimation Less space needed Other minor changes to ML with missing values still incomplete 2011 11 14 R forge revision 184 Fix memory leaks in calculation of rate statistics 2011 11 11 R forge revision 183 Fix bug stopping interruption in phases 1 and 3 since recent change Check whether dfra from maxlike or not when using prevAns 2011 11 11 R forge revision 182 fix bug in ML Bayes returning acceptances fix bu
5. s alters who are also adopters of the innovation n ais y gt ZjZijtj j 1 infection by covariate effect infectCovar defined as the sum of covariate values of 1 s alters who are also adopters of the innovation n aisly X 2324305 j l susceptibility to average exposure by indegree effect susceptAvIn defined as the interaction between it s indegree and 2 s average exposure jai ATi ay tpi E gt jet tij susceptibility to average exposure by covariate effect susceptAvCovar defined as the interaction between 2 s covariate value and i s average exposure ais y YA Ed i Ui n 2 j 1 ij 143 13 Parameter interpretation The main driving force of the actor oriented model is the evaluation function extended with the creation and or endowment function if these are part of the model specification For the network this is given in formula 9 as Pt z Ata k The evaluation function can be regarded as the attractiveness of the network or be havior respectively for a given actor For getting a feeling of what are small and large values is is helpful to note that the evaluation functions are used to compare how attrac tive various different tie changes are and for this purpose random disturbances are added to the values of the evaluation function with standard deviations equal to 1 28 An alternative interpretation is that when actor is making a ministep i e
6. where sim is the mean of all similarity scores which are defined as sim P with A max v u being the observed range of the covariate v this mean is given in the output file just before the initial data description it is also given e g for data set mydata and constant covariate mycov by attr mydata cCovars mycov simMean covariate related similarity x reciprocity simRecipX defined by the sum of cen tered similarity scores for all reciprocal dyads in which 1 is situated net v s364 0 gt 2 527 sim sim covariate related similarity x transitive triplets simXTransTrip defined by the sum of transitive triplets i h gt j i weighted by the centered similarity scores between i and j Jen sigs 1 gt Tij Tin Taj sim sim same covariate which can also be called covariate related identity sameX defined by the number of ties of to all other actors 7 who have exactly the same value on the covariate Sigg 0 D2 xij Hvi vj where the indicator function Tv u is 1 if the condition v v is satisfied j j and 0 if it is not same covariate x reciprocity sameXRecip defined by the number of reciprocated ties between 7 and all other actors j who have exactly the same value on the covariate sigr gt Tijtji Hvi vj 115 68 69 70 71 72 73 T4 T5 76 same covariate x transitive triplets sameXTransTr
7. x fil fi z 2 At z9 z c z ci z9 A z9 z e z e x This shows that the change in creation function plays a role only if a tie is created At x 7 1 and the change in endowment function plays a role only if a tie is dissolved A7 20 z 1 If also elementary effects are included then denote the linear combination for a tie variable z for general evaluation type elementary effects by n a for creation elemen tary effects by cf z and for endowment elementary effects by ef z To the objective function u x x we then still have to add el 7 0 el 0 el yl Ae cala A z z e 2 For behavior dynamics the definitions are analogous Here a basic assumption is that when there is an opportunity for change the possible new values for the behavior variable are the current value this value 1 and this value 1 as long as these changes do not take the value out of the permitted range More elaborate explanations are in Snijders et al 2007 2010b Steglich et al 2010 Veenstra et al 2013 5 2 Important structural effects for network dynamics one mode networks For the structural part of the model for network dynamics for one mode or unipartite networks the most important effects are as follows The mathematical formulae for these and other effects are given in Chapter 12 Here we give a more qualitative description A default model choice could consist of
8. 0 17 0 27 0 83 1 51 2 30 0 83 0 72 016 0 51 1 31 1 82 0 27 1 16 0 48 0 32 2 81 1 26 0 16 1 47 0 67 3 80 2 26 0 83 0 48 1 67 Qu gt WN NI The interpretation is that each row corresponds to a given common behavior of the focal actor s friends comparing the different values in the row shows the relative attractiveness of the different potential values of ego s own behavior The maximum in each row is assumed at the diagonal This means that for each value for the common friends behavior Z the focal actor prefers to have the same behavior as all these friends The differences in the bottom rows are larger than in the top rows indicating that in the case where the friends who do not drink at all the preference or social pressure toward imitating their behavior is less strong than in the case where all the friends drink a lot For the other model the objective function depends on the behavior of the focal actor s friends only as a function of their average behavior Filling in the estimated parameters in 41 yields fil 0 3820 z Z 0 5428 z Z 1 1414 25 2 Z 2 For a given average Z values of 2 s friends this is a quadratic function of zi The following table indicates the behavior evaluation function for z columns as a function of the average drinking behavior of s friends rows Zi V Z 1 2 3 4 5 1 187 1 59 0 22 2 23 5 76 2 0 55 0 32 0 09
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10. 9n while their estimates are denoted i 0 sad ON The package metafor can also be used for meta analysis This package is extensively documented in Viechtbauer 2010 In terms of Viechtbauer 2010 siena08 follows a random effects approach and presents the Hedges estimator which is the procedure of Snij ders and Baerveldt 2003 proposed by Cochran 1954 it also presents the maximum likelihood estimator In Viechtbauer 2005 an extensive study is made comparing the various approaches and it turns out that the comparison is not unequivocal His recom mendation however is to use the restricted maximum likelihood estimator Since this is not implemented in siena08 this recommendation suggests that one should rather use metafor with the option method REML Still another possibility is offered by the package mvmeta Gasparrini et al 2012 This was used in conjunction with SIENA by An 2015 who showed how to use this for incorporating group level explanatory variables using a fixed effects as well as a random effects approach the latter with restricted maximum likelihood 11 2 1 Meta analysis directed at the mean and variance of the parameters In this meta analysis it is assumed that the data sets can be regarded as a sample from a population i e a population of dynamic networks and accordingly the true parameters 0 are a random sample from a population If the number of data sets is small e g less than 20
11. Added a skeleton MCMC routine 2010 02 11 R forge revision 57 Fix to bug in siena01Gui where in conditional estimation the estimated values were not remembered for the next run 2010 02 11 R forge revision 56 RSiena only Multiple network effects constraints between networks 2010 02 11 R forge revision 55 RSienaTest only New silent option for siena07 2010 02 11 R forge revision 54 RSienaTest only Fix to covariate behavior effect bug 2010 02 11 R forge revision 53 Fixed bug in siena01 GUI which ignored changes to all effeccts 2010 02 07 R forge revision 52 RSiena only New silent option for siena07 2010 02 04 R forge revision 51 RSiena only Fix to covariate behavior effect bug Fix to default effects with multiple networks 2010 02 01 R forge revision 49 RSienaTest only Fixes to bugs in constraints 2010 01 28 R forge revision 48 Fix to bug in sorting effects for multiple dependent variables 2010 01 26 R forge revision 47 RSienaTest only New version 1 0 10 Multiple networks Constraints of higher disjoint atLeastOne between pairs of networks 2010 01 19 R forge revision 45 RSiena 46 RSiena Test New documentation for the effects object 2010 01 18 R forge revision 43 RSiena new behavior effects user specified interactions 201 new utilities to update the effects object e 2010 01 15 R forge revision 41 RSienaTest only new effect Popularity Alter and alter
12. Check your version of RSiena The News page of the SIENA website gives information about new versions of RSiena Details of the latest version available can be found at 20 http r forge r project org R group_id 461 The version is identified by a version number e g 1 1 289 and an R Forge revision number You can find both numbers of your current installed version by opening R and typing packageDescription RSiena The version is near the top the revision number near the end Both are also displayed at the start of SIENA output files produced by print01Report Check your version of R When there is a new version or revision of RSiena it will only be available to you automatically if you are running the most recent major version of R You can force an installation if necessary by downloading the tarball or binary and installing from that but it is better to update your R Check both repositories We have two repositories in use for RSiena CRAN and R Forge The latest version will always be available from R Forge Frequent updates are discouraged on CRAN so bug fixes are likely to appear first on R Forge Installation When using the repository at R Forge install the package rather than up dating it Then check the version and revision numbers Users group Consult the archives of the Users Group mentioned above or post a mes sage to the Users Group In your message please tell which operating system which ve
13. Expected R under the restricted model observed R Thus the test statistic has some appealing interpretation in terms of goodness of fit when reciprocated ties do have added value for the firms which means that the reciprocity parameter is not 0 other than the model assumes then the deviation of the observed R from the R that is expected under the model will be large large misfit and so will be the value of the test statistic Large values of the test statistic imply low p values which in turn suggests to abandon the model in favor of models incorporating reciprocity The null distribution of the test statistic c tends as the number of observations in creases to the chi square distribution with degrees of freedom equal to the number of restricted parameters The corresponding p value is given in the output file In the present case one parameter is restricted reciprocity hence there is one degree of freedom d f 1 The value of the test statistic c 3 9982 at one degree of freedom gives p 0 0455 That is it seems that reciprocity should be included into the model and estimated as the other parameters The one sided test statistic which can be regarded as normal variate equals 1 9996 indicating that the value of the transitivity parameter is positive The one step estimates are approximations of the unrestricted estimates that is the estimates that would be obtained if the model were estimated once again but without
14. The information necessary for working with interaction effects the interaction types short names and sequence numbers of the effects are contained in the document produced for a given effects object say myeff by the function call effectsDocumentation myeff Further see the help page for the function effectsDocumentation Chapter 12 of this man ual also gives the short names of all effects The short name of all unspecified interaction effects is unspInt for network effects and behUnspInt for behaviour effects 5 8 1 Interaction effects for network dynamics The following kinds of user defined interactions are possible for network dynamics a Ego effects of actor variables can interact with all effects b Dyadic effects can interact with each other Whether an effect is an ego effect or a dyadic effect is defined by the column interactionType in the effects data frame This column is shown in the list of effects that is displayed in a browser by using the function effectsDocumentation Thus a two way interaction must be between two dyadic effects or between one ego effect and another effect A three way interaction may be between three dyadic effects two dyadic effects and an ego effect or two ego effects and another effect All effects used in interactions must be defined on the same network in the role of dependent variable that for which the unspecified interaction effects is defined And all must be of the sa
15. X ey yoofqo Jo d oy suINyoY T3 u sse o x sse1o sse o Z sourely Jep YH 799U X1 178ur se JOU PU S NIJLU YPM SIOM U IS XTIJBUI Y OJUT x yoofqo ue SULIOJsURIT gt you x xt1yeur se XIIJBUI Se Z syusum31e 19q30 AJro9 ds 09 uorpouny aq uo doy y 998 197 eururoo veds se Yons 1930818 Joyeredos ploy Iy st dos soureu UUIN OD oY surejuoo VJep JO MOI ISIY OY JOyJoYM Suryeorpur JUOWINSIe 7 oyo0nb BOLSO St Jopeoy SMOI pue suumoo Jo JoquINU owes y SALY p nous U qJ Joproy 4 des ayy sooriyetr Aou oe pe jo ases oy UJ eyep oY Sururejuo5 AY AY SI lU yep TIOMU AISTVA 9peoy JUSUIN31e uT Y WOI cure UJEP e S97E99 pue YLULIOJ q e1 ut U e speoy a qeypeol gt Jou 9 9 91qy peo 918 peo T osexped poweu Ae 1qt oy speor euorsy 41e1qH o3exqoed A1e1q1 Arq I p l re3sur useq Apeolye sey oseyoed oy Jt Aress 5 u JOU SI SITI TTeJSUL pue PROTUMOP 03 JURA A eyg Soseyoed oY PUR 9318 IOIITUL Y JAS 09 IND X su do y1 poptaoid are squsum3 e ou J sadexped pegsur 03 pasn ST 9 soseyped Teysut Sosesped 89sUuL T LUISA poses ST BVP oy OTOL aq poys squsumoog ATA O AIOPOIP BSULYIOM y JX9JUO9 SIU UJ JTP 0 AIOPOIIP SUINIOM S S payjes 1rp pmgos Pagas T RUSS TA I0J99 11P SUTYIOM JUSIIMO oY ST TP popraoid st quotun3 e ou JT syon oq N tp AIOPOITIP oY UL SAY oy JO s ureu IY YPM 4o199A Jayoerey e SUMPY 2
16. a single change in his outgoing ties where no change also is an option and z and z are two possible results of this ministep then fnet z f xa is the log odds ratio for choosing between these two alternatives so that the ratio of the probability of z and a as next states is exp fp zs fP a Note that when the current state is x the possibilities for z and z are z itself no change or z with one extra outgoing tie from i or z with one fewer outgoing tie from i Explanations about log odds ratios can be found in texts about logistic regression and loglinear models For dependent behavior variables the interpretation is similar keeping in mind that permitted changes in the behavior variable are 1 0 and 1 as far as these changes do not lead beyond the permitted range 13 1 Networks The evaluation function is a weighted sum of effects s t x Their formulae can be found in Section 12 1 1 These formulae however are defined as a function of the whole network x and in most cases the contribution of a single tie variable x is just a simple component of this formula The contribution to s x of adding the tie i gt h minus the contribution of adding the tie J is the log odds ratio comparing the probabilities of sending a new tie to h versus sending the tie to j if all other effects snet z yields the same values for these two hypothetical new configurations For example su
17. here too the other dependent behavioral variables are centered so that they have overall mean 0 alter s covariate average effect on behavior z avXAlt formerly called AltsAvAlt defined as the product of i s behavior z and 2 s alters covariate average 0 as defined in 14 sbeh z z zi i This is similar to the average alter effect for v z it would reduce to the latter effect 137 42 43 44 45 46 alter s covariate total effect on behavior z totXA1t defined as the product of 7 s behavior z and 1 s alters covariate sum zi 0 as defined in 14 sbeh z z Zi Tip i This is similar to the total alter effect for u z it would reduce to the latter effect in alter s covariate average effect on behavior z avXInAlt defined as the product of i s behavior z and 2 s in alters covariate average 0 as defined in 2 THY vi C44 0 if r4 0 the effect being Shas a z z Bi This is similar to the average in alter effect for u z it would reduce to the latter effect in alter s covariate total effect on behavior z totXInAlt defined as the product of i s behavior z and 1 s alters covariate sum zi 0 as defined in 26 Corea 2 Z upi This is similar to the total in alter effect for u z it would reduce to the latter effect alter s distance two covariate average effect on behavior z avXAltDist2 defi
18. 0 395 0 180 0 032 0 049 0 003 0 130 0 378 0 795 0 117 0 001 0 223 0 037 0 074 0 007 0 062 The diagonal values are the variances i e the squares of the standard errors e g for the reciprocity effect 0 069 is the square of 0 2625 Below the diagonal are the cor relations E g the correlation between the estimated outdegree effect and the estimated reciprocity effect is 0 468 These correlations can be used to see whether there is an im portant degree of collinearity between the effects Collinearity means that several different combinations of parameter values could represent the same data pattern in this case the same values of the network statistics When one or more of the correlations are very close to 1 0 or 1 0 this is a sign of near collinearity This will also lead to large standard errors of those parameters It may then be advisable to omit one of the corresponding effects from the model because it may be redundant given the other strongly correlated effect but see below It is possible that the standard error of the retained effect becomes much smaller by omitting the other effect which can also mean a change of the t test from non significance to significance The suggestion of omitting effects that lead to high parameter correlations with other effect does not directly apply to effects that should be included for other reasons such as the density effect for network dynamics and the linear and quadratic shape
19. 1 the out degree and reciprocity effects 2 one network closure effect e g transitive triplets transitive ties or gwesp the transitive 39 reciprocated triplets effect and or the 3 cycles effect 3 the in degree popularity effect raw or square root version the out degree activity effect raw or square root version and either the in degree activity effect or the out degree popularity effect raw or square root function The two effects 1 are so basic they cannot be left out The effects selected under 2 represent the dynamics in local triadic structure also see Block 2015 for the transitive reciprocated triplets effect and the three effects selected under 3 represent the dynamics in in and out degrees the first for the dispersion of in degrees the second for the dispersion of out degrees and the third for the covariance between in and out degrees and also should offer some protection albeit imperfect for potential ego and alter effects of omitted actor level variables The basic list of these and other effects is as follows 1 The out degree effect which always must be included 2 The reciprocity effect which practically always must be included 3 There is a choice among several network closure effects Usually it will be sufficient to express the tendency to network closure by including one or two of these They can be selected by theoretical considerations and or by their empirical statistical significan
20. 10 11 12 13 5 3 The out degree activity effect with or without sqrt reflects tendencies for actors with high out degrees to send out extra outgoing ties because of their high current out degrees This also leads to dispersion in out degrees of the actors The in in degree assortativity effect where parameter 2 is the same as the sqrt version while parameter 1 is the non sqrt version reflects tendencies for actors with high in degrees to preferably be tied to other actors with high in degrees The in out degree assortativity effect with parameters 2 or 1 in similar roles reflects tendencies for actors with high in degrees to preferably be tied to other actors with high out degrees The out in degree assortativity effect with parameters 2 or 1 in similar roles reflects tendencies for actors with high out degrees to preferably be tied to other actors with high in degrees The out out degree assortativity effect with parameters 2 or 1 in similar roles reflects tendencies for actors with high out degrees to preferably be tied to other actors with high out degrees Important structural effects for network dynamics two mode networks The Stochastic Actor Oriented Model for two mode or bipartite networks is treated in Koskinen and Edling 2012 The co evolution of one mode and two mode networks is treated in Snijders et al 2013 The most important effects are as follows The mathematical formulae fo
21. 6 O Be HEHE salli 3 3 k where m denotes the period from wave m to wave m 1 in the panel data set and am are parameters for the effects interacted with time dummies You can include these in your model simply via the function myeffects lt includeTimeDummy myeffects density reciprocity timeDummy 2 3 6 which would add three time dummy terms to each effect listed in the function We recommend that you start with simple models and base the decision to include time heterogeneous parameters on your theoretical and empirical insight in the data e g whether the different waves cover a period where the importance of some of the modeled mechanisms may have changed and the score type test that is implemented in the siena TimeTest function see Section 8 6 See Lospinoso et al 2011 for a technical presentation and examples of how the test works and Lospinoso 2010 for a walkthrough on model selection 5 10 Limiting the maximum outdegree It is possible to request that all networks simulated have a maximum outdegree less than or equal to some given value This is meaningful only if the observed networks also do not have a larger outdegree than this number for any actor at any wave This is carried out by specifying the maximum allowed value in the MaxDegree param eter of the sienaAlgorithmCreate function which determines the settings of the algorithm MaxDegree is a named vector which means that its element
22. However mostly this is not what is desired and therefore it usually will be preferable to proceed as follows First update the initial values using updateTheta then set the hypothesized value by setEffect and then carry out the estimation and score type test by siena07 The following is an example assuming that an earlier reasonable estimate was found in sienaFit object myansO and the user wishes to use this as starting values myeff lt updateTheta myeff myans0 myeff lt setEffect myeff transTies fix TRUE test TRUE initialValue 0 myansi lt siena07 estimationSettings data mydata effects myeff summary myans1 77 8 3 Example one sided tests two sided tests and one step estimates Suppose that it is desired to test the goodness of fit of the model restricted by the null hypothesis that the reciprocity parameter is zero The following output may be obtained 2 Generalised score test lt c gt 1 eval reciprocity 0 0000 c 3 9982 d f 1 p value 0 0455 one sided normal variate 1 9996 One step estimates 1 constant network rate period 1 6 3840 1 constant network rate period 2 6 4112 eval outdegree density 0 9404 eval reciprocity 1 2567 To understand what test statistic lt c gt is about consider the case where the network is observed at two time points and let R be the number of reciprocated ties at the second time point Then it can be shown that the test statistic is some function of
23. L Pattison P E and Wang P 2009 Closure connectivity and degree distributions Exponential random graph p models for directed social networks Social Networks 31 105 117 205 Schwabe R and Walk H 1996 On a stochastic approximation procedure based on averaging Metrika 44 165 180 Schweinberger M 2012 Statistical modeling of network panel data Goodness of fit British Journal of Statistical and Mathematical Psychology 65 263 281 Schweinberger M and Snijders T A B 2007a Bayesian inference for longitudinal data on social networks and other outcome variables Working Paper Schweinberger M and Snijders T A B 2007b Markov models for digraph panel data Monte Carlo based derivative estimation Computational Statistics and Data Analysis 51 9 4465 4483 Snijders T A B 1996 Stochastic actor oriented dynamic network analysis Journal of Mathematical Sociology 21 149 172 Snijders T A B 2001 The statistical evaluation of social network dynamics In Sobel M E and Becker M P editors Sociological Methodology 2001 volume 31 pages 361 395 Boston and London Basil Blackwell Snijders T A B 2005 Models for longitudinal network data In Carrington P Scott J and Wasserman S editors Models and Methods in Social Network Analysis chapter 11 pages 215 247 New York Cambridge University Press Snijders T A B 2007 Analysing dynamics of non directed social networ
24. LSP dA Jo soo11yeur sreds jo 4st 10 sonyea Jo ferre LOTARTOQ 10 ATUO JOLABUOQ odA XLIJOUI Y SI ARIT YOU SODLIYRUL e 1990 u11p 9 wtp ayyrediq gPOJA9UO o os reds 10 S R IIC s orryeur se poyuosoidal SUOTYLAIOSqO YOM eyou zyau 30u o d jou Jo Aexre ue Sururoj Aq 199 qo x10MJI9U BUAS V 89V amp erre qu pu d Greu rs Aeirejou gu pu d qeu rs yu pu d qeu rs e reuorado opou yore Jo soureu oY YI u YSU YPM 103994 SULIJS Y ST SOUTLU PUR S1OPV 0 siimejop 398 pou oY WLU 04 FUIS JoJORVIVY Y SI DULBNISSIPOL TINN soureu SOPOU IO SIOL JO JOqUINU OY ST U YIOMJOU BUIIS Y UL SIOPV ureN19 S pou s pou oY Se p sn oq ULI YIM Jos opou VUY Y SOJBOIL t u JOSIPONBUIIS JOSopoNeudIS LE pue uomo s UL PUNO oq URI AH oy Jopun uomnseurqs oY UNI 0 MOY UO SEJA Y UHM JIOM 0 YIM WOT UOISSOS Y 9169129 0 JO UOTJBUITISO Opou oY UNI 03 pasn oq 03 159 su do syuouNSie rmb you s oq m gt 510 eu rs myTQeUSIS G E syusum3 1e zmb z you soq SMOPUTAA 103 AUO EUdISY JO UOISIOA uo epuvjs OY 107 ol e3sur Y SVIS morqssur moojregsur I uorjdraos rT s durexri xeqrg oureN 23eIS uormno xr JO I9PIO UL SUOTJYUN Y PUSSY JO ISTI P ALL 171 p nunuoo gueuouornrsodurooSxu rs ut yey UOIIATIDSIP owes oy seu T 0 sypnejop uomndo siroljoe Jo 398 oY Jo ureu 91 SI J2Gepou SUTeUETY uo SIUTTPLAI Jo NSI
25. Solutions Check your data look at the description of the variables given as the output of print01Report Check your model specification 14 2 As result of a score type test including time test Error in solve default v9 Lapack routine dgesv system is exactly singular Error in if cvalue lt 0 cvalue lt 0 missing value where TRUE FALSE needed This can happen as the result of a score test requested in function siena07 or the score test requested in function sienaTimeTest In the first case it indicates that there are linear dependencies in the list of effects estimated and fixed that are used for siena07 If this error message occurs for siena TimeTest it indicates linear dependencies in the list of effects estimated in the siena07 run analyzed by this sienaTimeTest together with the interactions with time dummies tested by sienaTimeTest See Sections 5 9 and 8 2 Solutions For siena07 drop some of the requested score type test retaining only a set of tested effects between which there are no linear dependencies For sienaTimeTest exclude some of the requested time heterogeneity tests by the excludeEffects parameter 14 3 In sienaGOF Error in if attr obsData groupName depvars varName sparse 4 argument is of length zero This can happen directly when calling sienaGOF It indicates that you used a wrong name for groupName or varName See the help file for sienaGOF Solutions Use a correct gro
26. a 2 2i Dj wig ajaj LND al Zy ti Eni Bin a 2 mu and the mean behavior i e 0 if the ratio is 0 0 total average alter effect at distance 2 totAAltDist2 defined by s behavior mul tiplied by the total of the alter averages aa from a tie j gt i if any Stegall g average incoming alter effect at distance 2 avInAltDist2 defined by i s behavior of his alters excluding the contribution multiplied by the average of the incoming alter averages 9 of his alters excluding the contribution from a tie i gt j if any defined by ni Zhj Zh ri gt 0 E 2 Tj Tij a 25 0 if T j Lig 0 cf 24 a 4 De Mag and the mean behavior i e 0 if the ratio is 0 0 135 26 27 28 29 30 31 32 33 34 total incoming alter effect at distance 2 totInAltDist2 defined by i s behavior multiplied by the total of the incoming alter totals of his alters excluding the con tribution from a tie i gt j if any beh i 8196 0 2 zi D1 Tij 2 onzi Thy Zh 24 Dj Tij 4j Tij 2 average total incoming alter effect at distance 2 avTInAltDist2 defined by 1 s behavior multiplied by the average of the incoming alter totals of his alters excluding the contribution from a tie i j if any shh a 2 u Ey aig z zu E a and the mean behavior i e 0 if the ratio is 0 0 total average incoming alter effect at d
27. and especially if this number is less than 10 this assumption is not very attractive from a practical point of view because the sample then would be quite small so the information obtained about the population is very limited The mean and variance in this population of parameters are denoted tg 0 2 _ o var 0 Each of these parameters must have been estimated in a run of siena07 yielding the estimate 0 which is the true parameter plus a statistical error Ej 0 0 Ej The standard error of this estimate is denoted by s For each of the parameters 0 the function siena08 estimates the mean pg and the variance 0 of the distribution of 0 and tests several hypotheses concerning these meta parameters 91 1 Test HO po 02 0 all 0 0 i e effect 0 is nil altogether This is done by means of a chi squared test statistic T with N d f 2 Estimate uo 3 Test HP fg 0 This is done by means of a standard normal test statistic t being the ratio of the estimate for ug to its standard error 4 Test He og 0 i e 0 ug for all j This is done by means of a chi squared test statistic Q with N 1 d f 5 Estimate og Two approaches are followed and presented in the output The first is an iterative weighted least squares method based on Cochran 1954 and Snijders and Baerveldt 2003 The second is a likelihood based method under the assumption of normal distributions the
28. compiled to produce pdf files The file Siena_Algorithms tex contains a lot of details about algorithms used For code developers important files are HowToCommit tex and RSienaDeveloper tex The latter file will guide you to the further documentation The file Siena_Algorithms pdf can also be downloaded from the SIENA website 16 Other tools you need Windows 1 Download and install the appropriate version number depending on which R you are using Rtools exe from http www murdoch sutherland com Rtools I think this is not the right place any more should be down loaded from CRAN 2 Make sure you check the box to amend your path during installation 3 Beware if you later install other programs containing utilities such as tar delphi is one offender you may need to uninstall and reinstall Rtools as you need Rtools at the start of your path 4 Add the path to the file R exe to your path Right click on My Computer icon select Properties Advanced Environment variables Restart your computer to put the new path into effect Mac 1 Make sure the Xcode tools are installed 2 Add the path to the file R exe to your path 159 linux Add the path to the file R exe to your path 17 Building installing and checking the package In a command prompt or terminal window navigate to the directory immediately above the siena source tree Here we assume the source tree is in a directory called RSiena You may have minor diffic
29. covariate average between 1 and all actors j to whom i has a tie sis z 2 Tij sim 8 sim im where the sens scores sim v are defined as 6 sim j A gt while A maxi v v is the observed range of the original covariate v and sim is the mean of all similarity scores as used also for the simX effect this centering is applied since version 1 1 285 For a constant covariate mycov this mean is given by attr mydata cCovars mycov simMean Note that for both ego i and alter j their alters covariate average is used so that this effect is about a comparison between the out neighbourhoods of i and j covariate in alter at distance 2 altInDist2 This is defined as the sum of alters values for the average of the covariate values of all their incoming ties except for the possibly tie from ego Pl i Sigo TA Tij f where dni Zhj Vh 4 E 1 zi gt 0 ol i y ae H Tj Tij 16 0 if Tj Tij 0 total covariate in alter at distance 2 totInDist2 This is defined as the sum of alters values for the total of the covariate values of all their incoming ties except for the possibly incoming tie from ego sost i Sig7 U e big z Z ego in alter distance 2 covariate similarity simEgoInDist2 defined as the sum of centered similarity between and alters covariate in average for all actors 7 to whom i has a tie sme z
30. exploring the relative importance of individual contextual and social factors in network change The second and related point is that like other generalized regression models SIENA does not by itself solve all causal questions When inferring causality from model results one has to face difficulties very similar to those with other statistical methods see e g Lomi et al 2011 and Goldthorpe 2001 In any case causal interpretations should be supported by further results from the discipline the explanations originate in However Stochastic Actor Oriented Models do allow research to profit from a longitudinal design therefore they may be helpful in tackling some issues related to causality like the selection influence problem Steglich et al 2010 Lomi et al 2011 2 1 1 Types of Stochastic Actor Oriented Models evolution of one mode networks two mode networks and behaviors So far we have mostly talked about SIENA as a tool to analyze the evolution of a single network However there are different variants of Stochastic Actor Oriented Models that can be applied to more complex data structures The availability of these options depends on the research question and the quantity and type of data one has In this section we briefly discuss the currently implemented model types which will help researchers determine what kind of analyses they are able to carry out with Stochastic Actor Oriented Models given the data at hand A
31. is as above in effect altDist2 and sim is the mean of all similarity scores as used also for the simX effect this centering is applied since version 1 1 285 For a constant covariate mycov this mean is given by attr mydata cCovars mycov simMean covariate similarity at W distance 2 simDist2W defined as the sum of centered similarity values for alters covariate average between and all actors j to whom i has a tie sigo z Ser simy sim j 128 33 where the similarity scores sim W are defined as A v 67 _ l sim 9W while A maxi v u is the observed range of the original covariate v and sim is as above ego in alter W distance 2 covariate similarity simEgoInDist2W defined as the sum of centered similarity between 2 and alters covariate in average for all actors j to whom 7 has a tie se gt zy sim sim j where the similarity scores sim W are defined as A v sim 0 j A 3 while 6 is as in the definition of altInDist2W A max u v is the observed range of the original covariate u and sim is as above The following is an effect for three networks the dependent network is X the two ex planatory networks are W and Z 34 from W agreement weighted by Z indegrees from w ind defined as the sum of Z indegrees of all actors who have incoming W ties from and from those
32. o cs si y sim 119 where the similarity scores sim 0 are defined as A ju A s sim ij while wo is as in the definition of altInDist2 A max v v is the observed range of the original covariate v and sim is as above see simDist2 Note that for ego i the own value is used and for alter j the alters covariate average these are alter s alters so that this effect is about a comparison between i and the out neighbourhoods of the j s 12 1 2 Multiple network effects An introduction to the analysis of multiple multivariate networks with a discussion of the basic effects is given in Snijders et al 2013 If there are multiple dependent networks the definition of cross network effects is such that always one network has the role of the dependent variable while the other network or networks have the role of explanatory variable s In the following list the network in the role of dependent variable is denoted by the tie variables z while the tie variables wij denote the network that is the explanatory variable Various of these effects are applicable only if the networks X and W satisfy certain conditions of conformability for example the first effect of W on X is meaningful only if W and X have the same dimensions i e either both are one mode networks or both are two mode networks with the same actor set for the second mode as another example the secon
33. sn O SAPASI arp s U 3sT S U 1ST I syu9um3 1e 91mba1 you s90 A10399 11P SUTY IOM 1u 1rro 979 Jo oureU oY SUMIOY payos pagos I uomo unj styg Jo suorydo 1979107 ynoqe UOTFBULIOJUL 393 0 AVM e1OUOS 91 SI SIT losuoo5 Y UI ureunj Aq poMoT OJF in suUIdAY Aq ouop oq ose ued sy ureunj poweu uomnounj oy uo droy oy suo do my 7gtusrs djoy ureunj di u Hoy T uorjdraos T s durexri xeyu g oure N 23eIS 170 v p nunuoo sioqoe JO yas ay JO ureu Y st 39S pou porad y L 10 uum oo uo pue 10398 YORO IO MOI UO YPM SoNTeA DJBLIVAO DUI YPM T Juego reaop ea gt ueo LLVq ueyo qey pea S10O V Jogepou XIIJBUI Y SI JVA OIOM yoolGo JBLIBAO Surgueuo Y SoyRoID xueurse gt wey TRA TRAD IBA IeAOD IVA T suoo reaogoo gt TSUOD sioyoy T oq poys ea Jo UOISUDUIP OT Jos LV suo SIOJ08 OY JO WLU 91 st 39S9pou PUL SINTLA oyzeLIeAOD JO a qey peal x117eur se S1O Y J9gapou 103994 Y ST BA ITIM yoalqo DJBTIVAO YURYSTIOD Y SIJBILL gt suoo TRA TEAC OO IAO 09 OSIMI9YIO ASTV PUI xuryeur sreds ut st e1ep OY Jf HAUL 09 998 st Y1 pue eorso ST osreds NIOMIDU 931 IBATQ Y 1OJ S UTIJS OMY YHA 10199A SI 9 JOS SPOU oY JO ureu I SI JOSIPOU ANOTARUYI erregou 351 si osiedsS Jo oyyrediq 4Nejop pour uo 19YHO SI OAA XII S10 OV 9Sopou RIN
34. the t ratio for convergence for this parameter also is acceptable less than 0 2 preferably less than 0 1 Since normally rate parameters are nuisance parameters i e not of focal interest this can be an acceptable way out 6 3 Some important components of the sienaFit object If a user would like to do further calculations it can be useful to know about the following components of sienaFit objects Suppose the object is called ans Some of the components are the following Further details are in the help file for siena07 ans theta estimates but not for the rate parameter used for conditioning if time dummies were requested using sienaTimeFix these are also in theta ans covtheta covariance matrix of the estimates ans se standard errors of the estimates ans pp number of parameters ans targets targets observed statistics for Method of Moments estimation ans tconv t ratios for convergence for each of the parameters ans tmax maximum absolute value of these ratios for non fixed parameters ans tconv max maximum t ratio for convergence for any linear combination of the parameters called the overall maximum convergence ratio ans sf generated statistics in Phase 3 targets subtracted ans msf covariance matrix of ans sf ans dfra estimated derivative of expected statistics w r t parameters for Methods of Moments estimation ans sims simulated values of dependent variables in Phase 3 of the algorithm 61 for Methods of Moments
35. 0 indicates absence of this tie 2 reciprocity effect recip defined by the number of reciprocated ties sia 1 D Tij Tji 103 transitive triplets effect transTrip defined by the number of h transitive patterns in s relations ordered pairs of actors j h to both of whom is tied while also j is tied to h for directed networks s f x pees Lij Lih Zhj and for non directed networks s x D jch apinata s ae there was an error here until version 3 313 which amounted to a j combining the transitive triplets and transitive mediated triplets effects transitive triplets effect type 1 transTrip1 may also be called transitive closure effect the elementary effect corresponding to creating or maintaining the tie i gt j in the figure above this is transitive closure in the strict sense of the term The effect is s z Zij Xp Tih Thj transitive triplets effect type 2 transTrip2 may also be called h two out star closure effect the elementary effect corresponding to creating or maintaining the tie J in the figure here this could be called structural equivalence for outgoing ties but note that there is also the balance effect which is another o __ gt e implementation of structural equivalence equivalence for outgoing i j ties The effect is s x Lij Xp Tin Zjh transitive mediated triplets effect transMedTrip defined by the number of tran sitive pattern
36. 1 p value lt 0 0001 one sided normal variate 4 8464 One step estimates 1 constant network rate period 1 7 4022 1 constant network rate period 2 6 4681 eval outdegree density 0 4439 eval reciprocity 1 1826 eval transitive triplets 0 1183 79 eval covariate_ij centered 0 4529 eval covariate_i alter 0 1632 eval covariate_i similarity 0 4147 In the example output three parameters are restricted The joint test has test statistic c which has under the null hypothesis a chi squared distribution with d f 3 The p value corresponding to the joint test indicates that the restricted model is not tenable Looking at the separate tests it seems that the misfit is due to all three parameters Thus it is sensible to improve the goodness of fit of the baseline model by including all of these parameters and estimate them 8 4 Alternative application convergence problems An alternative use of the score test statistic is as follows When convergence of the esti mation algorithm is doubtful it is sensible to restrict the model to be estimated Either problematic or non problematic parameters can be kept constant at preliminary esti mates estimated parameters values Though such strategies may be doubtful in at least some cases it may be in other cases the only viable option besides simply abandoning problematic models The test statistic can be exploited as a guide in the process of restricting
37. 98 bipartite networks could not have loops 2010 06 08 R forge revision 98 Fix to bug in constant dyadic covariates with missing values 198 Changes to treament of bipartite networks The processing of these is still under development we need to add the possibility of no change to the ministeps Code to deal with composition change has been added and the treatment of missing values in sparse matrix format networks has been corrected further the change in revision 96 was not quite correct e 2010 06 04 R forge revision 97 RSiena includeTimeDummy not exported so not available to the user e 2010 06 04 R forge revision 96 RSiena bug fixes as in revisions 92 93 Changes and bug fixes to sienaTimeTest etc as in revisions 85 89 includelnteractions now will unInclude too e 2010 06 04 R forge revision 93 RSienaTest only New algorithms function not in package in the examples directory Progress on maximum likelihood code Bug fixes print empty effects object misaligned print sienaFits crash in print sienaEffects with included interactions silent parameter now supresses more Added time dummy field to setEffects and removed from includeEffects includelnteractions now will unInclude too includeTimeDummy now sets or unsets the include flag and prints the changed lines Using composition change with bipartite networks will give an error message until
38. Apply this function and make a histogram mkc lt sapply simusnas max kcores hist mkc Another possibility is to use the extractor functions sparseMatrixExtraction networkEx traction or behaviorExtraction that are also used for sienaGOF 9 2 Conditional and unconditional simulation The distinction between conditional and unconditional simulation is the same for the simu lation as for the estimation option of SIENA described in Section 6 7 1 The choice between conditional and unconditional simulation is made in the sienaAlgorithmCreate function by setting the cond parameter possibly also the condvarno and condname parameters If the conditional option is chosen then the simulations carry on until the desired distance is achieved on the dependent variable used for conditioning For networks the distance is the number of differences in the tie variables for behavioral variables the sum across actors of the absolute differences This is determined as the distance between the consecutive networks or behaviors if such a variable is used for conditioning given in the call of sienaDataCreate The rate parameter for this dependent variable then has no effect If the conditional simulation option was chosen which is the default and the simu lations do not succeed in achieving the condition required by its stopping rule see Sec tion 6 7 1 then the simulation is terminated with an error message saying Unlikely to terminate this e
39. Bootstrap Methods and Their Application Cambridge University Press Oxford Efron B 1987 Better bootstrap confidence intervals Journal of the American Statistical Association 82 397 171 185 Fisher R A 1932 Statistical Methods for Research Workers Oliver amp Boyd 4th edition Gasparrini A Armstrong B and Kenward M G 2012 Multivariate meta analysis for non linear and other multi parameter associations Statistics in Medicine 31 29 3821 3839 Gelman A Carlin J B Stern H S Dunson D B Vehtari A and Rubin D B 2014 Bayesian Data Analysis Chapman amp Hall CRC Boca Raton FL 3d edition Geyer C J and Thompson E A 1992 Constrained Monte Carlo maximum likelihood for dependent data Journal of the Royal Statistical Society Series B 54 657 699 Goldthorpe J H 2001 Causation statistics and sociology European Sociological Review 17 1 20 Greenan C C 2015 Diffusion of innovations in dynamic networks Journal of the Royal Statistical Society Series A 178 147 166 Hauck W W J and Donner A 1977 Wald s test as applied to hypotheses in logit analysis Journal of the American Statistical Association 72 851 853 Hedges L V and Olkin I 1985 Statistical Methods for Meta analysis New York Academic Press Hintze J L and Nelson R D 1998 Violin plots A box plot density trace synergism The American Statistician 52 181 184 Holland P W and Lein
40. For a bipartite network the two dimensions will normally be distinct numbers create empty adjacency matrix adj lt matrix 0 n n put edge values in desired places adjledges 1 2 lt edges 3 Note that this starts with a matrix having all 0 entries and results in a matrix with no 0 entries at all To check the results after doing these two operations the command 25 length which a adj should return the value 0 Note that the basic edge list edges lacks information as to the size of the adjacency matrix tmp above is a sparse matrix which is in edge list format but includes information on the size of the adjacency matrix and can be used in a similar way to the original matrix a while saving memory space 4 1 3 Behavioral data SIENA also allows dependent behavior variables This can be used in studies of the co evolution of networks and behavior as described in Snijders et al 2007 and Steglich et al 2010 These behavior or action variables represent the actors behavior attitudes beliefs etc The difference between dependent behavior variables and changing actor covariates see below is that the latter have values determined by the input data and are assumed to change exogenously i e according to mechanisms not included in the model while the dependent action variables change endogenously i e depending on their own values and on the changing network Unlike the changing individual co
41. GS a wee e q w 2 KlN 23 Using SIENA withit R oon daa aska s a e Se teak S E a Ree se k aa 2 4 Example R scripts for getting started lt s s e s i soom ari o as s W UQ q aq y a 2 5 Steps for looking at results Executing SIENA X o 2 6 Getting help with problems ssa secs w aae g bebe e e s Wg SU a CY II Users manual 3 Steps of modelling 4 Input data dl Date paq uta aa tg a Sh he e da BLA we a od ee 4il Network data e ent eae ee Ad ee Ee ee 4 1 2 Transformation between matrix and edge list formats 4 3 Behavioral data ooo re 44 G2 Ae ee ee eet Wa 41 4 Individual covariates oso 464 4554 2466 8 26 See eee eed 415 Dyadic covariates oa s 24 w won doa e Q w W a a ed ee 4 2 Internal data treatment oops isa eR EE SUQ ee ee 4 2 1 Interactions and dyadic transformations of covariates 422 Centon Q 2 uu Yus da 0 w W e wR EER REE OEE RS 4 2 3 Monotonic dependent variables wa wu s eu s a e w wU a 4 3 Further data specification options ccce s e z q s k a k q s e 4 3 1 Structurally determined values _ aaa aa 4 0 2 Missing data si esed 00 G8 ere be bed QU Q SOMO alus Ee eee 4 3 3 Composition change joiners and leavers o 5 Model specification os ll Definition of the model 4 04 sus 6 poi a ba ee a EOS pad A SLI Elementary elects sonia ee ee ee we Q W UQ SUR WO u WOW E N Bula Speciicati n mm SIENA comas Wad oe a ee ee oe kee es S
42. N a3e1S a3ed snotacid woaz p nurt uoo y lqery 174 ponurguop S 094H9PN 9UL pue uor OVIOJUTIPNIOUL ur se pouy p 918 ZUOTJVIJUL pue Tuor Se1 oqur pue ad y ureu syueumnsie AQL ATAUL 91 syImej p yapa oy opn oxa apn out 09 JULM M I YJ YM uo surpu d p ASTVA 10 ANUL opnput 0197 09 s mepoq n A RIPIUL s 3o 9p oy AJrpour o 19quinu porIsop AU 10 M eA JOTJUL Joyourered yey 9893 09 YSIM A JL ANUL 3893 Jojourvred yey XY 03 YS M om FI HAN L XD Ajddns ued m Payipour aq 0 Ppalisop st Yt eym uo Sur us Guomowa lur iy Tuomnoweas lur Jeao od TJoureug g Xur ureu ANUL epnpur puadag 19y9Ure red o10Z 0 synejop yey onyea 1 S9 lur L opnpout Q on eA erp u pormbol e pue ureN34ous JIPOUI 0 yoyo oy Jo oureu e n e6AI eTyrur ASUL ASTVA 899 910U8 oy oXu yoofqo yp ue ore syusum31e p zmb BAAIN 19H H 908 ASTVA xXy 19y9Uure red sy oye Iepnoryied e jo soq 999 IBUBYI 0 998319JUT gt HAN ureN34ous g Kur 1o prr3 s 99998 v pa3yruuo oq feu Sxue q SUMRI ureu QerIeA JOLABYoq IO IMVU 9JBLIVAO 39 Woo oy Ajryuepr Afeyapduios 09 papasu ateym sy fqo U IS JO 103994 Y SI ZUOTJOVIOJUL poyyTuo oq few syue q SUT IVIT OWVU Q LIGA IOLARTO IO OWIVU DIBLIVAOI 3 9 4909F Jo oy Ajtquept AT 93 duroo 04 p p u a
43. Oriented Models and gives practical information on running RSiena We start with section 2 1 which gives a brief and non technical introduction to the types of Stochastic Actor Oriented Models to the most important concepts related to them to the data required to apply SIENA and to further features of the program In Section 2 2 we explain how to install and run SIENA as the package RSiena from within R Section 2 4 and Section 2 5 provide example R scripts and guidance for understanding the results If you are looking for help with a specific problem read Section 2 6 2 1 The logic of Stochastic Actor Oriented Models SIENA Simulation Investigation for Empirical Network Analysis is a statistical tool de veloped for the analysis of longitudinal network data collected in a network panel study with two or more waves of observations It incorporates different variants of a dynamic network model family the Stochastic Actor Oriented Model SAOM In this section we give a very concise introduction to how these models work in principle and what type of data they are suitable to analyze For sake of simplicity SAOMs implemented in SIENA are often referred to as SIENA models In this subsection we only consider the case of network evolution see below for the more complex cases of coevolution For a further in troduction consult Snijders et al 2010b An introduction for applications in the context of adolescent development is Veenstr
44. Vi Ziy Balter JN Lig Vj Psim gt xij sim sim 35 where the similarity score is f ae dy ee ol ij Ay gt with Ay max v v being the observed range of the covariate v and where sim is the mean of all similarity scores The superscript t is left out of the notation for the parameters in order not to clutter the notation 146 Similarly to how it was done above the contribution to 35 of the tie from i to J represented by the single tie variable x i e the difference between the values of 35 for xj 1 and zij 0 can be calculated from this formula It should be noted that all variables are internally centered by SIENA and that the mean values used for the centering are given near the beginning of the input file More precision can be obtained by requesting the mean attributes of the covariates as explained in Section 4 2 2 This is made explicit in the following by the subtraction of the mean vu The contribution of variable V to the network evaluation function of actor 1 is given by Bego vi v alter u v Psim sim sim a Bego vi v 7 Balter u _ v Psim 1 gt E sim 36 From this equation a table can be made that gives the outcome of 36 for some values of u and vj This can be concretely carried out using the data set s50 which is an excerpt of 50 girls in the data set used in Pearson and Michell 2000 Pearson and West 2003 Steglich e
45. actors j to whom 7 has a tie t sa a D gt aig Y Win Win zn j h For internal effect parameter p 2 the effect is t sta Y wig Y win Win y Zn l j h W is given as interaction1 Z as interaction2 This effect also is available if all or some of X W and Z are the same If X and W are the same this effect is defined as an elementary effect see Section 5 1 1 129 12 1 3 Network creation and endowment functions The network creation function is one way of modeling effects which operate in different strengths for the creation and the dissolution of relations The network creation function is zero for dissolution of ties and is given by G x Y G sia 19 k for creation of ties In this formula the are the parameters for the creation function The potential effects spnet z in this function and their formulae are the same as in the evaluation function except that not all are available as indicated in the preceding subsection For further explication consult Snijders 2001 2005 here the gratification function is used rather than the creation function Snijders et al 2007 and Steglich et al 2010 here only the endowment function is treated and not the creation function but they are similar in an opposite way The network endowment function is another way of modeling effects which operate in different strengths for the creation and the dissolution of relations The network endow ment func
46. and estimating models as small values of the test statistic indicate that the imposed restriction on the parameters is not problematic 8 5 Testing differences between independent groups Sometimes it is interesting to test differences between parameters estimated for indepen dent groups For example for work related support networks analyzed in two different firms one might wish to test whether the tendency to reciprocation of work related sup port as reflected by the reciprocity parameter is equally strong in both firms Such a comparison is meaningful especially if the total model is the same in both groups as control for different other effects would compromise the basis of comparison of the parameters If the parameter estimates in the two networks are Ba and By with standard errors S a and s ep respectively then the difference can be tested with the test statistic Bo A 8 e2 s e which under the null hypothesis of equal parameters has an approximating standard nor mal distribution 5 80 8 6 Testing time heterogeneity in parameters We initially assume that 6 does not vary over time yielding a restricted model Our data contains M observations and we estimate the restricted model the method of moments We wish to test whether the restricted model is misspecified with respect to time heterogeneity Formally define a vector of time dummy terms h m f 1 m wm VV m Z 1 ura 0 elsewhere 6 wher
47. ans sf ans targets or stats lt ans sf rep ans targets each nrow ans sf The tconv components are used in the function siena07ToConvergence presented above 62 6 4 Algorithm The estimation algorithm is an implementation of a procedure of which the original version was proposed by Robbins and Monro 1951 The algorithm is described in Snijders 2001 2005 and in Siena_Algorithms pdf which can be downloaded from the SIENA website It has three phases 1 In phase 1 the parameter vector is held constant at its initial value This phase is for having a first rough estimate of the matrix of derivatives 2 Phase 2 consists of several subphases More subphases means a greater precision The default number of subphases is 4 The parameter values change from run to run reflecting the deviations between generated and observed values of the statis tics The changes in the parameter values are smaller in the later subphases The program searches for parameter values where these deviations average out to 0 This is reflected by what is called the quasi autocorrelations in the output screen These are averages of products of successively generated deviations between gener ated and observed statistics It is a good sign for the convergence of the process when the quasi autocorrelations are negative or positive but close to 0 because this means the generated values are jumping around the observed values When estimating by th
48. are given When these new effects have been added follow the same steps estimate check convergence if this is not yet satisfactory estimate again with the new initial values and interpret the results when converged has been obtained To continue non significant effects may be excluded but it is advised always to retain the out degree and the reciprocity effects and other effects may be included as suggested in Section 5 86 10 1 Model choice For the selection of an appropriate model for a given data set it is best to start with a simple model including e g 2 or 3 effects delete non significant effects and add further effects in groups of 1 to 3 effects Like in regression analysis it is possible that an effect that is non significant in a given model may become significant when other effects are added or deleted When you start working with a new data set it is often helpful first to investigate the main endogenous network effects reciprocity transitivity etc to get an impression of what the network dynamics looks like and later add effects of covariates The most important effects are discussed in Section 5 the effects are defined mathematically in Chapter 12 Approaches to model specification are presented in Chapter 5 and in Snijders et al 2010b When the distribution of the out degrees is fitted poorly which can be inspected using the sienaGOF function of Section 5 11 an improvement usually is possible either
49. being fixed without your having requested this This automatic fixing procedure is used when in phase 1 one of the generated statistics seems to be insensitive to changes in the corresponding parameter This is a sign that there is little information in the data about the precise value of this parameter when considering the neighborhood of the initial parameter values However 69 it is possible that the problem is not in the parameter that is being fixed but is caused by an incorrect starting value of this parameter or one of the other parameters When the warning is given that the program automatically fixed one of the parameter try to find out what is wrong In the first place check that your data were entered correctly and the coding was given correctly and then re specify the model or restart the estimation with other e g 0 parameter values Sometimes starting from different parameter values e g the default values implied by the model option of standard initial values will lead to a good result Sometimes however it works better to delete this effect altogether from the model It is also possible that the parameter does need to be included in the model but its precise value is not well determined Then it is best to give the parameter a large or strongly negative value and indeed require it to be fixed see Section 10 1 6 7 4 Required changes from conditional to unconditional estimation Even though conditional est
50. by including non linear effects of the out degrees in the evaluation function or by other improvements of the model This totally depends on the data set at hand 87 11 Multilevel network analysis For combining SIENA results of several independent networks there are four options Independent networks here means that the sets of actors are disjoint and it may be assumed that there are no direct influences from one network to another The first two options assume that the parameters of the actor based models for the different networks are the same except for the basic rate parameters and for those differences that are explicitly modeled by interactions with dummy variables indicating the different networks All but the second option require that the number of observations is the same for the different networks These methods can be applied for two or more networks In the following discussion the terms networks and sub projects are used inter changeably The four options are 1 Combining the different networks in one large network indicating by structural zeros that ties between the networks are not permitted This is explained in Section 4 3 1 The special effort to be made here is the construction of the data files for the large combined network 2 Combining different sub projects into one multi group project and analyzing this by siena07 The sub projects are the same as the different networks me
51. by outdegree effect on rate xxxxxx infectOut susceptibility to av exp by zzzzzz effect on rate xxxxxx susceptAvCovar infection by zzzzzz effect on rate xxxxxx infectCovar WW gt X cyclic closure of xxxxxx cyWWX WW gt X shared incoming xxxxxx InWWX WW gt X shared outgoing xxxxxx Out WWX xxxxxx alter at distance 2 altDist2 xxxxxx similarity at distance 2 simDist2 transitive triplets xxxxxx similarity simXTrans Trip transitive triplets same xxxxxx sameXTransTrip 189 transitive triplets jumping xxxxxx jumpXTransTrip transitive reciprocated triplets transRecTrip GWESP I gt K gt J gwespFF GWESP I lt K lt J gwespBB GWESP I lt K gt J gwespFB GWESP I gt K lt J gwespBF GWESP I lt gt K lt gt J gwespRR isolate popularity isolatePop in isolate Outdegree inlsDegree network isolate isolateNet outdegreen 1 34 xxxxxx popularity outPoplntn closure jumping yyyyyy jumpWWClosure mixed xxxxxx closure jumping yyyyyy jumpWXClosure cyclic closure of xxxxxx cyClosure shared incoming xxxxxx sharedIn Outdegree popularity effect multiplication by n dropped GWESP effects default parameter changed from 25 to 69 corresponding to a log 2 See earlier in this manual Added to siena07 defined by sienaAlgorithmCreate option Dolby for variance reduc tion Correlations between scores and statistics are reported in output
52. change in truncation from version 1 1 227 to the earlier procedure Added function descriptives sienaGOF with numerical results of plot sienaGOF Minor changes of output in siena table and various reports and in error message for includeEffects Change artificial missing results of siena07 from 999 to NA Added autocorrelations during phase 3 to print summary sienaFit for ML estimation Start of the manual reorganized and partially rewritten with help from Zs fia Boda and Andras V r s instructions for siena01Gui separated in siena01gui pdf e 2013 10 09 R Forge Revision 244 Changes in RSienaTest Repair bug that prevented compilation for Mac e 2013 09 17 R forge revision 243 Changes in RSiena and RSiena Test Correct bug in EffectFactory for isolatePop effect Improved plotting of sienaGOF objects so that observed values outside of the range of simulated values don t run off the chart Improve treatment of structural values in sienaGOF Changes in RSiena Add functions AntilsolateEffect h and AntilsolateEffect cpp which were forgotten to in clude in revision 242 e 2013 08 27 R forge revision 242 Changes in RSiena as well as RSienaTest Correction to Dolby option for the case of more than 2 waves in phasel r and phase3 r scores are added instead of averaged over waves Averaging was wrong because in phase 2 they are added New effects anti isolates anti in isolates and anti in ne
53. covariates and dyadic covariates must be the same for the various sub projects Also their names must be the same The number of actors and the number of waves can be different however These sub projects then are combined into one project where the number of actors is the largest of the number of actors of the sub projects and the number of observations is the sum of the observations of the sub projects This is done by the function sienaGroupCreate which creates a so called sienaGroupEffects object which is a list of sienaEffect objects with some additional information 89 As an example suppose that three projects with names subi sub2 and sub3 are combined Suppose subi has 21 actors and 2 observations sub2 has 35 actors and 4 observations and sub3 has 24 actors with 5 observations Then the combined multi group project has 35 actors and 11 observations The step from observation 2 to 3 switches from sub project sub1 to sub project sub2 while the step from observation 6 to 7 switches from sub project sub2 to sub3 These switching steps do not correspond to simulations of the actor based model because that would not be meaningful The different sub projects are considered to be unrelated except that they have the same model specification the same variable names and the same parameter values It is important to check that this is a reasonable assumption One aspect of this is by looking at the descriptives for change produced by print01Re
54. dependent on z although it might depend on z for other actors j and therefore would not be affected by the outcome of a behavior ministep of actor i Examples are the main effect of an actor attribute but also the average alter effect For such effects when a ministep in behavior occurs the contribution on the probability distribution of the change is as follows a change of z by 1 will decrease the evaluation function by pbens x z and a change by 1 will increase it by the same amount Note that this amount does not depend on the value of z because of the mentioned condition Therefore the log odds ratio of an increase in behavior compared to staying constant that can be attributed to a difference of 1 in the value of the predictor function s a z is equal to a The odds ratio is exp Gbe For example later in this section results are presented where for an analysis of drinking behavior the estimated parameter for average alter is 1 1414 This means that when comparing two individuals who are equal in all respects except that the friends of the first on average are 1 higher on the drinking scale than those of the second individual the odds of increasing drinking behavior compared to no change in the event of a ministep with respect to drinking behavior are exp 1 1414 3 1 times higher for the first individual than for the second The interpretations of total and average similarity are more laborious to explain than th
55. earlier called out degree 1 5 defined by net AN Sa z z Tip y Zi4 endowment effect only likelihood based reciprocal degree related activity effect reciAct defined by the degree of 7 multi plied by 2 s reciprocal degree Sis 2 Ti a gt where the reciprocal degree is defined as above out degree up to c truncated out degree where c is some constant internal effect pa rameter see above there are two implementations here outTrunc and outTrunc2 to enable the simultaneous use of this effect with 2 different internal effect parame ters the effect is defined by sigs a min z note that for c 1 this represents inversely the tendency to be an isolate with respect to outgoing ties i e have out degree equal to 0 min x 1 0 if zi 0 and min zi 1 1 if xi gt 1 Since the representation is inverse a result like a negative coefficient 1 2 for outTrunc internal effect parameter c 1 is interpreted as a positive tendency 1 2 toward outdegrees equal to 0 the standard error is unchanged In the case of c 1 an alternative and more directly comprehensible name is outdegree at least 1 effect 110 36 37 38 39 40 41 42 43 44 square root out degree defined by S 36 z yTi this is left out in later versions of SIENA squared out degree c where c is some constant defined by sit ri 0 where c is chosen
56. effect may be useful e g as a control effect for the average similarity x popu larity alter effect total similarity x popularity alter effect totSimPopAlt defined by the sum of centered similarity scores simf between i and the other actors j to whom he is tied multiplied by their indegrees beh z spo z z gt Z jz j simz sim average similarity x reciprocity x popularity alter effect avSimRecPop defined by the sum of centered similarity scores sim between and the other actors j to whom he is reciprocally tied multiplied by their indegrees 1 sa pls Titr gt Z j2Z jim 4 sim sim and 0 if i 0 total similarity x reciprocity x popularity alter effect totSimRecPop defined by the sum of centered similarity scores sim between and the other actors j to whom he is reciprocally tied multiplied by their indegrees sia z z oy 242 Lj simi sim average alter effect avAlt defined by it s behavior multiplied by the average be havior of his alters a kind of ego alter behavior covariance shes a z X tij z X tiz and the mean behavior i e 0 if the ratio is 0 0 total alter effect totA1t defined by it s behavior multiplied by the sum of behavior of his alters sue o 2 z Xy ti 25 average in alter effect avInAlt defined by s behavior multiplied by the average behavior of his in alters a kind of ego alter behavior covariance si
57. estimation see Section 9 1 if returnDeps TRUE in the call of siena07 ans estMeans estimated expected values of the target statistics if the Dolby option was chosen this is not equal to the average of the simulations ans effects the effects object with only the requested effects Like for any R object the internal structure of the sienaFit object can be requested by requesting sink ans txt str ans sink This writes the structure to the external file ans txt which may be better than printing it to the console because it is a long story A limited representation of the structure of this object is obtained from sink ans txt str ans 1 sink To get some further understanding one could investigate some of the components of this object as follows Note that putting a statement between parentheses like in A lt B is just a way for constructing the object A and showing it at the same time Compute the covariance matrix of the generated statistics print covsf lt cov ans sf This is the same as ans msf provided there are no fixed parameters The means and standard deviations of the generated statistics minus targets v lt colMeans ans sf s lt apply ans sf 2 sd This also allows to compute the convergence t ratios v s To get the generated statistics without subtracting the targets we have to add the targets To do this repeated transposition t can be used stats lt t t
58. estimators are maximum likelihood estimators the associated confidence intervals are based on profile likelihoods and therefore will be asymmetric The reported p values for the population mean hypothesis H are based on the t distribution with N 1 d f In all cases it is possible that some of the data sets j are dropped for some of the parameters because the standard error s is too large see below in that case the number N used here is the number of data sets actually used for the parameter under consideration For both of these two approaches it is assumed that the true deviations 0 0 and the random errors E are uncorrelated This is not always a plausible assumption Fisher s combination mentioned below does not make this assumption The plots of estimates versus standard errors produced by using siena08 and following it up by plot sienaMeta can be used as information about the plausibility of this assumption For testing the hypotheses mentioned here it is also assumed that given the true parameter values 0 the estimates 0 are approximately normally distributed with mean 0 and variance 83 This is often a reasonable assumption The likelihood based methods also assume that the true values 0 are normally dis tributed in the population If this is a reasonable approach the likelihood based methods are preferable A disadvantage of the iterative weighted least squares method is that re sults are possible where the ou
59. file this is a measure for the amount of variance reduction Added to siena07 option diagonalize for having more possibilities for tuning the algo rithm extent of diagonalization of matrix D in Robbins Monro update sienaTimeTest updated now also contains effect wise tests groupwise tests for group objects automatic exclusion of collinear effects and has prettier output and improved summary Overall maximum convergence ratio x tconv max maximum value of t ratio for con vergence for any linear combination added to result of siena07 This is a very severe convergence criterion and not meant as a default criterion to judge convergence in practical cases The print method for objects of class siena created by sienaDataCreate has been ex tended with printing uponly and downly attributes if these are TRUE A bug in the starting values for two mode networks was corrected Small bug fixed in print01Report for reporting of uponly and downonly in the case where this does not affect all periods Changed almost all Rd documentation files sometimes to make them better under standable or complete sometimes to make more appropriate examples sometimes only minor prettifications Updated scripts Rscript01DataFormat R Rscript02VariableFormat R Rscript03SienaRunModel R Rscript04SienaBehaviour R of RSienaDescriptives only the date was changed e 2012 12 24 R forge revision 222 Cha
60. function setEffect The default is that only the out degree density effect is randomly varying but it is advisable to specify this for a larger set of effects Specifying it for too many effects may however lead to unstable estimation The analysis is done by a Bayesian estimation method For the groupwise parame ters normal distributions are assumed with conjugate priors The prior distribution for the basic rate parameters is determined in a data dependent way For the non varying parameters a flat prior is assumed 94 The procedure consists of three parts initialization warming main phase 1 In the initialization phase initial parameter values and the proposal covariance ma trix for Metropolis Hastings steps for groupwise parameters are obtained from first Method of Moments estimation of a parameter vector assumed to be the same across the groups in a multi group estimation with step size initgainGlobal followed by one subphase of the Robbins Monro algorithm for Method of Moments estimates for the groups separately with step size initgainGroupwise The proposal covariance matrices then are scaled in the function improveMH to achieve about 25 out of 100 acceptances of Bayes proposals after single MH steps 2 After initialization and scaling of the proposal covariance matrices a warming phase is done of nwarm Bayesian proposals each with a number of MH steps followed again by the function improveMH 3 Finally nmain r
61. in 43 It should be noted that generally effects can be defined either by the one or the other combination Since our new effect cannot be expressed in a straightforward way by an equation of the type 45 we chose to use the files InverseOutdegreeEffect h and InverseOutdegreeEffect cpp as templates This has a second advantage the outInv effect has an effect parameter which we also need to represent the parameter c in 43 As a first step the files InverseOutdegreeEffect h and InverseOutdegreeEffect cpp were saved under the new names TruncatedOutdegreeEffect h and TruncatedOutdegreeEf fect cpp For the header file TruncatedOutdegreeEffect h all strings inverseoutdegreeeffect were changed into truncatedoutdegreeeffect while retaining the original use of up per and lower case The explanation also was adapted The header file now implies that for the function TruncatedOutdegreeEffect functions are needed of the types calculateContribution endowmentStatistic and egoStatistic This was implemented in the file TruncatedOutdegreeEffect cpp which just was cre ated by renaming InverseOutdegreeEffect cpp First all strings outdegreeactivitysqrt effect were changed into truncatedoutdegreeeffect again retaining the original use of upper and lower case 164 To understand the C syntax keep into account the object oriented nature of C The keyword this is a pointer referring to the object in which the current f
62. in the behavior evaluation function are as follows 15 eval behavior drink linear shape 0 3618 0 1946 16 eval behavior drink quadratic shape 0 0600 0 1181 17 eval behavior drink average similarity 3 9689 2 2053 The dependent behavior variable now is indicated Z In the preceding section the letter V was used but this referred to any actor variable predicting network dynamics irrespective of whether it was also a dependent behavior variable The formulae in Section 12 2 1 show that the evaluation function for this model specification is 1 gt pen Ptrend zi _ z Barink zi z 2 Bav sim T 5 Tij sim sim 40 i J In the second model the table gave the following results 17 eval behavior drink linear shape 0 3820 0 2421 18 eval behavior drink quadratic shape 0 5423 0 2839 19 eval behavior drink average alter 1 1414 0 6737 152 Here the evaluation function is Pek Btrenad zi Z Bdrink zi z Bav alter zi Z Z z gt 41 where 2 is the average Z value of 1 s friends 0 Y Zo Tij Zi i m4 E ij Zj Equation 41 is simpler than equation 40 because 41 is a quadratic function of zi with coefficients depending on the Z values of i s friends as a function of their average whereas 40 depends on the entire distribution of the Z values of s friends Suppose that in model 40 the similarity coefficient Bav sim is positive and compa
63. is a vector of length equal to the number of varying param eters In the object produced by sienaBayes let us call it ans this length is stored as ans p1 For example in a model with 4 waves one dependent network variable and varying parameters specified for outdegree reciprocity transitive ties and similarity for 97 some covariate V the length would be 3 4 7 The prior covariance matrix priorSigma is a symmetric square matrix of dimension equal to the length of priorMu Rate parameters Special attention must be given to the rate parameters Sometimes for small groups and complicated models some of the rate parameters may be estimated in the multi group option by very high numbers This may be the case especially for groups with low Jaccard coefficients or for groups that deviate strongly from the other groups It may be advisable to take out the groups with extremely high rate parameters e g larger than 50 or 80 To try and include some groups with high rate parameters the prior distribution for these parameters may be employed By default the prior for the basic rate parameters is data dependent To try and include some groups with high rate parameters this can be turned off by using priorRatesFromData FALSE Then the choice for priorMu and priorSigma is going to matter Consider the rate parameters as estimated in the multi group analysis of the same data set Suppose the total number of groups is N For each separate rate
64. itself in a probability distribution ML estimation is done by the function siena07 using a set of options created by sienaAlgorithmCreate with maxlike TRUE Bayesian estimation is done by the function sienaBayes The following further information in this section is about ML estimation Bayesian estimation is as yet implemented only for multilevel network modeling group2 Section 11 3 For ML estimation the method of joiners and leavers Section4 3 3 is not available Further R may run into an error the program will hang if there are any actors who are inactive at the first wave as indicated by all structural zeros For ML estimation an important parameter for tuning the algorithm is the so called Multiplication factor given in sienaAlgorithmCreate as the argument mult This deter mines the number of Metropolis Hastings steps taken for simulating each new network The number of steps sometimes called sampling frequency in the literature is the mul tiplication factor multiplied by the sum over dependent variables of the distances between successive waves When this is too low the sequentially simulated networks are too simi lar which will lead to high autocorrelation in the generated statistics This leads to poor performance of the algorithm These autocorrelations are given in the output file When 67 some autocorrelations are more than 0 4 it is good to increase the Multiplication factor When the Multiplication fac
65. long computation times The reason is that likelihood based computa tions are used as distinct from the Method of Moments approach If all individual groups have enough information for good estimation by the Method of Moments according to the intended model the use of siena07 with the default Method of Moments followed by a meta analysis by means of siena08 may be preferable It is advisable to first do a multi group analysis of the same model followed by a sienaTimeTest to get an initial understanding of where problems might occur You may then later use the result for the prevAns parameter of sienaBayes 95 11 3 2 Model specification The extra part of model specification compared to siena07 is that it is required to specify which parameters are randomly varying from group to group and which are fixed across groups The basic rate parameters always are randomly varying Other rate parameters can not yet be included The specification of fixed vs randomly varying is done in the function setEffect There currently is little advice about this The basic issues are the following interest is variability of the effect across groups a primary part of the research question Usually not such research questions about variability are of a quite secondary nature knowledge is there prior knowledge about whether effects differ between groups Usually not It is possible to first do a multi group analysis of the same model follo
66. may be too high to consider the data as an evolving network and perhaps the SIENA method is not suitable for the 19 data set Jaccard values of 3 and higher are good lower than 2 indicates that there might be difficulties in estimation lower than 1 is quite low indeed Using the SIENA method for two waves with an extremely low Jaccard index and average degrees that remain more or less constant will mean that the first wave hardly plays a role in the results and for non conditional estimation it will be close to treating the second wave as a sample from the stationary distribution of the network dynamics If Jaccard indices are low because the network is mainly increasing creation of new ties or decreasing termination of ties this is no problem for the SIENA method 2 When parameters have been estimated first look at the overall maximum convergence ratio and the t statistics for deviations from targets We say that the algorithm has converged if the former is less than 0 25 and the latter all are smaller than 0 1 in absolute value and that it has nearly converged if the former is less than 0 35 and the latter are all smaller than 0 15 Results obtained for non converged estimation runs may be misleading Very small deviations from these values are of course immaterial See Section 6 1 2 3 In rare circumstances when the data set leads to instability of the algorithm the following may be of use The Initial value of the gain
67. o 6 2 What to do if there are convergence problems o oo 6 3 Some important components of the sienaFit object 0 GA Algorith acc p ee be Gee e ss ss Go Outpt as sna ea a rnea E a ae A e Ea EAA E eee Go Convergence check ocs a sue su Su Ye a q w OW US s ue ee A 6 5 2 Parameter values and standard errors _ aa 6 5 3 Colingarity Check a idos sos s soq oh e s suls aa Q U 6 6 Maximum Likelihood and Bayesian estimation 0204 6 7 Other remarks about the estimation algorithm 0 6 7 1 Conditional and unconditional estimation 0 2 FNS Parameters epica mus a wa Ce GOR Ee ee eS 6 7 3 Automatic fixing of parameters e eee 6 7 4 Required changes from conditional to unconditional estimation 6 8 Using multiple processes ae aoa ok ee a Standard errors TAL Moulticolmearity e co Wee eho whee ee bow aa dw A 7 2 Precision of the finite differences method 0 0 000000000 0G Tests Sl Wald type tests u Cu e e est Ua eA DMO be A ees Kua 8 1 1 Standard errors of linear combinations 0005 S2 Score type tests acca aw we ee ee d wO ee a A 8 3 Example one sided tests two sided tests and one step estimates 8 3 1 Multi parameter tests e coeca v e e co kew dae eme es 8 4 Alternative application convergence problems o a 8 5 Testing differences bet
68. of actors at distance two effect expresses network closure inversely stronger network closure when the total number of ties is fixed will lead to 40 fewer geodesic distances equal to 2 When this effect has a negative parameter actors will have a preference for having few others at a geodesic distance of 2 given their out degree which is the number of others at distance 1 this is one of the ways for expressing network closure 4 The three cycles effect which can be regarded as generalized h reciprocity in an exchange interpretation of the network but also as the opposite of hierarchy in a partial order interpreta A tion of the network A negative three cycles effect together with a positive transitive triplets or transitive ties effect may be interpreted as a tendency toward local hierarchy The three cycles effect also contributes to network closure Block 2015 has argued convincingly that instead of the three cycles effect it is often advisable to use the transitive recipro cated triplets effect In a non directed network the three cycles effect is identical to the transitive triplets effect O i j 5 Another triadic effect is the betweenness effect which represents brokerage the tendency for actors to position themselves between not directly connected others i e a preference of for ties i j to those j for which there are many h with h gt i and h j The following eight degree related
69. of right one sided p values and combination of right one sided p values It is advisable to use for each the significance level of a 2 e g 0 025 if a 0 05 which yields an overall combined test at significance level a Note that four different overall results are possible Indicating the right sided and the left sided p values by pr and p respectively these possible results are a Pr gt a 2 pi gt a 2 No evidence for any nonzero parameter values This correlation is defined for the population of networks and if the population does not exist then also the correlation is not defined 93 b Pr lt a 2 py gt a 2 Evidence that some networks have a positive parameter value no evidence for any negative parameter values c Pr gt a 2 pi lt a 2 Evidence that some networks have a negative parameter value no evidence for any positive parameter values d pr lt a 2 pi lt a 2 Evidence that some networks have a negative parameter value and some others have a positive parameter value If all networks have a zero true parameter value i e under the combined null hypothesis that 0 0 for all 7 the probability of result 1 is less than or equal to a this is the way in which this combined test respects the overall probability of an error of the first kind 11 2 3 Contrast between the two kinds of meta analysis To understand the contrast between the method following the Cochran approach for inf
70. parameter for a given wave and for a given dependent variable there then are N estimates some of which may be too high denote the average and the variance of the subset of not too high values by m and s respectively These are specific for the given wave and the given dependent variable These values for mean and variance should represent what one might find plausible values for this rate parameter The corresponding elements of priorMu and diagonal elements of priorSigma should be then set respectively to values close to these m and s As an example suppose there are N 20 groups 3 waves and one dependent variable a network and 5 varying parameters in addition to the rate parameters Then p1 2 5 7 Suppose that plausible values for the first rate parameter would be centered about 4 and for the second about 5 in both cases with a standard deviation of 1 4 corresponding to a variance of about 2 One could use the following piece of code m7 lt c 4 5 O O O O 0 S7 lt matrix 0 7 7 diag S7 lt c 2 2 1 1 1 1 1 ans lt sienaBayes priorMu m7 priorSigma S7 priorDf 20 priorRatesFromData FALSE priorDf is the prior degrees of freedom for the covariance matrix It can be interpreted as the sample size on which hypothetically the prior knowledge about the covariance matrix of the parameters is based By choosing it as suggested here equal to the number of groups the prior will have a non
71. restricting the reciprocity parameter The one step estimate of reciprocity 1 2567 hints that this parameter is positive which agrees with the one sided test 78 8 3 1 Multi parameter tests In the case where K gt 1 model parameters are restricted SIENA evaluates the test statistic with K degrees of freedom A low p value of the joint test would indicate that the goodness of fit of the model is intolerable However the joint test with K degrees of freedom gives no clue as to what parameters should be included into the model the poor goodness of fit could be due to only one of the K restricted parameters it could be due to two of the K restricted parameters or due to all of them Hence SIENA carries out in addition to the joint test with K degrees of freedom additional tests with one degree of freedom that test the single parameters one by one The goodness of fit table is as follows 02 Generalised score test lt c gt Testing the goodness of fit of the model restricted by 1 eval covariate_ij centered 0 0000 2 eval covariate_i alter 0 0000 3 eval covariate_i similarity 0 0000 c 92 5111 d f 3 p value lt 0 0001 1 tested separately two sided c 62 5964 d f 1 p value lt 0 0001 one sided normal variate 7 9118 2 tested separately two sided c 16 3001 d f 1 p value lt 0 0001 one sided normal variate 4 0373 3 tested separately two sided c 23 4879 d f
72. the parameter random in function setEffect 88 The first and second options will yield nearly the same results with the differences depend ing on the basic rate and perhaps other parameters that are allowed to differ between the different networks and of course also depending on the randomness of the estima tion algorithm The second option is more natural given the design of SIENA and will normally run faster than the first Therefore the second option seems preferable to the first The third option makes much less assumptions because parameters are not constrained at all across the different networks The fourth option is a middle ground between the first two and the third Therefore the arguments usual in statistical modeling apply as far as assumptions is concerned options 3 and 4 are safer but if the assumptions are satisfied or if they are a good approximation then options 1 and 2 have higher power and are simpler Option 3 requires that each of the different network data sets is informative enough to lead to well converged estimates this will not always be the case for small data sets and then option 4 may be preferable When the data sets for the different networks are not too small individually then a middle ground might be found in the following way Start with option 3 This will show for which parameters there are important differences between the networks Next follow option 2 with interactions be
73. the distinction between evaluation and endowment ef fects The formulae of the effects that can be included in the behavioral endowment function eb h are the same as those given for the behavioral evaluation function However they enter calculation of the endowment function only when the actor considers decreasing his behavioral score by one unit downward steps not when upward steps or no change are considered For more details consult Snijders et al 2007 and Steglich et al 2010 141 The statistics reported as dec beh decrease in behavior are the sums of the changes in actor dependent values for only those actors who decreased in behavior More precisely it is M 1 n gt gt I zi ta i lt zi ta sic 2 tm sie 2 tm 1 33 m 1 i 1 where M is the number of observations x t is the observed situation at observation m and the indicator function A is 0 if event A is true and 0 if it is untrue 12 2 4 Behavioral rate function The behavioral rate function AP consists of a constant term per period beh beh A Pm for m 1 M 1 which can be called the basic rate multiplied potentially by the following further effects 1 The dependence on the position of the actor can be modeled as a function of the actor s out degree outRate in degree inRate and number of reciprocated re lations recipRate the reciprocated degrees These can be defined by Ti gt Tij Thi gt L
74. the other actors j to whom he is tied sbeh y z gt Vij sim sim indegree effect indeg ss a 4 yu miu outdegree effect outdeg ay 1 2 eas isolate effect isolate the differential attractiveness of the behavior for isolates seh a z at x44 0 where again J A denotes the indicator function of the condition A average similarity x reciprocity effect avSimRecip defined by the sum of centered similarity scores sim between and the other actors j to whom he is reciprocally tied S sg a z Er gt 227 simi sim and 0 if Li r 0 total similarity x reciprocity effect totSimRecip defined by the sum of centered similarity scores sim between 7 and the other actors j to whom he is reciprocally tied aaa gt 25525 simi sim average similarity x popularity alter effect avSimPopAlt defined by the sum of centered similarity scores sim between i and the other actors j to whom he is tied multiplied by their indegrees sito 2 z ta gt Z jz sim sim and 0 if zi 0 AA 13Tf this behavior variable is the only dependent variable then this is not necessary But this seldom happens 133 11 12 13 14 15 16 17 18 19 popularity alter effect popAlt defined by the average in degrees of the other ac tors j to whom 7 is tied SAT z 2 zi 8 Dj Tila and 0 if zi O this
75. the presence of ties 13 Table 1 Possible tie change patterns for two observations t and t2 ti to i j i j creation of a tie i j i j maintenance of a tie i j i j termination of a tie i j i j maintenance of a no tie regardless of whether they were newly created or maintained evaluation These are the three possible values of the change in tie variables constituting the dependent variables of the network evolution model The effects model the odds more precisely they are com ponents of the linear predictor for the log odds for the creation maintenance or presence of network ties Table 2 helps to imagine what the odds refer to in each case we compare the probability of green cases to that of blue cases Table 2 Tie changes considered by the evaluation creation and endowment functions a evaluation b creation c endowment tH ta According to this distinction network evolution may be modeled in SIENA by three functions the evaluation creation and endowment functions Effects can appear as com ponents of one or two of these functions in a single model but never in all three this would lead to perfect collinearity Using only the evaluation effect assumes that the cre ation and endowment effects are equal and equal to the evaluation effect The estimated parameters for each effect should be interpreted as log odds ratios From a practical point of view it is meaningful to start mo
76. the score type test of Section 8 2 See the script RscriptSienaMultiple R on the SIENA webpage for an example 74 Multi parameter Wald tests Now suppose that we wish to test another null hypothesis which can be represented as a linear constraint on 60 Ho A0 0 where A is ar x p matrix the dimension of 0 being p For example if p 5 for testing Ho 02 93 we would use the matrix A 0 1 1 0 0 while for testing Ho 02 63 0 if p 5 we would use the matrix A varon Then the function Wald RSiena can be used to produce the Wald type test the chi squared value of the test statistic the number of degrees of freedom and the p value As an example for the first two waves of the klas12b data the following results were obtained collected in the sienaFit object ans Estimate Standard t statistic Error Rate parameters 0 Rate parameter 10 4625 1 8917 1 eval outdegree density 1 8760 0 1883 0 0173 2 eval reciprocity 1 1405 0 3397 0 0430 3 eval transitive triplets 0 3703 0 0639 0 0425 4 eval 3 cycles 0 3373 0 1238 0 0020 5 eval primary 0 6718 0 2125 0 0619 6 eval sex alter 0 1390 0 2011 0 0545 7 eval sex ego 0 3165 0 1938 0 0055 8 eval sex similarity 0 8197 0 2126 0 0298 The output of summary ans also contains the covariance matrix of the estimates Covariance matrix of estimates correlations below diagonal 0 035 0 030 0 009 0 011 0 009 0 004 0 003
77. values of the variables are not centered but the means are subtracted during the program calculations Thus dyadic covariates are treated internally by the program differently than individual covariates in the sense that the mean is subtracted at a different moment 28 but the effect is the same except for multi group projects see below Unlike the covariate similarity effect the same covariate effect is not centered but keeps its 0 1 values For the multi group option section 11 1 dyadic covariates are treated differently from individual covariates for dyadic covariates in multi group projects centering is done by the within group mean actor covariates in multi group projects are centered by the overall mean For dependent behavioral variables the effects are defined in Section 12 2 as functions of centered variables The means of covariates are stored as attributes on the object created by SienaData Create If you wish to access them the following steps can show where these means can be found For example suppose that the command given was mydata lt sienaDataCreate friendship smokel alcohol The structure of this object is obtained by requesting str mydata 1 Looking at the response you will see that this object contains among other things 1 the constant actor covariates as mydata cCovars 2 the varying actor covariates as mydata vCovars 3 the constant dyadic covariates as mydata dycCovars 4 the var
78. with time dummies Fix bug where print from siena08 was not produced if a previous display to the screen had occurred New parameter in siena08 to control number of iterations RSienaTest only added validation to updateTheta e 2011 08 08 RSienaTest only R forge revision 168 9 More work on maximum likelihood When using finite difference derivative estimation or maxmimum likelihood estimation return of derivatives by wave is optional controlled by parameter byWave to siena07 Format of derivatives by wave has altered sienaTimeTest will be incompatible with older objects which used finite differences or maximum likelihood New function updateTheta to copy theta values from a fit to an effects object Time dummies in siena07 are created before the initial values are updated from any prevAns so values may be copied to time dummies also Amended headings in print and summary for siena fit objects New function bayes is now fully available with a help page and no need to use RSiena when calling it e 2011 08 03 R forge revision 167 Fix another display of manual in siena01Gui Added network names to relevant behavior effects if there is more than one network Altered names of interaction effects to remove duplicate network names Renamed avSimX totSimX avAltX to avSimEgoX totSimEgoX avAltEgoX Trapped error caused by omitting Actors node set when specifying others e 2011 07 27 R forge revision 164 Include quadra
79. 0 018 0 470 0 115 0 009 0 031 0 003 0 009 0 002 0 006 0 767 0 432 0 004 0 006 0 003 0 001 0 000 0 005 0 475 0 731 0 761 0 015 0 005 0 001 0 001 0 005 0 218 0 044 0 246 0 180 0 045 0 004 0 003 0 011 0 096 0 132 0 067 0 058 0 090 0 040 0 017 0 002 0 092 0 029 0 017 0 037 0 079 0 437 0 038 0 009 0 442 0 076 0 369 0 172 0 234 0 054 0 208 0 045 75 To test the null hypothesis that the three sex effects ego alter similarity are zero the matrix A is constructed as follows and the Wald test then is requested A lt matrix 0 3 8 A 1 6 lt 1 A 2 7 lt 1 A 3 8 lt 1 Wald RSiena A ans The result is chisquare d pvalue 16 556 3 000 0 000872 The value p lt 0 001 expresses strong evidence that the network dynamics depends on sex The Wald test is frequently applied to test the null hypothesis that several parameters are 0 The extra work to define the matrix A above can be automated by using the following function Multipar RSiena The test of the preceding example is then produced by the command Multipar RSiena ans 6 7 8 8 1 1 Standard errors of linear combinations Sometimes there can be interest in a linear combination of parameters Suppose this is for a sienaFit object called ans The number of parameters is ans pp which is the same as length ans theta This is the number of estimated parameters excepting if any the rate parameters used for conditioning in conditional estimat
80. 059 6 eval number of actors at distance 2 1 0011 0 2275 7 eval drink alter 0 1041 0 1348 8 eval drink squared alter 0 0141 0 1329 9 eval drink ego 0 0078 0 1157 10 eval drink ego x drink alter 0 1655 0 1095 11 eval drug use alter 0 2603 0 2436 12 eval drug use squared alter 0 0249 0 1945 13 eval drug use ego 0 0214 0 1454 14 eval drug use ego x drug use alter 0 1976 0 1146 Behavior Dynamics 15 rate rate drink period 1 1 3218 0 3632 16 rate rate drink period 2 1 7884 0 5053 17 eval behavior drink linear shape 0 3820 0 2421 18 eval behavior drink quadratic shape 0 5423 0 2839 19 eval behavior drink average alter 1 1414 0 6737 For this specification the formulae in Section 12 1 1 imply that the components in the network evaluation function corresponding to the effects of variable V are Bego v 0 Ti Balter gt Tij vj v Bsq alter gt Tij v 0 Bexa gt Tij v 0 uj U j j J The contribution of the single tie variable z to this formula is equal to Bego vi b Batter 0 B Bsq alter Vj D Bexa vi D vj D 38 Filling in the estimates for the effects of drinking behavior yields 0 0078 v 5 0 1041 v 0 0 0141 u 0 0 1655 v 5 u D This can be represented in R as follows First define a function that incorporates the relevant part of the evaluation function dependen
81. 1 22 3 61 3 2 96 0 95 0 04 0 20 1 46 4 5 37 2 22 0 16 0 81 0 70 5 7 78 3 49 0 29 1 82 2 85 We see that even though the squared function does not necessarily draw the actors to ward the average of their friends behavior for these parameters the highest values of the behavior evaluation function are obtained indeed when the focal actor i behaves just like the average of his friends The values far away from the maximum contrast in this case more strongly than in the case of the model with the average similarity effect but neither of these models fits clearly better than the other These tables present only the contribution of some of the terms of the objective func tion and the behavior dynamics will of course be compounded if the objective function contains more effects Another way to look at the behavior evaluation function is to consider the location of its maximum This function here can be written also as fo 0 3820 1 1414 Z Z zi Z 0 5428 z 2 154 Differentiating with respect to z shows that this function is maximal for _ 0 38820 1 1414 Z Z GOs Aes we 2 x 0 5428 s a just a little bit larger than Z Indeed in the table we see that if Za has integer values 1 2 3 4 or 5 the highest values are obtained exactly for zi 24 155 14 Error messages This chapter contains some error messages with their explanations Currently it is not very extensive n
82. 1Type 1 is not used for non directed networks 2 Forcing model mode1Type 2 one actor takes the initiative and unilaterally imposes that a tie is created or dis solved 3 Unilateral initiative and reciprocal confirmation modelType 3 one actor takes the initiative and proposes a new tie or dissolves an existing tie if the actor proposes a new tie the other has to confirm otherwise the tie is not created for dissolution confirmation is not required 4 Pairwise disjunctive forcing model modelType 4 a pair of actors is chosen and reconsider whether a tie will exist between them the tie will exist if at least one of them chooses for the tie it will not exist if both do not want it 5 Pairwise conjunctive model modelType 5 a pair of actors is chosen and reconsider whether a tie will exist between them the tie will exist if both agree it will not exist if at least one does not choose for it 6 Pairwise compensatory additive model modelType 6 a pair of actors is chosen and reconsider whether a tie will exist between them this is based on the sum of their objective functions for the existence of this tie In the first two of these models where the initiative is one sided the rate function is comparable to the rate function in directed models In the last three models however the pair of actors is chosen at a rate which is the product of the rate functions A and for the two actors This means that opport
83. 2 1 Network 6yolition ssa Sus ow yuy s hehe abe ee Cee a de ee Ree OS 102 1211 Network evaluation Tunetion 24 26 4 a be ee a a s Qua Oa 103 12 1 2 Multiple network effects cs e sus a k k s 4 eee ate w eee 120 12 1 3 Network creation and endowment functions s 130 12 14 Network rate function sa s oew s ddu s s e 3 k bee AA 131 12 2 Behavioral evoliitia opos te sZ RR eA wR Re Ua S p eee a 132 12 2 1 Behavioral evaluation function o e 132 172 22 Behavioral creation TUNGOR e e o c e a a a s g uq usu m eu us sua s U 141 12 2 3 Behavioral endowment function e 141 12 2 4 Behavioral rate function o ao s G ua 24 4 ce S s w ee Boe Ree ee eS 142 13 Parameter interpretation 144 151 Networks 214564424444 4446448 8 Geen bu ee Pee bb bien dG 144 13 2 BEMOL 2864 44 44 RPA Oe REESE Dae eR ee ee e SS a A 145 13 3 Ego alter selection tables 2 2 a s s sanan s a cakare es n as snn a 146 13 4 Ego alter influence tables osa ca s sa s g a w e ap hoa ee a w Q 152 14 Error messages 156 14 1 Daring estimation e eee ae eR eo ea a Ee ee ew Se a N 156 14 2 As result of a score type test including time test 00 157 iS Usenet ice la Bawa ab aod Gok aa A Roe Gb Gok 4 eed oe ee BS 157 III Programmers manual 159 15 Get the source code 159 16 Other tools you need 159 17 Building installing and checking the package 160 18 Understa
84. 4 extended to non directed one mode networks for directed one mode networks this is sharedPop Effect jumpXTransTrip ported to non directed networks gwesp effects modified and ported to nondirected networks Also take account of behavior user specified interactions in includelnteraction and set Effect Correction Effect to is not a dyadic effect Manual added paragraph about how to import results from xtable and siena table into MS Word sienaGOF added the name of the sienaFit object as attribute sienaFitName to each of the sienaGofTest objects 185 Correction in sparseNetworkExtraction to avoid errors occurring when the extracted network has no edges In the help page for sienaGOF auxiliary geodesic distances changed to non directed which avoids a further error when the extracted network has no edges Correction of an error in print siena for data sets including other types than oneMode Changed bandwidth selector for violin plots in plot sienaGOF to nrd to avoid long violins in cases where all simulations have the same outcome Changes in RSienaTest Further work on SienaBayes Changes in RSiena Ported effects outRateLog and outTrunc2 from RSienaTest e 2013 12 04 R Forge Revision 250 Changes in RSiena and RSiena Test New option centered in coCovar and varCovar setEffect updateTheta and prevAns in siena07 now also work properly for user specified in
85. A is a program for the statistical analysis of repeated measures of social networks and requires at the very least network data collected at two or more time points It is also possible to include other types of variables in the models these are discussed in Section 4 1 Section 4 2 describes the most commonly occuring data transformations that are done internally by SIENA Finally Section 4 3 shows further options for users to define their data 4 1 Data types As we discussed in Section 2 1 2 dependent variables in Stochastic Actor Oriented Models are defined from network or behavioral data Independent variables effects are defined from individual or dyadic covariate data which can be constant or varying SIENA requires each of these data types to have a specific format this is presented in the current section In general data specification in RSiena consists of two steps First the role of each variable to be used must be defined using the functions sienaDependent coCovar varCo var coDyadCovar varDyadCovar or sienaCompositionChange Second the variables must be combined into one RSiena data set by the function sienaDataCreate This func tion puts together the data set and carries out some preliminary calculations It is advisable to use names of variables consisting of at most 12 characters This is because they are used as parts of the names of effects which can be included in the model and the effect names
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89. LI Mathematical specication l aoee e i ho gema a SUQ a 5 2 Important structural effects for network dynamics One mode e networks o 5 a v a sa sikek a q hee AA 5 3 Important structural effects for network dynamics two mode networks 6 v lt scoa s waw ee a e a eee QU QUQ Q w aa 10 11 15 16 16 19 19 20 22 22 23 23 23 25 26 26 27 28 28 28 30 30 30 32 33 5 4 Effects for network dynamics associated with covariates 5 5 Cross network effects for dynamics of multiple networks 5 6 Effects on behavior evolution o a o s a ioe arame siarada g aa i 5 7 Model Type non directed networks 1 1 ee ee 5 8 Additional interaction effects a a sa sa ae se eee ee ee 5 8 1 Interaction effects for network dynamics o 5 8 2 Interaction effects for behavior dynamics o 5 9 Time heterogeneity in model parameters o e o 5 10 Limiting the maximum outdegree eee 5 11 Goodness of fit with auxiliary statistics o oe aos coe socit ps s a e e w 5 11 1 Treatment of missing data and structural values in sienaGOF Estimation 6 1 The estimation function sienaQ7 lt GLI Initial Values ss os cd 4 weed Oho ro A EEE 6 1 2 Convergence Check 4 04 04 G ead bea AA Ba PE RR A 6 1 3 Continued estimation to obtain convergence o o
90. Manual for RSiena Ruth M Ripley Tom A B Snijders Zs fia Boda Andras V r s Paulina Preciado University of Oxford Department of Statistics Nuffield College September 10 2015 Abstract SIENA for Simulation Investigation for Empirical Network Analysis is a computer pro gram that carries out the statistical estimation of models for the evolution of social networks according to the dynamic actor oriented model of Snijders 2001 2005 Snijders et al 2007 and Snijders et al 2010a This is the manual for RSiena a contributed package to the statistical system R It complements but does not replace the help pages for the RSiena functions It also contains contributions written earlier for the manual for SIENA version 3 by Mark Huisman Michael Schweinberger and Christian Steglich This manual is frequently updated mostly only in a minor way This version was renewed for RSiena version 1 1 289 Contents 1 General information I Minimal Intro LI Giving TESTER ar a GR dhe le ee Pe Gee UQ ee ee eee oe 2 Getting started with SIENA 2 1 The logic of Stochastic Actor Oriented Models o oo 2 1 1 Types of Stochastic Actor Oriented Models o oo 2 1 2 Data variables and effetti oe a 24 442 s S q MA Qua un u A ee 3 W 2 1 3 Outline of estimation procedure 0 000022 e eee 2 1 4 Further useful options in RSiena o e e 22 Installing R and SIENA 2 oes aca a re
91. MaxDegree specification Correction of printing errors arising when result of score type test is NA maxRatio checked for NA or NaN in phase2 r Siena_algorithms4 tex renamed Siena_algorithms tex this document now is made available as a pdf file at the SIENA website 183 Some improvement of error messages for sienaTimeTest p value for goodness of fit sienaGOF rounded to 3 decimal places File effects pdf dropped from inst doc it can be created by effectsDocumentation Changes in RSienaTest sienaBayes new parameters nImproveMH and priorRatesFromData these give the possibility to truncate initial rate parameters depending on prior glueBayes corrected so that it can be applied sequentially multipleBayesTest now allows matrix parameter to test linear combinations Improved plot multipleBayesTest to show truncation at 0 2014 07 08 Revision 278 Changes in RSiena and RSienaTest Added s50s to data set Corrected se component of sienaFit objects should be standard error was its square new effects totDist2 altInDist2 totInDist2 totDist2W altInDist2W totInDist2w Some warnings for calculations of z regrCor and z regrCoef avoided in siena07 print01Report errors corrected and slightly improved for descriptives for changing dyadic covariates and for upOnly downOnly cases Changes in RSienaTest sienaBayes Internally multiplied the data depend
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93. R forge revision 78 fix minor bugs in reports allow character input to effect utility functions include effect1 3 etc on display of included effects in siena01Gui 2010 04 12 R forge revision 77 RSiena only As for RSienaTest revision 76 Report of 0 missings corrected display of effect1l effect3 in siena01Gui allow entry of character strings or not in includeEffects etc 2010 04 12 R forge revision 76 RSienaTest only Various bug fixes Memory problems when calculating derivatives with many iterations and parameters Occasional effects not being included correctly due to trailing blanks Some minor details of reports corrected 2010 03 31 R forge revision 75 fixed bug with dyadic covariates and bipartite networks 2010 03 27 R forge revision 71 RSienaTest only Fixes as for RSiena in revision 68 69 70 for RSiena New version number 1 0 12 2010 03 27 R forge revision 70 RSiena only Fix to crash at end of phase 3 with multiple processes and conditional estimation Correct carry forward backward use mode for behavior variables Fix bug causing crash in Finite Differences with only one effect 2010 03 24 R forge revision 69 RSiena only New features and bug fixes as for revision 63 in RSienaTest 4 cycles effect has new shortName cycle4 some percentages on reports were proportions not percentages Sped up treatment of missing values in sparse format networks Fix now
94. RSiena only e 2010 09 20 R forge revision 120 Bug fixes Multiple groups with 2 dyadic covariates had incorrect names Multiple processes failed RSiena only Minor print format corrections Bug in calculation of starting values for behavior variables RSienaTest only e 2010 08 20 R forge revision 117 RSienaTest only Documentation updates algorithms may work again e 2010 08 20 R forge revision 116 forgotten part of change for print of sienaF it RSiena only e 2010 08 20 R forge revision 115 fixed bug in siena08 p values on report and minor correc tions to layout of print of sienaFit e 2010 07 19 R forge revision 114 fix a bug in initial report names of multiple behavior variables were incorrect e 2010 07 10 R forge revision 113 fix bugs 1 endowment effect unless using finite differences failed 197 2 could not return bipartite simulations 2010 07 04 R forge revision 112 fix bug in groups with constant dyadic covariates and only 2 waves Introduced in revision 109 2010 07 03 R forge revision 111 bipartite networks now have a no change option at each ministep of simulation 2010 06 25 R forge revision 110 updated manual pages for dyadic covariates 2010 06 25 R forge revision 109 Dyadic covariates may have missing values and sparse input format Removed some inappropriate dyadic covariate effects for bipartite networks Score test output now available via summary on a f
95. a et al 2013 The defining characteristic of Stochastic Actor Oriented Models is their actor oriented nature which means that they model change from the perspective of the actors nodes That is Stochastic Actor Oriented Models always imagine network evolution as indi vidual actors creating maintaining or terminating ties to other actors When thinking about network dynamics researchers usually assume that these decisions conscious or subconscious of actors are influenced by the structure of the network itself and the char acteristics and behaviors of the focal actor ego who is making a decision and those of other actors in the network alters Stochastic Actor Oriented Models provide a means to quantify the ways the extent and the uncertainty with which these factors are associated with network evolution between observations The Stochastic Actor Oriented Modelcan be regarded as an agent based actor based simulation model of the network evolution where all network changes are decomposed into very small steps so called ministeps in which one actor creates or terminates one outgoing tie These ministeps are probabilistic and made sequentially The transition from the observation at one wave to the next is done by means of normally a large number of ministeps The actors respond to the network in the sense that the probabilities of these changes depend on the current unobserved state of the network Each further mini
96. a special orientation like the 2PU two paths up effect for k 2 for directed ERGMs proposed in Robins et al 2009 Therefore the statistic is called the e number of 2 2PU configurations Y IN e i h for two mode networks and for non directed networks the number of four cycles with shortName cycle4 for the two mode and cycle4ND for the non directed case net E si z al different Vij Vik Uhj Thk 5 for parameter p 2 the square root is taken note that this is like the sharedPop effect above but for the two mode and non directed cases the directionality plays no role transitive ties effect transTies earlier called direct and indirect ties effect defined by the number of actors to whom 7 is directly as well as indirectly tied a j Tij MAXp Lin Zhj betweenness count between Sit3 Dj n Uni Tij 1 Zhj balance balance defined by the similarity between the outgoing ties of actor 7 and the outgoing ties of the other actors 7 to whom 7 is tied n n sala D zy Y bo z zjx j nei where bo is a constant included to reduce the correlation between this effect and the density effect defined by M 1 n n 1 a M 1 n n 1 n 2 3 gt y Zin tm Z h tm m 1ij 1 h 1 h i j 105 15 16 17 18 This may also be regarded as structural equivalence with respect to outgoing ties In SIENA versions be
97. a threshold of 0 25 is used for the overall maximum convergence ratio and a threshold of 0 1 for the absolute value of the t statistics for deviations from targets the estimation must be repeated Standard errors for the parameters are also estimated in this phase If the estimation has to be repeated this can be done by employing the argu ment prevAns in the call of siena07 See the help page for siena07 15 2 1 4 Further useful options in RSiena e Checking for time heterogeneity Sections 5 9 and 8 6 e Goodness of fit Section 5 11 e Meta analysis of SIENA results Section 11 2 e Simulation without estimation Section 9 2 2 Installing R and SIENA This and the next section give an overview of steps one needs to go through from installing R to running models in RSiena Installing needs to be done only once but should be repeated when next versions of the software appear 1 Install R This can be done from http cran r project org Many users prefer some kind of additional environment such as RStudio or the combination of Notepad with NppToR 2 Install the package RSiena or RSienaTest with dependencies The other packages used are tcltk parallel and tools all included in the basic R distribution Matrix MASS lattice codetools recommended packages included in most R distributions and network and xtable For goodness of fit testing it will be useful also to install sna and igraph You can just ins
98. aTest New defaults for siena07 in sienaAlgorithmCreate doubleAveraging 0 diagonal ize 0 2 for MoM Improved one step approximations to expected Mahalanobis distances in sienaGOF control variates for score function Permit 3 way interactions with one ego and two dyadic effects initializeFRAN r this was erroneously not allowed New effects Jin Jout JinMix JoutMix altXOutAct doubleInPop doubleOutAct print01Report now reports in degrees also for two mode networks Better error handling for siena Time Test and score Test inOutAss is dyadic Corrected effectName and functionName of inPopIntn outPopIntn inActIntn and outActIntn in and out were missing Check for positive derivative matrix at the end of phase 1 non positive estimated derivatives lead to repeating a prolonged phase 1 omitted for effects with fixed pa rameters Changes in RSiena New effects homXOutAct FFDeg BBDeg RFDeg diffXTransTrip ported from RSiena Test sameXInPop and diffXInPop also added for two mode networks but they are not dyadic In names of behavior effects and statistics dropped the redundant parts behavior and beh Changes in RSienaTest New function extract sienaBayes sienaBayes options diagonalize 0 2 doubleAveraging 0 for estimation of initial models in initialization phase save initial results in case of divergence duri
99. al networks and individual academic performance Social Science Research 40 1506 1520 Lospinoso J A 2010 Testing and modeling time heterogeneity in longitudinal studies of social networks A tutorial in RSiena In progress Lospinoso J A 2012 Statistical Models for Social Network Dynamics PhD thesis University of Oxford U K Lospinoso J A Schweinberger M Snijders T A B and Ripley R M 2011 Assess ing and accounting for time heterogeneity in stochastic actor oriented models Advances in Data Analysis and Computation 5 147 176 Pearson M A and Michell L 2000 Smoke rings Social network analysis of friendship groups smoking and drug taking Drugs Education Prevention and Policy 7 1 21 37 Pearson M A and West P 2003 Drifting smoke rings Social network analysis and Markov processes in a longitudinal study of friendship groups and risk taking Connec tions 25 2 59 76 Rao C R 1947 Large sample tests of statistical hypothesis concerning several pa rameters with applications to problems of estimation Proceedings of the Cambridge Philosophical Society 44 50 57 Robbins H and Monro S 1951 A stochastic approximation method Annals of Math ematical Statistics 22 3 400 407 Robins G L and Alexander M 2004 Small worlds among interlocking directors network structure and distance in bipartite graphs Computational amp Mathematical Organization Theory 10 69 94 Robins G
100. alk 1996 Kushner and Yin 2003 which can be more efficient Try doubleAveraging 0 which starts using this step from phase 2 1 e diagonalize This parameter may range from 0 to 1 and determines the extent to which the matrix of derivatives of expected values with respect to parameters is diagonalized The value 1 the default gives greatest stability smaller values may give greater efficiency Very small values less than 0 2 may lead to an unstable algorithm Advice try values such as 0 7 0 5 or even 0 2 if the algorithm becomes unstable reduce firstg e g to 0 005 or 0 001 but if this does not help the value used for diagonalize is too small e n2start This is the minimum length of phase 2 1 i e the first subphase of phase 2 The default value is 2 52 x p 7 where p is the number of estimated parameters The minimum lengths of the subsequent subphases are 2 52 x n2start for sub phase k This implies the total duration of the algorithm will be roughly proportional to n2start One may try using a value higher than the default 58 e firstg This determines the step sizes in the estimation algorithm If the algorithm is unstable use a smaller value but greater than 0 If convergence is not very good even with repeated estimation with the prevAns option sometimes it can be useful to try and use updateTheta to copy the results from the earlier estimation rather than prevAns this will use the same starting values b
101. allows more than one value to indicate missing in covariates 2010 03 12 R forge revision 68 new version number for RSiena In siena01Gui allow waves for SienaNet inputs to be numbered arbitrarily rather than in sisting on 1 n Change simply allows this the actual wave numbers are not yet used on reports etc 2010 03 17 R forge revision 66 Corrected processing of user specified interaction effects with multiple processes This had originally worked but failed when one no longer had to include the underlying effects 200 2010 03 16 R forge revision 64 covarBipartite ego effect had been given type dyadic rather than ego 2010 03 16 R forge revision 63 RSienaTest only new functions siena08 and iwlsm for meta analysis can now use different processes for each wave Not recommended usually slower than by iteration but will be useful with ML routines when they are completed No longer crashes with missing dyadic covariates 2010 02 27 R forge revision 61 RSiena only bug fix random numbers used with multiple processes were the same in each run Now seed is generated from the usual R random number seed Also fixed a display bug if running phase 3 with few iterations 2010 02 16 R forge revision 60 RSienaTest only added average indegrees to reports Also constraints 2010 02 12 R forge revision 59 RSienaTest only Fix to bugs in printing version numbers and in using multiple processes would revert to RSiena package
102. ally determined values can be different for the different time points The diagonal of the data matrix for a one mode network always is composed of structural zeros but this does not have to be indicated in the data matrix by special codes The correct definition of the structurally determined values can be checked from the brief report of this in the output file of print01Report If there are a lot of structurally determined values then unconditional estimation see Section 6 7 1 is preferable Structural zeros offer the possibility of analyzing several networks simultaneously under the assumption that the parameters are identical However a preferable option to do this is given in Section 11 E g if there are three networks with 12 20 and 15 actors respectively then these can be integrated into one network of 12 20 15 47 actors by specifying that ties between actors in different networks are structurally impossible This means that the three adjacency matrices are combined in one 47 x 47 data matrix with values 10 for all entries that refer to the tie from an actor in one network to an actor in a different network In other words the adjacency matrices will be composed of three diagonal blocks and the off diagonal blocks will have all entries equal to 10 In this example the number of actors per network 12 to 20 is rather small to obtain good parameter estimates but if the additional assumption of identical parameter values for t
103. analyses technically because estimation will be less stable substantively because the assumption of non informative missingness often is not quite justified Up to 10 missing data will usually not give many difficulties or distortions provided missingness is indeed non informative Huisman and Steglich 2008 When one has more than 20 missing data on any variable however one may expect problems in getting good estimates In the current implementation of SIENA missing data are treated in a simple way trying to minimize their influence on the estimation results The basic idea is the following A brief sketch of the procedure is that missing values are imputed to allow meaningful simulations for the calculation of the target statistics in the Method of Moments tie variables and actor variables with missings are not used More in detail the procedure is as follows The simulations are carried out over all variables as if they were complete To enable this missing data are imputed In the initial observation missing entries in the adjacency matrix are set to 0 i e it is assumed that there is no tie this is done because normally data are sparse so no tie almost always is the modal value of the tie variable In the further observations for any variable if there is an earlier observed value of this variable then the last observed value is used to impute the current value the last observation carry forward option cf Lepkow
104. aning that covariate multiple network effects did not appear if the co variates was a behavior variable 196 Can now run sienaTimeTest on fits from finite differences and maximum likelihood User defined interactions and time dummies can be expanded when printing the effects object use parameter expandDummies TRUE e 2010 11 25 R forge revision 126 Changed version of RSiena to be 1 0 12 and copied all new features which were only in RSienaTest to RSiena RSiena and RSienaTest are functionally the same at this time New version of sienaTimeTest and sienaTimeFix Bayesian routine experimental can be used with multiple dependent variables e 2010 11 05 R forge revision 125 Corrected bug in report from siena07 about detailing network types Networks appear in data object before behavior variables regardless of order of sub mission to sienaDataCreate RSienaTest only new effect in structural equivalence RSienaTest only new models for symmetric networks bug fixed to sienaTimeTest non included underlying effects for user defined interac tions multiple dependent networks and multiple groups e 2010 10 22 R forge revision 124 Fixed bug in sienaTimeTest when only one effect Removed standalone siena01Gui Still available within R e 2010 10 09 R forge revision 122 Distance two effects added parameter Bug in calculation of starting values for behavior variables
105. ant in most cases 0 these constant values define the null hypothesis being tested This can be obtained in RSiena by appropriate choices in the effects dataframe Parameters can be restricted by putting TRUE in the fix and test columns and the tested value in the initialValue column The function setEffect is available to do this For example a score test for the evaluation effect of transitive ties in a network can be requested as follows myeff lt setEffect myeff transTies fix TRUE test TRUE initialValue 0 0 The score type test then proceeds by simply estimating the restricted model not the unrestricted model with unrestricted parameters by the standard SIENA estimation algorithm The result of the score type test is presented in the summary of the estimation results the sienaFit object obtained from siena07 and also in the output file The t ratios for convergence can be disregarded for the parameters that are fixed and estimated by the score test as convergence is not an issue for these parameters It should be noted that using the prevAns option in siena07 overrides the initial values in the effects object so that using siena07 for an effects object with fix TRUE for some of the effects jointly with the prevAns option will lead to score type tests of hypothesized values as given by the prevAns option Since the presentation of the results includes the hypothesized value there is no reason for doubt as to what has been done
106. ape effect is pZ and for the effect of Z on itself or quadratic shape effect is pe I then the contributions of these two effects are jointly Bf z z P 2 2 With a negative coefficient 8 this is a unimodal preference function with the maximum attained for z Z 2 62 82 Of course additional effects will lead to a different picture but as long as the additional effects are linear in z which is not the case for similarity effects this will change the location of the maximum but not the unimodal shape of the function This can also be regarded as negative feedback or a self correcting mechanism when z increases the further push toward higher values of z will become smaller and when z decreases the further push toward lower values of z will become smaller On the other hand when the coefficient Be is positive the feedback will be positive so that changes in z are self reinforcing This can be an indication of addictive behavior The average similarity effect expressing the preference of actors to being similar with respect to Z to their alters where the total influence of the alters is the same regardless of the number of alters The total similarity effect expressing the preference of actors to being similar to their alters where the total influence of the alters is proportional to the number of alters The average alter effect expressing that actors whose alters have a higher average val
107. ar isolates Effect inIsolatePop dropped it was shortlived Improved printing of results of siena07 in the case simOnly Prettier response printed to console for includeEffects and setEffect z estMeans added to sienaFit objects z vector of estimated expected values of statis tics this is colMeans z sf z targets but if dolby the regression on the scores is subtracted e 2013 08 23 R forge revision 241 Changes in RSiena as well as RSienaTest 187 Corrected bug leading to error message that occurred if there was only one option for choice of alter It appeared mainly in cases where all changes were upward only or downward only in practice it only was observed yet for two mode networks with upward changes only Drop the unintended multiplication of the target statistic for the inPop effect by n Trapped some execution errors mainly associated with inversion of singular matrices and allowed the functions to end properly with a warning message Added various degree related effects to bipartite networks New effect inIsolatePop e 2013 08 08 R forge revision 240 Changes in RSienaTest Added the parameter reduceg to siena07 Changes in RSiena and RSienaTest Added effects crprod and inPopIntn for two mode networks e 2013 06 18 R forge revision 232 Changes in RSiena The possibility to use the obsolete packages snow and rlecuyer for R versions older than 2 14 0 was dropped their functionality was replac
108. b3 lt 0 8994 Define the value of v for which the table is to be given vv lt c 1 2 3 4 5 And calculate the table sel_tab lt outer vv vv obj_n It can be displayed sel_tab and if package xtable is loaded also be written to a latex or html file For example tab_sel lt xtable sel_tab print tab_sel file tab_sel htm type html html table attributes rules none The html table attributes option gives the lt table gt tag used in the html file The results can be tabulated as follows 148 U Uj 1 2 3 4 5 1 0 10 0 03 0 17 0 30 0 44 2 0 13 0 18 0 05 0 09 0 22 3 0 37 0 05 0 26 013 0 01 4 5 0 60 0 29 0 03 0 34 0 21 0 84 0 52 0 21 0 11 0 42 This table shows the preference for similar alters in all rows the highest value is at the diagonal v vi The ego and alter parameters are close to 0 therefore the similarity effect is dominant However note that the formula uses raw values for v and vj but divides the values for the absolute difference v u by Ay which here is 5 1 4 Therefore the weight of 0 09 for the alter effect is not completely negligible compared to the weight of 0 90 for the similarity effect The positive alter effect leads to a preference for ties to alters with a high v value which goes against the similarity effect for v 1 but strengthens the similarity effect for v 5 The table shows that the net resulting pr
109. beh z z v gt Vij sim sim 55 interaction of ego tie sender variable with average alter avA1tEgoX beh ss z z vi zih X wig 24 9 215 and the mean behavior i e 0 if the ratio is 0 0 56 interaction of alter tie receiver variable with average similarity avSimA1tX so 2 z 1 2i4 DO viz vj simz sim and the mean behavior i e 0 if xj 0 57 interaction of alter tie receiver variable with total similarity totSimA1tX PO as gt Tij uj simz sim 58 interaction of alter tie receiver variable with average alter avA1tA1tX sim 0 2 2i Xy tij u 23 2 zig and the mean behavior i e 0 if the ratio is 0 0 User defined interaction effects The user defined interaction effects of Section 5 8 2 are defined as follows Suppose we consider two effects s x z and sbeh z z Then their interaction effect is defined by 1 siaz sex 2 e2 2 140 For three effects speh z z sbeh z z and sbeh z z the interaction effect is defined by 1 beh beh beh beh Sifaxbxc 2 2 Sia x z s 1 2 Sie 5 2 30 2 The division by z or z respectively is necessary to offset the fact that all behavior effects of interactionType OK contain a factor z and further do not depend on z For example the interaction between two main effects effFrom of actor covariates v1 and v9 is the same as the main effect of the product variabl
110. bjects of class matrix 17 2 3 10 11 All missing data should be set to NA see Section 4 3 2 Check whether your data objects meet the following criteria a Each object contains the same nodes actors b Nodes are in the same order in each object c Nodes are in the same order in rows and columns of matrix objects in case of one mode networks If a two mode network is studied then of course there will be two node sets Create SIENA objects for each data object using the appropriate functions see Sec tion 4 1 a sienaDependent for networks and behavior variables b only for two mode networks sienaNodeSet for defining nodesets c coCovar and varCovar for constant and changing varying individual covari ates respectively d coDyadCovar and varDyadCovar for constant and changing varying dyadic covariates respectively e In case of two mode networks for each object it should be specified which nodeset it is defined on using the nodeSets argument in the above functions Create a SIENA data object containing all the SIENA objects specified above using the function sienaDataCreate see Section 4 1 Use getEffects to create an effects object This already gives a very simple model specification containing the outdegree and a reciprocity effects see Section 5 2 for two mode networks see Section 5 3 Use sienaAlgorithmCreate to create an algorithm object se
111. by the sum of the covariate over the actors to whom 7 is tied indirectly at a geodesic distance of 2 sist x gt aij max Lin Bpj V The following group of effects uses an auxiliary variable 0 which can be called alters v average It is described as the average value of vp for those h to whom j is tied and defined mathematically by gt ATGhUh y EL fej oO vj Tj 14 Since v is centered the value of 0 in case zj 0 is also the mean value of the original variable It may be noted that this constructed variable will not itself have exactly a zero mean generally Note that this value is being updated during the simulations Network changes will change if vj is a dependent behavior variable then behaviour changes will also change Uj In the following list there is no ego effect because the ego effect of would be the same as the alter effect of u 82 covariate alter at distance 2 altDist2 This effect is associated with an effect parameter which can have values 1 or 2 For parameter 1 it is defined as the sum of alters covariate average over all actors to whom 7 has a tie sigo z gt L550 parameter 1 j 117 83 84 For parameter 2 it is defined similarly but for an alters covariate average excluding ego sigo z gt ry parameter 2 j where Tinh co _ 2 TINH Lap Hae gt 0 15 j CA ji 15 0 if Lip Tji 0 To compute the con
112. calculated from the observed data Conditioning is possible for each of the dependent variables network or behavior where conditional means conditional on the observed number of changes on this dependent variable 68 Conditioning on the network variable means running simulations until the number of different entries between the initially observed network of this period and the simulated network is equal to the number of entries in the adjacency matrix that differ between the initially and the finally observed networks of this period Conditioning on a behavioral variable means running simulations until the sum of ab solute score differences on the behavioral variable between the initially observed behavior of this period and the simulated behavior is equal to the sum of absolute score differences between the initially and the finally observed behavior of this period Conditional estimation is slightly more stable and efficient because the correspond ing rate parameters are not estimated by the Robbins Monro algorithm so this method decreases the number of parameters estimated by this algorithm The choice between unconditional and the different types of conditional estimation is made in the sienaAlgorithmCreate function by setting the cond parameter For data specifications with multiple dependent variables at most one dependent variable can be used for conditioning This choice is made dependent on the condvarno and condname pa
113. ce Some researchers may find the last effect distances two less appealing because it expresses network closure inversely a The transitive triplets effect which is the classical rep h resentation of network closure by the number of tran sitive triplets For this effect the contribution of the tie i j is proportional to the total number of tran sitive triplets that it forms which can be transitive triplets of the type i gt j gt h i gt h as well as i gt h j i gt j e i J The balance effect which may also be called structural equivalence with respect to outgoing ties This expresses a preference of actors to have ties to those other actors who have a similar set of outgoing ties as themselves Whereas the transitive triplets effect focuses on how many same choices are made by ego the focal actor and alter the other actor the number of h for which i h and j h i e Zip Zin 1 where 7 is ego and j is alter the balance effect considers in addition how many the same non choices are made Tih Lin 0 The transitive ties effect is similar to the transitive triplets effect but instead of considering for each other actor 7 how many two paths i h j there are it is only considered whether there is at least one such indirect connection Thus one indirect tie suffices for the network embeddedness The gwesp effect see later in this manual The number
114. ckage for the R statistical system which can be downloaded from http cran r project org For the operation of R the reader is referred to the corresponding literature and help pages RSiena was originally programmed by Ruth Ripley and Krists Boitmanis in collab oration with Tom Snijders Since May 2012 the maintainer is Tom Snijders Further contributions were made by Josh Lospinoso Charlotte Greenan Christian Steglich Jo han Koskinen Mark Ortmann Nynke Niezink and Robert Hellpap In addition to the official R distribution of RSiena there is an additional distribution at R Forge which is a central platform for the development of R packages offering facilities for source code management It is quite usual that later versions of RSiena are available at http r forge r project org R group_id 461 before being incorporated into the R package that can be downloaded from CRAN In addition at R Forge there is a package RSienaTest which may include additional options that are still in the testing stage Some of the options described in this manual may apply to RSienaTest only with the plan to transfer this to RSiena in the future This program was first presented at the International Conference for Computer Simulation and the Social Sciences Cortona Italy September 1997 which originally was scheduled to be held in Siena See Snijders and van Duijn 1997 We are grateful to NIH National Institutes of Health USA for their fund
115. cludeInteraction myeff quad avAlt name drinkingbeh interactioni c friendship define a model with the average alter effect representing social influence and an interac tion between this and the quadratic shape effect Recall that the latter can be regarded as the effect of drinking behavior on drinking behavior Briefly the interaction is between current drinking behavior and the average drinking behavior of friends By consulting Section 12 2 1 on the mathematical definitions of the effects one can derive that this leads to the following objective function where it is assumed that also the linear and quadratic shape effects are included in the model pen uj Vis Z beh 2 Dj Tij 2 j FP a z Pads LA PA i y mE Taj In addition there are predefined interactions available between actor variables and influence as described in Section 12 2 1 The value is OK for the effects of which the formula as defined in Section 12 2 1 is given by z multiplied by something not dependent on zi 50 5 9 Time heterogeneity in model parameters When working with two or more periods i e three or more waves there is the question whether parameters are constant across the periods This can be tested by the sienaTime Test function as explained in Section 8 6 To specify a model with time heterogeneous parameters the function includeTimeDummy can be used as follows Consider the refor mulation of the evaluation function into
116. covariate alter a positive parameter will imply the tendency that the in degrees of actors with higher values on this covariate increase more rapidly the effect of the squared variable on the actor s popularity to other actors squared covariate alter included only if the range of the variable is at least 2 This normally makes sense only if the covariate alter effect itself also is included in the model A negative parameter implies a unimodal preference function with respect to alters values on this covariate the interaction between the value of the covariate of ego and of the other actor covariate ego x covariate alter a positive effect here means just like a positive similarity effect that actors with a higher value on the covariate will prefer ties to others who likewise have a relatively high value when used together with the alter effect of the squared variable this effect is quite analogous to 43 the similarity effect and for dichotomous covariates in models where the ego and alter effects are also included it even is equivalent to the similarity effect although expressed differently and then the squared alter effect is superfluous 6 the same covariate or covariate identity effect which expresses the tendency of the actors to be tied to others with exactly the same value on the covariate whereas the preceding four effects are appropriate for interval scaled covari ates and mostly also for or
117. ctors at distance 2 0 9947 0 2173 7 eval drink alter 0 0899 0 1184 8 eval drink ego 0 0100 0 1087 9 eval drink similarity 0 8994 0 5864 10 eval drug use alter 0 1295 0 1282 11 eval drug use ego 0 1362 0 1253 12 eval drug use similarity 0 6650 0 3381 147 Behavior Dynamics 13 rate rate drink period 1 1 3376 0 3708 14 rate rate drink period 2 1 8323 0 4546 15 eval behavior drink linear shape 0 3618 0 1946 16 eval behavior drink quadratic shape 0 0600 0 1181 17 eval behavior drink average similarity 3 9689 2 2053 We interpret here the parameter estimates for the effects of drinking behavior and drug use without being concerned with the significance or lack thereof For the drinking behavior formula 36 yields vi vs 0 0100 v 0 0 0899 v 0 0 8994 1 0 6983 V In R the following code can be used to construct the selection table Note that the function outer here is very convenient First define a function that incorporates the relevant part of the evaluation function dependent on the parameters bl b2 b3 the overall average v_av the similarity average sim_av and the range ran_v obj_n lt function vi vj bi vi v_av b2 vj v_av b3 1 abs vi vj ran_v sim_av Now fill in the values of the parameter estimates and the averages v_av lt 3 113 sim_av lt 0 6983 ranv lt 4 bi lt 0 0100 b2 lt 0 0899
118. d e endowment or maintenance function The endowment function which also may be called maintenance function also distinguishes between new and old network ties when evaluating possible network changes and between increasing or decreasing behavioral scores when evaluating possible behavioral changes It is a component of the probabilities of change only for changes in a downward direction maintenance vs termination of existing ties decrease of values of the behavior dependent variable Again endowment effects can be the maintenance parts of an evaluation effect or elementary effects see below In the interpretation using satisfaction the endowment function models the loss in satisfaction incurred when network ties are dissolved or behavioral scores are decreased hence the label endowment Leaving aside the rate effects a given effect can normally be included in the model in any of the three types or roles of evaluation creation or endowment effect In almost all cases the advice is to start modeling without any creation or endowment effects and add them perhaps at a later stage For example if the network dynamics in a given data set is such that ties mainly are created and they are dissolved rather rarely then the data will contain little information about the question whether creating ties follows different rules than dissolving ties and if one would try to include creation or endowment effects for eff
119. d effect of incoming W on X is applicable only if W and X are one mode networks These conditions are hopefully clear from logical considerations and drawing a little diagram of the involved nodes and arrows will be helpful in cases of doubt In the SIENA output for projects with multiple networks the dependent network in each given effect is indicated by the first part of the effect name In the list below a more or less normally formulated name is given first then the name used in SIENA between parentheses using X as the name for the dependent network and W as the name for the explanatory network then between parentheses in typewriter font the shortName as used by RSiena Since this is a co evolution model SIENA will include also the effects where the roles of X and W are reversed The first three effects are dyadic The first can be regarded as a main effect the reciprocity and mutuality effects will require rather big data sets to be empirically distin guished from each other 1 Effect of W on X X W crprod sii z gt Tij Wij i j leads to 13 j 2 Effect of incoming W on X X reciprocity with W crprodRecip Sin z D Tij Wji this can be regarded as generalized exchange j W i leads to i g 120 3 Effect of mutual ties in W on X X mutuality with W crprodMutual 533 0 D Tij Wij Wji Y i leads to i j The following six are degree related effects where nodal degrees in the W network
120. d the network In the explanation the dyadic co variate is regarded as a weighted network which will be reduced to a non weighted network if w j only assumes the values 0 and 1 By way of exception the dyadic covariate is not centered in these three effects to make it better interpretable as a network In the text and the pictures an arrow with the letter W represents a tie according to the weighted network W WW gt X closure of covariate WWX net h sisa z D Vij Wih Whj gt this refers to the closure of W W two paths each W W two path 7 wn j is weighted by the product winwpj and w w the sum of these product weights measures the strength of the gt EN lt 2 J tendency toward closure of these W W twopaths by a tie i Since the dyadic covariates are represented by square arrays and not by edgelists this and the following effects will be relatively time consuming if the number of nodes is large mized cyclic WW gt X closure X cyclic closure of W cyWWX h Oo sisa z Bees Tij Wjh Whi this refers to the cyclic closure of W W two paths weighted W W if the dyadic covariate W does not only have 0 and 1 values ee m ee e the contribution of the tie i gt j is proportional to the number X j i W l of product of weights of W W two paths j h Ei i incoming shared WW X X incoming shared W InWWX sist z ith Zij Whi Whj x this refers to shared incoming W ti
121. d to have constant values from one observa tion moment to the next If observation moments for the network are t1 t2 tm then the changing covariates should refer to the M 1 moments t through tyy_ and the m th value of the changing covariates is assumed to be valid for the period from moment tm to moment tm 1 The value at tm the last moment does not play a role Changing covariates as independent variables are meaningful only if there are 3 or more observa 26 tion moments because for 2 observation moments the distinction between constant and changing covariates is not meaningful Each changing individual covariate must be specified in a separate call of varCovar using for input an nx M 1 matrix where the columns correspond to the M 1 periods between observations The mean is always subtracted from the covariates See Section 4 2 2 on centering When an actor covariate is constant within waves i e within each wave it has the same value for all actors or more generally when within each wave it has the same value for all actors within components separated by structural zeros which means that ties between such components are not allowed then only the ego effect of the actor covariate is made available This is because the other effects then are meaningless This may cause problems for combining several data sets in a multi group project see Section 11 If at least one case is missing i e has the missing val
122. dditional work on the goodness of fit functionality see sienaGOF 2011 02 21 R forge revision 136 Fixed bug in bipartite network processing Diagonal up to number of senders was being zeroed siena01Gui corrected test for maximum degree in display 2011 02 05 R forge revision 134 Enhanced features and minor bug fixes in siena08 report in revision 133 in RSiena Test Bug fix in iwlsm sienaDataCreateFromSession sienaTimeTest improved error messages ML support for bipartite networks still work in progress particularly for missing data 2011 01 17 R forge revision 131 2 RSienaTest only New goodness of fit functions work in progress 2011 01 16 R forge revision 130 Fix bug for bipartite networks which usually crashed but could have given incorrect answers Fix bug with multiple processes and sienaTimeTest Default value of siena07 argument initC is now TRUE 2011 01 08 R forge revision 129 fix to sienaTimeF ix for time dummies on covariate effects etc Suppressed warning message when loading snow package 2010 12 02 R forge revision 128 Corrections to scores for symmetric pairwise models ML now runs with missing data Not yet sure it is correct New multiple network effects To altDist2W simDist2W Can now use setEffects to update basic rate initial values multiplication factor for ML now a parameter in sienaModelCreate Fixed bug me
123. deling with evaluation effects unless one has a clear idea about how tie creation and endowment may be different in the analyzed data set Separating the contribution of an effect into two functions requires more of the data and if a given effect is similarly strong for the creation and maintenance of ties the statisti cal power will decrease by this split For these reasons most SIENA studies limit their attention to evaluation effects However if there is enough data the distinction between creation and maintenance of ties can produce powerful insights e g Cheadle et al 2013 Dependent variables behavior evaluation creation and endowment functions The distinction between the different behavior evolution functions follows a logic sim ilar to the case of network evolution The three possibilities for change in behavior are 14 increasing or decreasing the level of behavior by one unit or maintaining its actual level In case of the evaluation function the model does not distinguish between upward and downward changes only looks at the resulting level of behavior By using the creation and endowment functions we can obtain separate parameters and assess the different impact of effects for the increase and the decrease of behavior 2 1 3 Outline of estimation procedure SIENA estimates parameters by the function siena07 using the following procedure 1 Certain statistics are used that reflect the parameter values the fina
124. deviant in degrees Sometimes transitivity can better be modeled by the GWESP effects search for this term in the manual than by transitive triplers This may help with convergence Another possibility is that there is time heterogeneity Indications about this can be gathered also from the descriptives given in the start of the output file the number of changes upward and downward in the network and also if any in the dependent behavioral variable If these do not show a smooth or similar pattern across the observations then it may be useful to include actor variables representing time trends These could be smooth e g linear but they also could be dummy variables representing one or more observational periods these must be included as an ego effect to represent time trends in the tendency to make ties or to display higher values of the behavior in question Further see Section 5 9 for how to discover and handle time heterogeneity e Too many weak effects are included Use a smaller number of effects delete non significant ones and increase complexity step by step Retain parameter estimates from the last simpler model as the initial values for the new estimation proce dure provided for this model the algorithm converged without difficulties here also prevAns may be used Effects that are left out of the estimation can still be used in the model by specifying them with test TRUE fix TRUE this will not burden the es
125. dinal variables the identity effect is suitable for categorical variables 7 the interaction effect of covariate similarity with reciprocity 8 the effect of the covariate of those to whom the actor is indirectly connected i e through one intermediary but not with a direct tie this value at a distance can represent effects of indirectly accessed social capital The usual order of importance of these covariate effects on network evolution is evaluation effects are most important followed by creation endowment and rate effects Inside the group of evaluation effects for variables measured on an interval scale or ordinal scale with reasonable numerical values it is the covariate similarity effect that is most important followed by the effects of covariate ego and covariate alter When the network dynamics is not smooth over the observation waves meaning that the pattern of ties created and terminated as reported in the initial part of the output file under the heading Initial data description Change in networks Tie changes between subsequent observations is very irregular across the observation periods it can be important to include effects of time variables on the network Time variables are changing actor covariates that depend only on the observation number and not on the actors E g they could be dummy variables being 1 for one or some observations and 0 for the other observations For actor covariates that hav
126. dowment and creation effect score calculation for symmetric network pairwise models File cluster out is now removed before recreation Meta analysis summary now does not contain a list of NULLs at the end Minor changes to print and messages formats 2012 02 19 R forge revision 203 Fixed minor bug in ML initialisation will alter results slightly New check for updated version when using multiple processes Amended code in manual for making sparse matrices 2012 02 07 R forge revision 200 Bug fix to scores for behavior variable rate effects Siena07 now stops if cannot get a derivative matrix in phase 1 2012 01 29 R forge revision 198 Fix bug in initializing rate parameters for bipartite and behavior variables in maximum likelihood Will change results slightly 2012 01 29 R forge revision 197 Fix bug in effFrom with changing covariates The targets depended on the compiler Fix bug in creation effects in Maximum likelihood 2012 01 20 R forge revision 195 NaN s in covariates were causing problems now treated as though NA in C as hey always were in R t New file arclistdata dat added to examples directory New maintainers address rsienaUstats ox ac uk Print method for sienaFit objects now includes values of fixed parameters rather than NA e 2012 01 17 R forge revision 194 fix to prtOutMat to stop crash with null matrix relaxed restrictions on behavior interactions in line with the manual
127. e Method of Moments it is usual for the quasi autocorrelations to become close to 0 For estimation by Maximum Likelihood they will usually even tually tend to fluctuate about some positive values determined by the multiplication factor see Section 6 6 Large quasi autocorrelations larger than 5 when using the Method of Maximum Likelihood suggest that either the estimation process is still far from its eventual limit the final estimate or the multiplication factor may be too small But in this case the autocorrelations given in the output file are more important information than those given on the screen 3 In phase 3 the parameter vector is held constant again now at its final value This phase is for estimating the covariance matrix and the matrix of derivatives used for the computation of standard errors The default number of runs in phase 3 is 1000 This requires a lot of computing time but when the number of phase 3 runs is too low the standard errors computed are rather unreliable The number of subphases in phase 2 and the number of runs in phase 3 are determined by parameters nsub and n3 in the call of sienaAlgorithmCreate During the estimation process if the graphical user interface is used the default batch FALSE in the call of siena07 the user can break in and modify the estimation process in two ways 1 it is possible to terminate the estimation 2 in phase 2 it is possible to terminate phase 2 and cont
128. e Section 5 Use print01Report to produce an output file presenting some descriptive statistics for the objects included in the model Use functions includeEffects setEffect and includelnteraction to further specify the model see Sections 5 2 5 6 Use siena07 to run the estimation procedure Basic output is written to a log file in the actual working directory The filename is the project name specified in the sienaAlgorithmCreate function Results can also be inspected in R using various functions 2For directions on how to handle composition change see Section 4 3 3 3The use of multiple processes can speed up the estimation in siena07 For directions on how to utilize multiple processors see Section 6 8 18 2 4 Example R scripts for getting started The following scripts on the RSiena website go through the steps outlined in the previous section providing additional details and options e basicRSiena r a minimal example of a basic sequence of commands for estimating a model by function siena07 of RSiena e Rscript01DataFormat R gives a brief overview of R functions and data formats that are essential for using RSiena e Rscript02SienaVariableFormat R shows how to prepare data for a SIENA analysis including the creation of RSiena objects and how to specify effects for RSiena models e Rscript03SienaRunModel R shows how to carry out the estimation and look at the results e Rscr
129. e defined specifically for all dependent variables network behavior or more of these if included in the model These functions depend on the actor hence the name actor oriented and on the state of the network behavior and covariates All these func tions are constituted by a weighted sum of so called effects which define the characteristics of the network and behavior if this is included as a dependent variable that determine the probabilities of changes e rate function The rate function models the speed by which the dependent variable changes more precisely the speed by which each network actor gets an opportunity for changing her score on the dependent variable Advice in most cases start modeling with a constant rate function without addi tional rate function effects When there are important size or activity differences between actors it is possible that different advice must be given and it may be necessary to let the rate function depend on the individual covariate that indicates this size or on the out degree e evaluation function The evaluation function is the primary determinant of the probabilities of changes Probabilities are higher for moving towards states with a higher value of the evalu ation function One way of representing this is that the evaluation function models the actor s satisfaction with her his local network neighborhood configuration It is assumed that actors change their scor
130. e goodness of fit assessment only For tie variables that have a structural value at the end of the period but a free value value at the start of the period the reference value for the simulated values is lacking therefore the simulated values at the end of the period then are replaced by the structural value at the end of the period again for the goodness of fit assessment only 53 6 Estimation The model parameters are estimated under the specification given during the model spec ification part using an iterative stochastic approximation algorithm Three estimation procedures are implemented the Method of Moments MoM Snijders 2001 Snijders et al 2007 the Method of Maximum Likelihood ML Snijders et al 2010a and a Bayesian method Koskinen 2004 Koskinen and Snijders 2007 Schweinberger and Snij ders 2007a For non constant rate functions currently only MoM estimation is available The Method of Moments is the default the other two methods require much more com puting time Given the greater efficiency but longer required computing time for the ML and Bayesian methods these can be useful especially for smaller data sets and relatively complicated models networks and behavior creation or endowment effects In the following the number of parameters is denoted by p The algorithm is based on repeated and repeated and repeated simulation of the evolution process of the network These repetitions are called r
131. e interpretation of the average alter effect This is because total and average similarity For effects satisfying this condition the interactionType is defined as OK 145 are not of the form 34 To explain the log odds or odds ratios due to these effects it has to be understood how a change in the behavior z will affect the values of these effects Examining their formulae leads to the following For a given actor i the out degree number of friends is denoted x Let the number of friends whose values z are less than equal to or greater than the value z of i be denoted by a b and c Denote the range maximum minus minimum value of the behavior by r Then in the event of a ministep with respect to behavior the contributions of the total similarity effect to the log probabilities of changes 1 0 or 1 are given by Beeb a b c r 0 and BP c a b r respectively The contributions for the average similarity effect are Bb a b c raiz 0 and BP c a b rai This shows that the influence of the friends in the similarity effects depends only on whether they have larger or smaller values than the focal actor not on how much larger the values are It also shows that for the similarity effects the dispersion of the friends values matters and not only their average whereas for the average alter effect only the average matters To have a compact formulation without all this detail one could say the fo
132. e k corresponds to an effect included in the model The explanation here is formu lated for the network evaluation function but the principle can be applied more generally An unrestricted model which allows for time heterogeneity in all of the effects is considered as a modification of 9 3 O Be OL HL sie XE 3 il k where 5m are parameters for interactions of the effects with time dummies One way to formulate the testing problem of assessing time heterogeneity is the following Ho em 0 for all k m Ay am 0 for some k m 8 This testing problem can be addressed by the score test in a way that no extra esti mation is necessary This method was elaborated and proposed by Lospinoso et al 2011 and is implemented in RSiena To apply the test to your dataset run an estimation in the usual way e g as follows we specify nsub 2 n3 100 just to have an example that runs very quickly myalgorithm lt sienaAlgorithmCreate nsub 2 n3 100 mynet1 lt sienaDependent array c s501 s502 s503 dim c 50 50 3 mydata lt sienaDataCreate mynet1 myeff lt getEffects mydata myeff lt includeEffects myeff transTrip balance ans2 lt siena07 myalgorithm data mydata effects myeff batch TRUE and conduct the timetest through Conduct the score type test to assess whether heterogeneity is present tt2 lt sienaTimeTest ans2 plot tt2 effects 1 2 If as a consequence of this anal
133. e networks and as the number of units nodes in the second node set for two mode networks For cross network effects the network in the role of dependent variable is denoted by X and the network in the role of explanatory variable by W thus effects go from W to X All these effects are regarded as effects determining the dynamics of network X 1 If both networks have the same number of columns then the basic effect is the entrainment of X by W i e the extent to which the existence of a tie 2 W j X promotes the creation or maintenance of a tie i gt j 2 If both networks are one mode then a next effect is the reciprocity effect with W on X representing the extent to which the existence of a tie 7 Ki promotes the creation or maintenance of a tie in the reverse direction i gt j 3 If both networks are one mode then a next effect is the mutuality effect with W on X representing the extent to which the existence of a mutual tie i K j promotes a GN oe the creation or maintenance of a tie i gt j 4 The outdegree W activity effect where parameter 2 is the sqrt version while pa rameter 1 is the non sqrt version see above for explanations of this reflects the extent to which actors with high outdegrees on W will make more choices in the X network Several mixed transitivity effects can be important 5 If X is a one mode network the from W agreement effect rep h resents the extent to which agreem
134. e s50 data set that is distributed in the examples directory of the source code 3 Siena format These can be used in sienaDataCreateFromSession An edge list is a matrix containing three or four columns from to value wave optional Like the Pajek format this has the advantage that absent ties tie variables with the value 0 do not need to be mentioned in the data matrix By specifying the waves in the fourth column in the Siena format one matrix can be used to contain data for all the waves Missing values must be indicated in the way usual for R by NA For data specification by the graphical interface siena01Gui or by the function sienaDataCreateFromSession instead of NA any numerical code can be used given that this is indicated to be a missing value code If the data set is such that it is never observed that ties are terminated then the network dynamics is automatically specified internally in such a way that termination of ties is impossible In other words in the simulations of the actor based model the actors 24 have only the option to create new ties or to retain the status quo not to delete existing ties Similarly if ties never are created but only terminated then this will be respected in the simulations See Section 4 2 3 and note the possibility of using allowOnly TRUE 4 1 2 Transformation between matrix and edge list formats The following R commands can be used for transforming an adjacency matrix to an ed
135. e stream lined construction of effects Looking at the code starting with the file EffectFactory cpp may be helpful for understanding this construction of generic effects For example com pare the construction of sameXTransTrip to that of sameXInPop 1 Work out the definition of the effect and the contribution or change statistic For network effects the change statistic is Ay a si zT spil 42 where x Y is the network with the tie i gt j and z is the network without this tie 2 The list of all defined effects can be obtained from effectsDocumentation which produces a file effects html or effects pdf All effects are also listed with their defini tions in the manual Section 12 Determine an existing effect that is most similar to this effect or perhaps more than one In the file effects html or effects pdf the effects are grouped by effectGroup 3 Open the file allEffects csv located in RSiena data The default program for open ing a csv file usually is Excel but other editors may be more helpful for opening this particular file e g NotePad or NotePad It must not be saved as a Excel file e You will see that the first column is called effectGroup These groups define com binations of dependent variable effect type and covariates if any e g non SymmetricObjective bipartiteSymmetricObjective Identify the effectGroup where this effect belongs Determine which is which by considering
136. e the same value for all actors within observation waves or in the case that there are structurally determined values that are constant for all actors within the same connected components only the ego effects are defined because only those effects are meaningful This exclusion of the alter similarity and other effects for such actor variables applies only to variables without any missing values For each dyadic covariate the following network evaluation effects can be included in the model for network evolution e network evaluation creation and endowment functions 1 main effect of the dyadic covariate 2 the interaction effect of the dyadic covariate with reciprocity The main evaluation effect is usually the most important In the current version of SIENA there are no effects of dyadic covariates on behavioral evolution 44 5 5 Cross network effects for dynamics of multiple networks If there are multiple dependent network variables these can be one mode networks two mode networks or a combination of these The co evolution of one mode and two mode networks is treated in Snijders et al 2013 but this paper can also be used as an intro duction to the dynamics of multiple one mode networks For multiple dependent network variables the following effects may be important This is explained here jointly for the case of one mode and two mode networks The number of columns is defined as the number of actors for one mod
137. e vz x u with the proviso that the user defined interaction does not center the product variable the user defined interaction then is defined by 1 SH am 2 2 zi 015 24 Vai Z Ul U2 31 2 where both component variables v1 and va are internally centered but the product vari able will generally not have mean 0 12 2 2 Behavioral creation function Also the behavioral model knows the distinction between evaluation creation and endow ment effects The formulae of the effects that can be included in the behavioral creation function cP h are the same as those given for the behavioral evaluation function However they enter calculation of the creation function only when the actor considers increasing his behavioral score by one unit downward steps not when downward steps or no change are considered For more details consult Snijders et al 2007 and Steglich et al 2010 and replace going down by going up The statistics reported as inc beh increase in behavior are the sums of the changes in actor dependent values for only those actors who increased in behavior More precisely it is M 1 n Y Y Hziltner gt alt Hoi o tm 1 sie tm 32 m 1 i 1 where M is the number of observations x t is the observed situation at observation m and the indicator function A is 0 if event A is true and 0 if it is untrue 12 2 3 Behavioral endowment function Also the behavioral model knows
138. ects already included in the evaluation function this would lead to large standard errors Creation and endowment effects for behavior for behavior variables with more than 2 values are still under investigation and their interpretation for practical research still is uncertain A model specification with only evaluation effects and without creation and endowment effects leads to exactly the same network dynamics as a specification where these effects are turned into creation and endowment effects with the same parameters For any given effect normally it makes no sense to include the effect in all three roles evaluation creation endowment If one wishes to go beyond evaluation effects then the user has to choose between adding an effect in either the creation or the endowment role SA special case of the gratification function in Snijders 2001 The endowment function also is a special case of the gratification function in Snijders 2001 36 5 1 1 Elementary effects Not all contributions to the probability of change can be written as the change in some basic function evaluation function Therefore we sometimes need to directly represent contributions to a tie change or behavior change without invoking an evaluation func tion This can be done by using elementary effects In Snijders 2001 this was called a gratification function as a more neutral term we now use the word elementary effects The basic example here is
139. ed by package parallel The DESCRIPTION file was corrected to satisfy CRAN requirements e 2013 06 15 R forge revision 231 Changes in RSiena as well as RSienaTest Make the cumulative option operational in BehaviorDistribution for sienaGOF Correct bug in treatment of missing values in sparseMatrixExtraction for sienaGOF Allow sparse observed data matrices and structural zeros and ones in sparseMatrix Extraction and networkExtraction and bipartite networks in networkExtraction for sienaGOF Report correct centering by overall means of individual covariates for multi group objects in print01Report If there is a composition change object MoM estimation is forced to be non conditional This is reported in the help file for sienaCompositionChange e 2013 05 10 R forge revision 230 Changes in RSiena as well as RSienaTest Check whether the maximum observed degree is not higher than maxDegree Fix error in implementation of maxDegree Fix bug in print siena and extend print siena Make print method for class sienaDependent 188 e 2013 04 19 R forge revision 227 Changes in RSiena as well as RSienaTest both now are very similar sienaBayes algorithms and profileLikelihoods are the only functions in RSienaTest not in RSiena Available effects now are the same in both packages Main changes visible to users For Siena only function bayes was removed still under development in RSienaTest A
140. ed by vCovars for changing varying monadic covariates for centering issues further see Section 4 2 2 2 same V defined by 1 if v vj and O otherwise not centered V is the name of the variable This can also be referred to as dyadic identity with respect to V Dyadic similarity is relevant for variables that can be treated as interval level variables dyadic identity is relevant for categorical variables In addition SIENA offers the possibility of user defined two and three variable inter actions between covariates see Section 5 8 4 2 2 Centering Individual as well as dyadic covariates are centered by the program in the following way For individual covariates the mean value is subtracted by function SienaDataCreate The centered values then are stored see below and all calculations use these centered variables For the changing covariates the mean value used is the global mean averaged over all periods The values of these subtracted means are reported in the output of print01Report For the multi group option section 11 1 the subtracted values are the global means across all groups Centering of covariates can be turned off by specifying centered FALSE in the call of coCovar varCovar coDyadCovar or varDyadCovar respectively For the dyadic covariates and the similarity variables derived from the individual co variates the grand mean is calculated and stored by function SienaDataCreate the stored
141. ed effect1 3 to integers to correct bug in fix myeff new utility functions to update effects object no longer necessary to include underlying effects for interactions user parameter for number of unspecified behavior interactions remove extra sqrt roots in standard error of rates for conditional estimation see revision 31 e 2010 01 15 R forge revision 40 RSiena only remove extra sqrt roots in standard error of rates for conditional estimation see revision 32 e 2010 01 02 R forge revision 34 Corrected layout of print and xtable for SienaFit objects with both behavior and network variables e 2010 01 01 R forge revision 33 Updated change log and manual in RSiena and ChangeLog in RSienaTest e 2010 01 01 R forge revision 32 printO7report r corrected standard errors for rate estimate for conditional estimation needed square roots RSiena e 2009 12 31 R forge revision 31 print07report r corrected standard errors for rate estimate for conditional estimation needed square roots RSienaTest only more behavior effects in RSienaTest e 2009 12 17 R forge revision 30 Fixed bug in dyadic interactions in RSienaTest e 2009 12 17 R forge revision 29 Fixed bug in 3 way interactions in RSienaTest e 2009 12 14 R forge revision 28 Fixed bug in use of multiple processes for RSiena e 2009 12 14 R forge revision 27 Fixed bug in use of multiple processes for RSienaTest e 2009 12 01 R forge revision 26 Created RSienaTest which
142. ed popularity or popularity of alter effect defined by the sum of the in degrees of the others to whom 7 is tied s13 1 Zj Tij 43 DI Vij Dn Tg Dy iO ps Fag 1 in SIENA 3 until version 3 313 this effect was multiplied by a factor 1 n in RSiena this effect has had a bug until version 1 1 219 in RSiena the target statistic for this effect was multiplied by a factor n until version 1 1 241 in degree related popularity sqrt effect inPopSqrt earlier called popularity of alter sqrt measure effect defined by the sum of the square roots of the in degrees of the others to whom 7 is tied Sind Jj Vig YTF Diy Vig V Din Thi this often works better in practice than the raw popularity effect also it is often reasonable to assume that differences between high in degrees are relatively less important than the same differences between low in degrees out degree related popularity effect outPop earlier called activity or activity of alter effect defined by the sum of the out degrees of the others to whom is tied s335 12 j Tij zj DI Vij Dn jh until version 3 313 this effect was multiplied by a factor 1 n out degree related popularity sqrt effect outPopSqrt earlier called activity of alter sqrt measure effect defined by the sum of the square roots of the out degrees of the others to whom 7 is tied siz 0 2 Vig JTF 27 Cig V 2 h Zihi this often works better in practice than the raw activ
143. eference for similar others is strongest for actors egos high on drinking behavior and weakest for actors in the middle and low range of drinking behavior For drug use the formula yields 0 1362 v 0 0 1295 u 0 0 665 1 0 7533 V which leads to the following table u x Uj 1 2 3 4 1 0 16 0 19 0 54 0 89 2 0 08 0 17 0 18 0 53 3 0 01 0 08 0 17 0 18 4 0 10 0 00 0 09 0 18 In each row the highest value is at the diagonal which shows that indeed everybody prefers to be friends with similar others also with respect to drug use The negative alter effect supports this for low v values and counteracts it for high v values This is seen in the table in the strong preference of low drug users v 1 for others who are low on drug use and the very weak preference for high drug users v 4 for others also high on drug use An alternative specification uses the drink ego x drink alter interaction together with the drink squared alter effect in the network dynamics model and similarly for drug use for the behavior dynamics an alternative specification uses the average alter effect This leads to the following table of results Network Dynamics 1 rate constant network rate period 1 8 0978 1 5118 149 2 rate constant network rate period 2 5 7781 0 9474 3 eval outdegree density 2 1333 0 2196 4 eval reciprocity 2 3033 0 2184 5 eval transitive ties 0 2430 0 2
144. effects for behavior dynamics However correlations between parameter estimates close to 1 0 or 1 0 should not be used too soon in themselves as reasons to exclude effects from a model This is for two reasons In the first place network statistics often are highly correlated for example total number of ties and number of transitive triplets and these correlations just are one of the properties of networks Second near collinearity is not a problem in itself but the problem if any arises when standard errors are high which may occur because the value of the parameters of highly correlated variables is very hard to estimate with any precision The problem resides in the large standard errors not in itself in the strong correlation between the parameter estimates If for both parameters the ratio of parameter estimate to standard error i e the t ratio is larger than 2 in absolute value in spite of the high 66 correlations between the parameter estimates then the significance of the t test is evidence anyway that both effects merit to be included in the model In other words in terms of the signal to noise ratio the random noise is high but the signal is strong enough that it overcomes the noise As a rule of thumb for parameter correlations usually for correlations of estimated structural network effects there is no reason for concern even when these correlations are as strong as 9 In the example above the strongest corr
145. effects may be important especially for networks where degrees are theoretically important and represent social status or other fea tures important for network dynamics and or for networks with high dispersion in in or out degrees which may be an empirical reflection of the theoretical impor tance of the degrees Include them if there are theoretical reasons for doing so but only in such cases 6 The in degree popularity effect again with or without sqrt with the same consid erations applying reflects tendencies to dispersion in in degrees of the actors or tendencies for actors with high in degrees to attract extra incoming ties because of their high current in degrees 7 The out degree popularity effect again with or without sqrt with the same con siderations applying reflects tendencies for actors with high out degrees to attract extra incoming ties because of their high current out degrees This leads to a higher correlation between in degrees and out degrees 8 The in degree activity effect with or without sqrt reflects tendencies for actors with high in degrees to send out extra outgoing ties because of their high current in degrees This leads to a higher correlation between in degrees and out degrees The in degree activity and out degree popularity effects are not distinguishable in Method of Moments estimation then the choice between them must be made on theoretical grounds 41
146. egrees in W on X popularity X both indegrees W both defined by the sum of the W in degrees of the others to whom 1 is tied multiplied by the centered W in degree of i for parameter p 2 the square roots of the W in degrees sis z gt Tij w4i sE 10 wy w or for p 2 sig 2 gt tij y wii 10 Vw VD 121 10 this can be regarded as an interaction between the effect of W in degree on X popularity and the effect of W in degree on X activity Duplex XW out degree activity effect X duplex W outdegree activity doubleDutAct which is like the out degree activity effect but now for the degrees in the joined X and W network for parameter p 2 the square root of the out degrees is taken gt 2 sis a Dl ty wig or for p 2 sig x X Tij Wijy Dn Tin Wip 5 Duplex XW in degree popularity effect X duplex W indegree P popularity doubleInPop which is like the in degree popularity effect but now for the degrees in the joined X and W network for parameter p 2 the square root of the out degrees is taken sito gt Tij Wij Xop Enj Whj OF for p 2 sito x D Tij Wijy Dn Zhj Whj The betweenness effect is another positional effect a positional characteristic in the W network affects the ties in the X network but now the position is the betweenness count defined as the number of pairs of nodes that are not directly connected j Xh but that are connected t
147. ehavioral data can represent whether an actor is a smoker or not as well as a number of ordered categories express ing the number of cigarettes usually smoked The term behavior should not be taken literally here it is possible to model changes in attitudes or other actor attributes In the models behavioral variables can be binary or ordinal discrete the extension for con tinuous behavioral data is currently being developed The number of categories should be small mostly 2 to 5 larger ranges are possible In the case of behaviors Stochastic Actor Oriented Models express how actors increase decrease or maintain the level of their behavior A special case of the fourth type is the diffusion of innovations in dynamic networks Greenan 2015 here the behavior variable representing having adopted the innovation is binary coded 0 or 1 and once an actor has the value 1 s he is stuck with it The only possible transitions are 0 gt 1 representing that the actor adopts the innovation See Section 12 2 4 Covariates In every model type it is possible to define and use covariates which are variables that are exogenous in the sense that their values are not modeled but used to explain network or behavior change Covariates can be dummy variables e g sex or continu ous e g attitudes or age Also they may have constant values across all observations or their value may change across time periods this is the distinction be
148. elation was found between the parameter estimates for transitive triplets and three cycles This is not surprising because both are triadic effects In this case the three cycle effect was not significant and can be dropped for that reason 6 6 Maximum Likelihood and Bayesian estimation SIENA can estimate models by three estimation methods the unconditional or condi tional Method of Moments MoM the default Snijders 2001 Snijders et al 2007 the Maximum Likelihood method ML see Snijders et al 2010a and Bayesian methods see Koskinen 2004 Koskinen and Snijders 2007 Schweinberger and Snijders 2007a In nice situations data sets that are not too small model specifications that do not request too much from the data the three methods tend to agree and there seems not to be no reason to use the more time consuming ML or Bayesian methods In not so nice situations very small network data sets small network and behavior data sets in combination with complex models however ML and Bayesian methods tend to produce slightly more accu rate results than MoM Statistical theory suggests that ML is a more efficient estimation method than MoM in the sense of producing estimates with smaller standard errors But in the nice situations the efficiency advantage of ML is very small Bayesian estimation is based on a different statistical paradigm and assumes and requires that the uncertainty about parameters is expressed
149. en the list can be created by the following commands comp lt rep list c 1 6 50 comp 111 lt c 3 6 comp 20 lt c 1 4 comp 33 lt c 1 5 3 4 01 6 changes lt sienaCompositionChange comp The use of blanks in the line for comp 33 is only for visually keeping the pairs of start end times together The first line creating a list with the default first and last end point for everybody could also be replaced by comp lt vector list 50 comp lt list c 1 6 Here it may be noted that keeps structures etc unchanged while replicating the ex pression to fit The object changes created by the functions sienaCompositionChangeFromFile or siena CompositionChange is of class compositionChange and can be used in the function siena DataCreate The method of joiners and leavers for representing composition change does not com bine properly with the sienaGOF function Section 5 11 34 5 Model specification 5 1 Definition of the model After defining the data the next step is to specify a model The model specification consists of a selection of effects for the evolution of each dependent variable network or behavior To understand this first a brief review of the definition of the actor oriented model is given for further explanations see Snijders 2001 2005 Snijders et al 2007 2010b The model is based on four functions which first are explained in an intuitive way They ar
150. ent between and j with respect to outgoing W ties promotes the creation or mainte W w nance of a tie 3 j W jJ 6 If W is a one mode network the W to agreement effect rep h resents the extent to which a W tie i 4 h leads to agreement between and h with respect to outgoing X ties to others i e w x X ties to the same third actors j i 4 jand h 2 j o TE 2 45 7 If X and W both are one mode networks the closure of W 5 6 effect represents the tendency closure of W W two paths bg i nS j by an X tie j W W e i X J Effects on behavior evolution For models with one or more dependent behavior variables i e models for the co evolution of networks and behavior the most important effects for the behavior dynamics are the following see Steglich et al 2010 In these descriptions with the alters of an actor we refer to the other actors to whom the focal actor has an outgoing tie The dependent behavior variable is referred to as Z 1 The shape effect expressing the basic drive toward high values on Z A zero value for the shape will imply a drift toward the midpoint of the range of the behavior variable The effect of the behavior Z on itself or quadratic shape effect which is relevant only if the number of behavioral categories is 3 or more This can be interpreted as giving a quadratic preference function for the behavior When the coefficient for the sh
151. ent choice of priorSigma for rate parameters by priorKappa changed z nwarm to 0 if prevBayes is used dropped plotit functionality sienaBayes glueBayes and print sienaBayes adapted to allow inclusion of interac tion effects without the corresponding main effects Added parameter nwarm2 to glueBayes Checks of identical prior parameters in this function restricted to non rate parameters 2014 06 22 R Forge Revision 277 Changes in RSiena and RSienaTest Higher write to screen frequency for batch operation of siena07 Function includeEffects now includes parameters fix and test Various small bug corrections see the ChangeLog 1 1 275 Changes in RSienaTest Changes in sienaBayes and its print and summary methods Corrected starting printing sienaBayesFit at nfirst New function glueBayes for combining sienaBayesFit objects Added functions simpleBayesTest and multipleBayesTest 2014 04 26 R Forge Revision 274 Changes in RSiena and RSienaTest Correction of effect homWXClosure 184 Small change in print01Report to improve reporting two files of composition change sienaRI require that file argument is not NULL for non Windows operating systems e 2014 04 13 R Forge Revisions 267 271 Changes in RSienaTest Updates to let sienaBayes accept a wider range of data and models e g user defined interactions and various corrections to sienaBayes C
152. epeats of nrunMHBatches of a number of MH steps sampling chains plus nSampVarying MH steps sampling the varying parameters 6 plus nSampConst MH steps sampling the non varying parameters 7 plus one Gibbs step sampling the global mean and covariance matrix of the varying parameters u and are performed In the warming as well as the final phase the number of MH steps is determined by parameter mult multiplication factor in the call of sienaAlgorithm Create that created the algorithm object The function sienaBayes is time consuming When starting to use it it is advisable to start with low values of nmain to explore computing time When the procedure seems to diverge and for very small groups it is advisable to use smaller values of the parameters initgainGlobal and initgainGroupwise and perhaps reductionFactor 11 3 1 Which data sets to use for sienaBayes sienaBayes uses as data set a sienaGroup object with 2 or more groups The number of waves should be the same for all groups sienaBayes may run into an error the program will hang if there are any actors who are inactive at the first wave as indicated by all structural zeros sienaBayes should be possible for groups as small as 5 actors A restriction maybe to be lifted later is that the networks must not be empty at any wave and consecutive waves of networks must not be identical in other words all Jaccard indices should be strictly less than 1 Be prepared for
153. er ence about a population of networks and the Fisher approach for combining independent tests the following may be helpful Inferring about a population always adds some uncer tainty this is more serious when the sample size here number of combined networks is smaller In the extreme case consider the combination of N 2 networks with estimates 6 1 standard error s 0 1 and 65 5 8 0 1 Then for both of the groups the t statistic s is very large leading to the conclusion that parameters 01 and 62 are very likely to be positive This will lead to a significant result for Fisher s combination of tests On the other hand the mean in the population of networks given that there is available a sample of size as low as N 2 cannot be determined with any degree of precision so the confidence interval for this mean ug will be huge and the result for testing as null hypothesis HP will not be significant However the results for testing HO and He will be significant 11 3 Random coefficient multilevel Siena analysis The function sienaBayes is for Bayesian estimation of one group or of multiple groups all having the same number of waves and the same model specification The parameters excepting the basic rate parameters can be either randomly varying between groups according to a multivariate normal distribution or non varying and constant across groups The difference is made by setting the parameter random in the
154. er actors in the network before joining or leavers and other actors after leaving can be used if available Note that this second option of specifying entries always supersedes the first specification if a valid code number is specified this will always be used The functions used to specify the times actors join or leave the network i e the times of composition change are sienaCompositionChangeFromFile in case a file is used and sienaCompositionChange in case a list is used How to use a separate input file called the exogenous events file is described in the help page for sienaCompositionChangeFromFile In the second case a list must be given of length n where n is the number of actors in the node set The th element of this list must be a vector of numbers characters are also allowed composed of an even number of elements indicating the intervals during which actor was present For example 1 4 indicates that the actor was present from wave 1 to wave 4 end points included and 1 3 2 5 01 7 indicates that the actor was present from wave 1 to 20 of the time between waves 3 and 4 and then again from just after wave 5 to wave 7 As an example suppose we have 50 actors and 6 waves almost all actors were present all the time but actor 11 was present from wave 3 onward actor 20 was present until wave 4 and actor 33 was present from mid way between waves 1 and 2 until wave 3 and then again from just after wave 4 to wave 6 Th
155. ere the second network is one mode e covarABNetNetObjective is without restriction on the modes e covarANetNetObjective is for effects where if the second network is two mode the covariate is defined for the first node set e covarBNetNetObjective is for effects where if the second network is two mode the covariate is defined for the second node set Further some of the complex effectGroups are the following e tripleNetworkObjective is for combinations of three networks where for the two in the role of explanatory networks either both should be one mode or both should be bipartite with the same second node sets e behaviorOneOneModeObjective is for dependent behavioral variables and two ex planatory one mode directed networks e behaviorSymSymObjective is for dependent behavioral variables and two explanatory one mode non directed networks e behaviorOneModeSymObjective is for dependent behavioral variables and two ex planatory one mode networks the first directed the second non directed e behaviorBipBipObjective is for dependent behavioral variables and two explanatory two mode networks with identical actor sets 167 If you wish to add an effect with a combination of variables that is not yet implemented you have also to treat it in effects r 168 A List of Functions in Order of Execution This appendix provides a description of the functions that constitute the RSiena package This is intended as a quick refere
156. erent index numbers h this effect multiplies the factor Ant by exp an wit 1 131 e logarithmic outdegree effect outRateLog This effect multiplies the factor Ant by exp in ap zi 1 z 1 I This effect works properly only for non conditional estimation set cond FALSE in sienaAlgorithmCreate The exponential link function and logarithmic transformation collaborate to produce direct proportionality to outdegree 1 in case the parameter is Qh 1 For the two latter effects the addition of 1 to the outdegrees avoids problems divi sion by 0 logarithm of 0 that otherwise would occur when zi 0 12 2 Behavioral evolution The model of the dynamics of a dependent actor variable consists of a model of actors decisions according to evaluation creation and endowment functions and a model of the timing of these decisions according to a rate function just like the model for the network dynamics The decisions now do not concern the creation or dissolution of network ties but whether an actor increases or decreases his score on the dependent actor variable by one or keeps it as it is 12 2 1 Behavioral evaluation function The behavior evaluation function for actor i is defined as E ee 23 k where peeh are parameters and SPR aig are effects as defined below The behavioral dependent variable is denoted by z and the dependent network variable by z Here the dependent variable is transf
157. erval For example the adjusted percentile BCa method Efron 1987 Davison and Hinkley 1997 Chapter 5 which is available in function boot ci in R package boot 11 2 2 Meta analysis directed at testing the parameters Another method for combining the various data sets which does not make the assumption that the parameters are a sample from a population and also makes no assumptions of absence of correlation between the true deviations 6 0 and the random errors Ej is based on Fisher s method for combining independent p values the principle of this combination method of Fisher 1932 is described in Hedges and Olkin 1985 and briefly in Snijders and Bosker 2012 Chapter 3 This principle here is applied in a double test 1 for detecting if there are any networks with a positive parameter value the null hypothesis tested is Ho For all networks the value of this parameter is zero or less than zero with the alternative hypothesis H For at least one network the value of this parameter is greater than zero 2 for detecting if there are any networks with a negative parameter value the null hypothesis tested is Ho For all networks the value of this parameter is zero or greater than zero with the alternative hypothesis H For at least one network the value of this parameter is less than zero For each of these combined tests the p value is given In the output these are denoted respectively as combination
158. es contributing to the tie 1S j w w o __ e pote y 113 55 incoming shared WW X X incoming shared W OutWWwWX siss 0 jan Tij Wih Wjh this refers to shared outgoing W ties contributing to the tie aX a T 56 WX gt X closure of covariate WXX siso z Lith Tij Wih Thj this refers to the closure of mixed W X two paths each W X two path Mp j is weighted by wip and the sum of these weights measures the strength of the tendency toward closure of these mixed W X twopaths by a tie a j 57 XW gt X closure of covariate XWX Si57 0 D jn Tij Vin Why this refers to the closure of mixed X W two paths each X W two path i h x j is weighted by wp and the sum of these weights measures the strength of the tendency toward closure e h 0 x Ww i X of these mixed X W twopaths by a tie a J There are two partial variants of this effect they can be distinguished not by the Method of Moments but only by Maximum Likelihood and Bayesian estimation 58 XW gt X closure 1 of covariate XWX1 This is an elementary effect not an evaluation effect comprising of the XW gt X closure of covariate effect only the contribution of the the number of weighted X W two paths 7 Bae 5 j In other words only the i j tie in the figure is the depen dent variable here The effect is defined as si g 1 Tij minas Tih Whj 59 XW gt X clo
159. es on the dependent variable such that they improve their total satisfaction with a random element to represent the limited predictability of behavior In contrast to the creation and endowment functions described below the evaluation function evaluates only the local network neigh borhood configuration that results from the change under consideration without considering where you come from In most applications the evaluation function will be the main focus of model selection The evaluation function was called objective function in Snijders 2001 5The term satisfaction should be interpreted here in a very loose sense the satisfaction interpretation is not necessary at all but it does give a convenient intuitive way of thinking about the model 35 e creation function The creation function distinguishes between new and old network ties when eval uating possible network changes and between increasing or decreasing behavioral scores when evaluating possible behavioral changes It is a component of the prob abilities of change only for changes in an upward direction creation of new ties augmentation of values of the behavior dependent variable Creation effects can be the creation parts of an evaluation effect or elementary effects see below In the interpretation using satisfaction the creation function models the gain in satisfaction incurred when network ties are created or behavioral scores are increase
160. esult that the standard errors produced by this method are not very reliable if they are of the order of 0 02 or less The scales are determined by the variable z scale in function robmon A better procedure would be to set the scale adaptively but the finite differences method is hardly ever used any more having been superseded by the score function method and therefore this improvement has not been effectuated 73 8 Tests Two types of tests are available in SIENA 1 t type tests of single parameters can be carried out by dividing the parameter esti mate by its standard error Under the null hypothesis that the parameter is 0 these tests have approximately a standard normal distribution These may also be called Wald type tests Section 8 1 indicates how to construct multi parameter tests from the same principle 2 Score type tests of single and multiple parameters are described in Section 8 2 In addition there are procedures for assessing goodness of fit as explained in Section 5 11 8 1 Wald type tests Wald type tests are based on the parameter estimates and their covariance matrix Recall that the variances of the parameter estimates are on the diagonal of this covariance matrix and the standard errors are the square roots of these diagonal elements In Section 6 3 we saw that for a sienaFit object ans the estimates are given in ans theta the covariance matrix in ans covtheta and the standard errors in ans se For
161. etween i and the other actors j to whom he is tied 136 multiplied by ego s indegree Sisa 2 z T iy gt Vig simi sim and 0 if e 0 because of collinearity under the Method of Moments this cannot be estimated together with the average similarity x popularity alter effect Effects of multiple networks If there are more than one dependent network variables denoted X and X gt they can operate jointly on the behavioural dependent variable using the following effects Xi is given as interaction1 X as interaction2 For the combined degree effects mentioned first F means Forward B means Back ward and R means Reciprocal 35 36 37 38 39 double outdegree effect FFDeg sbeh z z Zi a Vig Vig double indegree effect BBDeg shg z z zi ar Tiji V2ji double reciprocated outdegree effect RFDeg sbeh z z zi gt Crag Fiji Z24g double reciprocated indegree effect RBDeg spy z z zi D Z1ij Tiji T2ji double reciprocated degree effect RRDeg beh E E E au S 39 z z i gt Vig Ciji T24j aji Covariate effects For each actor dependent covariate u recall that these are centered internally by SIENA as well as for each of the other dependent behavior variables for notational simplicity here also denoted v there are the following effects 40 41 main covariate effect effFrom spay z z 25065
162. ew error messages will be added as answerable questions about them arise Note that it is not difficult to find the source of error messages in the code The easiest way is searching for it by some search machine such as google You will probably find it points to R Forge or another repository of the code There you can see what led to the error message if you can understand some R An alternative if you know the function generating the error message is to search directly in the code for this function If the function is called e g siena07 you can write the code to a file called listing txt by the commands sink listing txt siena07 sink Note that you should give the function name without parentheses 14 1 During estimation Unlikely to terminate this epoch more than 1000000 steps This can happen in function siena07 in conditional estimation COND FALSE in sienaAlgorithmCreate when the rate parameter provisionally has hit a value such that the desired number of changes will probably never be reached or in non conditional estimation when the number of ministeps has become too large before arriving at the time for the next wave See Section 6 7 1 Solutions 1 Check whether your model specification is reasonable for example there might be doubts about the specification of the rate function 2 Use non conditional estimation Section 6 7 1 if you were not already doing so 3 If the model includes the outRate effect c
163. eym sy fqo eUdIS Jo IOJDOA Y St TUOTPORIOYUL MOPUOS IO J249 ATWO ATJUALINO P9J9819YUI q 03 SyooTo Jo od4q y st adAy yoolqo s1o lj oy ur 9813 Y 09 S Nejoq peuyop Sutoq ore suOTJRIOyUI YIM 10 YIOMJOU JO OW LU OY st OUIVU WOTJVIOYUT ue go WIN 04 AS TVA 09 POP pms oq ULI Y UOIJOBIDUL oY pn 5ur HOq O n do1 guoryoeJoqur 0 ANUL ANEP o qerIea ueoq e st opnpout U JO U01J98 193UL 4 do1 U01J9 19JUI Pe97SUL s ureu J1OUS ILI ST 998 19JUT 0 sqo g oy Ajroads yose d11 SUBI peso Od y OL SPPA Aq pajeazo se qo qo s1o g BUS V SI PoXu PH T ureu g Xur ureu yoofqo s p eu r e Ul MOI uotu peytoodsun ue jo AW uomnowsr oyu j pniIour A OML epnypout oyepdn Ases moje o 998 193Ut Ue SIPIAOIA WOTJOUN sr Y gt Ban g Kuruonoesr ojgu opn our Yorjoesoyupopnpour F uorjdraos rT s durexri xequrg oure N 238IS a3ed snoras1d woaz panurguos y a1qeL 175 p nunuoo eyep oY uo WOTYVULIOJ ur Areurur 4d surequos yeyy qmo euorg 3no ureu opour p urveu 9 y SOAVS PUL SFL 9 LUAS 09 symeJ p YI SUBU SPOUI ureu opour e pue j Kur 1o qo s499 Jo eu rs e esep polqo eyep eu r g e Ajddns 09 pasu M sq g JNPJOP SH pue 3o qo eyep eu r V Jo JLOAII Y sud eye Ay ytodoy ToyutAd AS TVA uoryeyUewNI0 403 TTON uotssos k gu r
164. fferences between the estimated standard errors and also to considerable differences between the parameter estimates when comparing the results produced by different estimation runs The remedy 9Since version 1 1 285 72 is to reduce the model to a more parsimonious one by excluding non significant effects of which the parameter estimates are highly correlated with others Provisionally until further experience has been collected the following may be a rea sonable guideline High parameter correlations with the outdegree effect are not a reason for worry but high parameter correlations with other effects are a reason for checking the stability of the estimated standard errors The threshold for finding a parameter cor relation too high in this respect can be quite high such as 0 95 or 0 90 In cases of high parameter correlations estimating the model twice or more and considering the stability of the standard errors will be a good way for seeing whether there are reasons for special caution If the standard errors are stable then parameter correlations above 0 90 still can be acceptable in particular when they are obtained for parameters that are significantly different from 0 and of which estimates as well as standard errors are stable across repeated runs of the estimation algorithm 7 2 Precision of the finite differences method The implementation of the finite differences method is not scale invariant with the r
165. fore 3 324 this was divided by n 2 which for larger networks tended to lead to quite large estimates and standard errors Therefore in version 3 324 the division by n 2 which had not always been there was dropped structural equivalence effect with respect to incoming ties inStructEq which is an analogue to the balance effect but now considering similarity with respect to incoming ties sita gt gt ndy 11a with n dij gt bo Ehi Thj 11b h 1 h i j This effect is not quite finalized yet because provisionally bo 0 instead of a mean of the subtracted values like in the balance effect Subtraction of the mean will lead to better convergence properties Jaccard similarity for outgoing ties effect Jout an elementary effect defined by the Jaccard similarity with respect to outgoing ties sme z gt Tij ered Ce where Y y Lin Zjh E ee outlt J Cpe gn ua Cay where 0 0 is taken as 0 Since the Jaccard measure has smaller variability than a lot of other effects the parameter estimates of this will often be larger with correspondingly larger standard errors than many other parameter estimates The same holds for the other Jaccard similarity effects Jaccard similarity for incoming ties effect Jin an elementary effect defined by the Jaccard similarity with respect to incoming ties sit7 gt Tij Jin i j where Talii nit is Lyi F Etj Don Thi Thj whe
166. g of degrees or geodesic distances it often is advisable to use the defaults center FALSE scale FALSE whereas for sets of statistics for which a common scale is less important e g triad counts a clearer picture may be obtained by plotting with center TRUE scale TRUE The method of joiners and leavers for representing composition change Section 4 3 3 does not combine properly with the sienaGOF function The examples in the help pages for sienaGOF and sienaGOF auxiliary give ample help for how to use this function Also see the script on the SIENA website 52 5 11 1 Treatment of missing data and structural values in sienaGOF Missing tie values and structurally determined tie values are treated in the estimation in such a way that they do not contribute directly to the target statistics This behavior is mirrored in their treatment in sienaGOF The aim is that such values do not contribute to any differences between observed and simulated values Tie variables that are missing at either the beginning or the end of the period are replaced by 0 both in the observed and in the simulated networks For behavioral variables they are replaced by missings NA If there are any differences between structural values at the beginning and at the end of a period these are dealt with as follows For tie variables that have a structural value at the start of the period this value replaces the observed value at the end of the period for th
167. g in sienaTimeFix with multi groups and differing actor set sizes 2011 11 04 R forge revision 181 reset random number type after using parallel package 2011 10 28 R forge revision 179 fix bug in forking processes 2011 10 27 R forge revision 177 8 Change to covariance matrix for effects which have been fixed Added new package for parallel running to be used from R 2 14 0 New option to use forking processes on non Windows platforms Changes from revision 175 copied to RSiena Updates to maximum likelihood estimation NB this is still under development and should not be used with missing data Added bayes updateTheta functions to RSiena sienaTimeTest for finite differences or ML now in RSiena 193 Space saving matrices used for derivatives in RSiena now and optional by wave in ML 2011 10 14 R forge revision 176 RSiena Test only bug fix in diffusion effects altered scripts in manual a little 2011 10 06 R forge revision 175 Fix bug with multiple symmetric networks Limit constraints to be between both symmetric or non symmetric networks Added scripts to package RSiena Test only siena07 called with batch FALSE no longer crashes if called on mac or linux with no X11 available RSienaTest only 2011 09 19 R forge revision 172 RSienaTest only Diffusion rate effects 2011 09 07 R forge revision 171 Fix bug in siena08 crashed if underlying effects for interaction were not selected Or possibly
168. ge list and back again If a is an adjacency matrix then the following commands can be used to create the corresponding edge list called edges here create indicator matrix of non zero entries of a ones lt a Zin 0 create empty edge list of desired length edges lt matrix 0 sum ones 3 fill the columns of the edge list edges 1 lt row a ones edges 2 lt col a ones edges 3 lt a ones if desired order edge list by senders and then receivers edges lt edgeslorder edges 1 edgesl 21 Some notes on the commands used here These commands can be used not only if the adjacency matrix contains only 0 and 1 entries but also if it contains values NA 10 or 11 The possibility of NA entries requires special attention 4in does just what we need as it quietly says that NA s are not in anything returning FALSE which is transformed to TRUE by the function The edge list is created having all 0 values and at the end should have no 0 values at all It is more efficient however to work with sparse matrices this also is done internally in RSiena Using the Matrix package for sparse matrix manipulations the same results can be obtained as follows library Matrix tmp lt as a dgTMatrix edges2 lt cbind tmp i 1 tmp j 1 tmp x Conversely if edges is an edge list then the following commands can be used to create the corresponding adjacency matrix called adj with n nodes
169. ger used as argument for print01Report A lot of new effects sameXInPop transRecTrip2 totAlt avInAlt totInAlt totRecAlt totXAlt avXInAlt totXInAlt avAltDist2 totAltDist2 avTAltDist2 totAAltDist2 avXAltDist totXAltDist2 avTXAltDist2 totAXAltDist2 avInAltDist2 totInAltDist2 avTInAltDist2 totAInAltDist2 avXInAltDist2 totXInAltDist2 avTXInAltDist2 totAXInAltDist2 XWX1 XWX2 cl XWX1 cl XWX2 Endowment and creation effects added for gwesp effects Some meaningless effects for two mode networks dropped For non invertible covariance matrices at the end of siena07 give diagnostic for the linear combination that gives trouble Correction of igraphNetworkExtraction in the help page for sienaGOF auxiliary the earlier version dropped isolated nodes from simulated networks In the help page for sienaGOF auxiliary Rd the example of constraint is replaced by the example of eigenvector centrality because constraint is undefined for isolated nodes leading to computational problems Set diagonal of observed networks to 0 in sparseMatrixExtraction sienaRIDynamics restored after corrections file parameter of sienaRI dropped implied platform dependence Section in manual about user defined interaction effects updated Parameter showA11 added to descriptives sienaGOF Small correction of print siena reporting uponly downonly Some changes in print sienaAlgorithm Check in siena07 for incorrect
170. hanges in RSiena and RSienaTest Added function sienaRI for assessment of relative importance of effects with print and plot methods In coDyadCovar and varDyadCovar centering now also is optional by the new option centered like it was done for coCovar and varCovar in revision 1 1 251 Corrected bug when printing siena object with a symmetric network and in varDyad Covar corrected a bug occurring when calling it with a named list Added standard errors as component se to sienaFit objects e Internal changes in the code version 1 1 255 to 1 1 267 see ChangeLog e No noticeable changes from version 1 1 251 to 1 1 254 e 2014 02 13 R Forge Revision 251 It should be noted that two changes were made that potentially have an influence on some results obtained First the effects guespFF gwespBB gwespFB gwespBF gwespRR were modified in RSiena Test to bring them in accordance with the literature This means that the old parameter a was effectively replaced by a log 1 exp a here a is the internal effect parameter divided by 100 For the default a log 2 this means no difference Second in the help page for sienaGOF auxiliary geodesic distances were changed to non directed This makes more sense usually and was done to avoid runtime errors that occurred very rarely Changes in RSiena and RSienaTest New effects cl XWX homXTransTrip homWXClosure and sharedPop Effect cycle
171. hardt S 1973 The structural implications of measurement error in sociometry Journal of Mathematical Sociology 3 85 111 204 Huisman M E and Snijders T A B 2003 Statistical analysis of longitudinal network data with changing composition Sociological Methods amp Research 32 253 287 Huisman M E and Steglich C 2008 Treatment of non response in longitudinal network data Social Networks 30 297 308 Hunter D R 2007 Curved exponential family models for social networks Social Networks 29 216 230 Koskinen J H 2004 Essays on Bayesian Inference for Social Networks PhD thesis Department of Statistics Stockholm University Koskinen J H and Edling C 2012 Modelling the evolution of a bipartite network peer referral in interlocking directorates Social Networks 34 309 322 Koskinen J H and Snijders T A B 2007 Bayesian inference for dynamic social network data Journal of Statistical Planning and Inference 13 3930 3938 Kushner H J and Yin G G 2003 Stochastic Approximation and Recursive Algorithms and Applications Springer New York second edition Lepkowski J M 1989 Treatment of wave nonresponse in panel surveys In Kasprzyk D Duncan G Kalton G and Singh M P editors Panel Surveys pages 348 374 Wiley New York Lomi A Snijders T A B Steglich C and Torlo V J 2011 Why are some more peer than others Evidence from a longitudinal study of soci
172. have effects on popularity or activity in the X network They use an internal effect parameter p which mostly will be 1 or 2 To decrease correlation with other effects the W degrees are centered by subtracting the value w which is the average degree of W across all observations 4 Effect of in degree in W on X popularity X indegree P W popularity inPopIntn defined by the sum of the W in degrees of the others to whom is tied for parameter p 2 the square roots of the W in degrees sia 2 gt Tij 01 0 or for p 2 sia Y zi yar VO Effect of in degree in W on X activity X indegree W activity inActIntn defined by the W in degrees of i for p 2 its square root times s X out degree sig 0 2 Tij Wea 0 xiy 44 0 or for p 2 si X tij Vui 10 zi ui V Effect of out degree in W on X popularity X outdegree W popularity outPopIntn defined by the sum of the W out degrees of the others to whom 7 is tied for param eter p 2 the square roots of the W out degrees sig 2 gt Lij wj w or for p 2 sig 1 0 ty yur V Effect of out degree in W on X activity X outdegree P W activity outActIntn defined by the W out degrees of for p 2 its square root times i s X out degree siy z 27 Tij Wit W Lit Wit W Or for p 2 sip D tij Vwi V ziy Vui VD Effect of both in d
173. he network evaluation function for actor is defined as FR aw gt Bosa 9 k where 62 are parameters and snet z are effects as defined below If the model also contains some elementary effects see Section 5 1 1 the objective function is the sum of this and fa Y sessh a 10 k see Section 5 1 3 Elementary effects are of the type s 5 fij s o where s 2 does not depend on zij The potential effects in the network evaluation function are the following Note that in all effects where a constants c occurs this constant can be chosen and changed by the user this is the internal effect parameter mentioned above which can be modified by the function setEffect parameter For non directed networks the same formulae are used unless a different formula is given explicitly Some of the effects are dropped for non directed networks because they are not meaningful and some of the names differ in the non directed case Structural effects Structural effects are the effects depending on the network only The following list also contains some elementary effects see Section 5 1 1 The type of the elementary effects in RSiena still is eval indicating that its parameter is applied both for creating new ties and for maintaining existing ties 1 out degree effect or density effect density defined by the out degree sii 1 ti4 B Tij where z 1 indicates presence of a tie from to j while z
174. he next opportunity for change one could say this is the focal actor Actor i then has the possibility to change one network tie or to keep the network as it is Denote by C the set of all networks that can be obtained as a result Then the probability of the network obtained from this step depends on something called the objective function u x x which will be defined in a moment The probability that the next network is x is given by exp u x x Laree exp uta 0 y 38 The numerator is required to make all probabilities for this step sum to 1 The objective function is defined as follows If there is only an evaluation function mathematically this means that the creation and endowment functions are 0 then the objective function is equal to the evaluation function for the new state u z z f z Because of the properties of the exponential function one can just as well define the objective function as the gain in evaluation function u x x file fila To define the general case note that if x and z are not the same then they differ in only one tie variable x Define A x z 1 if x has one tie more than z9 meaning that a tie is created by this change and At x z 0 otherwise Similarly define A7 x x 1 if x has one tie less than x meaning that a tie is dissolved by this change and AT 2 x 0 otherwise Then the general definition of the objective function is ula
175. he simulations are totally determined by the parameters and the first observation The second wave then must be present in the data set only because RSiena requires it for estimation and here we are using a function that is originally meant for estimation Parameter values are obtained from the effects object because of the option useStdInits FALSE If the name of the effects object is myeff the current parameter values are obtained from requesting myeff and different values can be specified by assigning the desired value to the vector myeff initialValue myeff include When artificial data sets are generated that have a close link to observed data the restriction that simulations follow the monotonicity patterns that might be present in the data see Section 4 2 3 can be undesirable This restriction can be lifted by using allowOnly FALSE in the call of sienaDependent see the help file for this function This parameter will then set any uponly and downonly flags to FALSE precluding monotonicity constraints The statistics generated which are the statistics corresponding to the effects in the model can be accessed from the sienaFit object produced by siena07 Denoting the name of this object by sim_ans its component sim_ans sf contains the generated deviations from targets As discussed also in Section 6 3 the statistics can be recovered from the deviations and the targets as follows To get the generated statistics without subtrac
176. he three networks is reasonable then the combined analysis may give good estimates In such a case where K networks in the preceding paragraph the example had K 3 are combined artificially into one bigger network it will often be helpful to define K 1 dummy variables at the actor level to distinguish between the K components These dummy variables can be given effects in the rate function and in the evaluation function for ego which then will represent that the rate of change and the out degree effect are different between the components while all other parameters are the same It will be automatically discovered by SIENA when monadic covariates depend only on these components defined by structural zeros between which tie values are not allowed For such variables only the ego effects are defined and not the other effects defined for the regular actor covariates and described in Section 5 4 This is because the other effects then are meaningless If at least one case is missing then the other covariate effects are made available When SIENA simulates networks including some structurally determined values if these values are constant across all observations then the simulated tie values are likewise constant If the structural fixation varies over time the situation is more complicated Consider the case of two consecutive observations m and m 1 and let X oo be the simu lated value at the end of the period from tm to tm 1 If
177. his can be e g because the tie is impossible or formally imposed respectively Structural zeros provide an easy way to deal with actors leaving or joining the network between the start and the end of the observations specify all their incoming and outgoing tie variables at the moment that they are not present as structural zeros Note that actors having all values specified as structural zeros in this way take part of the simulations only starting at the observation moment where they are not totally structurally zero therefore this way of representing partially absent actors is not meaningful for actors who are present only at the very last wave In particular this includes the case where there are two waves only for actors who join the network after the first wave Another way more complicated but more flexible because it gives possibilities to represent actors entering or leaving at specified moments between observations is the method of joiners and leavers described in Section 4 3 3 For actors present only at the last wave the method of joiners and leavers is preferable When endowment or creation effects are to be included in the model specification changing structural values should not be used and the method of joiners and leavers then 30 also is preferable Structurally determined values are defined by reserved codes in the input data the value 10 indicates a structural zero the value 11 indicates a structural one Structur
178. hrough i j W ih Again there is an internal effect parameter p usually 1 or 2 11 12 Effect of W betweenness on X popularity X betweenness W popularity betweenPop defined by the sum of the W betweenness counts of the others to whom is tied 1 p si z gt Tij Dans Whj Wik 1 wne mixed twopath activity effect X twopath W activity outOutActIntn defined by the outdegree of i multiplied by sum of X outdegrees of those to whom 7 has an X tie x for p 1 this is w sits x Ti Dip win Lh 2 gt and for p 2 there is a square root transformation 1 Sita 2 zq Dip ti VZ VE where 7 is the average degree over all waves Further there are a number of mixed triadic effects 122 13 agreement along W leading to X X from W agreement from sia jan Vij Wih Wjh this refers to agreement of actors with respect to their W w W choices structural equivalence with respect to outgoing W e choices the contribution of the tie J is proportional to i j the number of joint W choices of others i KpE j 14 agreement along mutual W ties leading to X X from W mu tual agreement fromMutual sita 2 X jn Vij Wih Whi Wjh Whj this refers to agreement of actors with respect to their mutual w W W choices structural equivalence with respect to mutual W Po s choices the contribution of the tie A j is proportional to the i j number of joint mu
179. hts in the evaluation function can be tested by t statistics defined as estimate divided by its standard error Do not confuse this t test with the t ratio for checking convergence these are completely different although both are t ratios Here the t values are respectively 2 5341 0 1445 17 54 2 1106 0 2625 8 04 0 5449 0 1781 3 06 0 0779 0 3425 0 23 0 4519 0 2497 1 81 Since the first three are larger than 2 in absolute value they are significant at the 0 05 significance level It follows that there is evidence that the actors have a preference for reciprocal and transitive relations For thee cycles the effect is not significant t 0 23 for smoking 65 similarity it is significant at the 0 10 significance level The value of the density parameter is not very important it is important that this parameter is included to control for the density in the network but as all other statistics are correlated with the density the density is difficult to interpret by itself 6 5 3 Collinearity check In the output file the covariance matrix of the estimates is presented This can also be requested by summary ans For conditional estimation the rate parameters of the dependent variables used for conditioning are not included in this matrix In this case the covariance matrix is as follows Covariance matrix of estimates correlations below diagonal 0 021 0 018 0 010 0 006 0 008 0 468 0 069 0 008 0 034 0 002
180. ices based on 1000 iterations 57 Information for convergence diagnosis Averages standard deviations and t ratios for deviations from targets 1 0 2460 16 1494 0 0152 2 0 0560 14 3829 0 0039 3 0 9520 44 5338 0 0214 4 0 5380 14 5726 0 0369 5 0 2080 4 8672 0 0427 Good convergence is indicated by the t ratios being close to zero Overall maximum convergence ratio 0 1608 For example for the fourth parameter 3 cycles the average deviation from the target value was 0 5380 and the standard deviation across the 1000 simulations in Phase 3 was 14 5726 This yields a t ratio of 0 5380 14 5726 0 0369 Large values of the averages and standard deviations are in themselves not at all a reason for concern only the t ratio is important 6 1 3 Continued estimation to obtain convergence Above the prevAns parameter was mentioned which will lead to using the result from a previous estimation as the initial value for the next estimation If convergence is difficult to obtain one may use other settings of the estimation algorithm given as parameters in the sienaAlgorithmCreate function to try and improve convergence The main parameters of sienaAlgorithmCreate that can be used for this purpose are the following For the technical background see Siena_Algorithms pdf which can be downloaded from the SIENA website e doubleAveraging This replaces the Robbins Monro updating step by a double averaging step Bather 1989 Schwabe and W
181. ienaBayes to use overdispersed starting points The difficulty is to get overdispersion while still retaining a reasonable convergence for each sequence The best option currently is to use independent restarts of the whole algorithm or to use one starting point and several continuations using prevBayes In the latter option one uses a long chain instead of parallel chains which is too bad but this is the best we have currently on offer and using monitor on such parts of a long chain still will give an acceptable impression of convergence Function monitor gives information about the potential scale reduction R of the posterior distribution if simulations were continued indefinitely and the effective sample size Neg 1 e the estimated equivalent sample size under independent sampling Rules of thumb given in Gelman et al 2014 p 287 are that for all parameters of interest R lt 1 1 and neg gt 5m where m is the number of chains Note that what is given by monitor as the semean is the standard error of the mean of the posterior distribution as an estimator for the global mean p i e this expresses the uncertainty due to the finite length of the MCMC chain it is not a measure of spread of the posterior distribution itself 11 3 8 Interpreting results of sienaBayes The print and summary functions give posterior means posterior standard deviations 95 credibility intervals and one sided posterior p values for testing
182. ifications of social influence The choice between them will be made on theoretical grounds and or on the basis of statistical significance Do not include them all together in one model as this would most likely lead to multicollinearity and non convergence For each actor dependent covariate as well as for each of the other dependent behavior variables the effects on Z which can be included is the following 1 The main effect a positive value implies that actors with a higher value on the covariate will have a stronger tendency toward high Z values 2 Various effects of the combination of covariate values for members of the personal network of the focal actor outgoing ties incoming ties distance two ties search in this manual for avXAlt avXInAlt avXAltDist2 avXInAltDist2 and their manifold variations 3 Interactions between two or three actor variables see Section 5 8 5 7 Model Type non directed networks Non directed networks are an undocumented option there currently only is the presenta tion Snijders 2007 SIENA detects automatically when the networks all are non directed and then employs a model for this special case For non directed networks the Model Type has five possible values as described in Snijders 2007 This is specified by the parameter modelType in function sienaAlgorithmCreate Value modelType 1 is for directed networks values 2 6 for non directed networks 47 1 Directed networks option mode
183. iles without changing their names Let us use the name NewEffect as the function name to be used replace this by whatever is appropriate e In the file AllEffects h you need to add the line include NewEffect h where it is alphabetically appropriate e In the file EffectFactory cpp at the appropriate place add the lines else if effectName newEf pEffect new NewEffect pEffectInfo e Now you will need to create two files namely header and source files for C that should be called NewEffect h and NewEffect cpp If there is a similar effect to the one you want to add it is usually easier to use it as a template We recommend opening any effect file to see how the syntax works but creating a new effect will be hard without knowing at least a bit of C 5 Once you are done editing you should build the package again and install it from the command prompt and then go to R to see if it is available to you It is a good idea to check the target statistics computed for a simple two wave data set such as s50 162 As examples start with simple effects For example a network effect depending on a nonlinear transformation of outdegree or a behavior effect depending nonlinearly on the behavior and nothing else After having obtained experience with such a simple effect continue with the effect that you are interested in Note that if your new effect could usefully be used as part of a multiple network effect you sho
184. imation is slightly more efficient than unconditional estima tion there is one kind of problem that sometimes occurs with conditional estimation and which is not encountered by unconditional estimation It is possible but luckily rare that the initial parameter values were chosen in an unfortunate way such that the conditional simulation does not succeed in ever attaining the condition required by its stopping rule see Section 6 7 1 The solution is either to use different perhaps standard initial values or to go over to unconditional estimation 6 8 Using multiple processes 1 If multiple processors are available then using multiple processes can speed up the estimation in siena07 2 For estimation by Method of Moments MoM in Phases 1 and 3 the simulations are performed in parallel In Phase 2 multiple viz nbrNodes which is a parameter given in the call of siena07 simulations are done with the same parameters and the resulting statistics are averaged for the updating step in the Robbins Monro algorithm The gain parameter is increased and the number of iterations in phase 2 reduced to take advantage of the increased accuracy of the update When using the MoM decrease in computation time will be somewhat less than proportional to the number of processes used if this number is less than say 10 larger number of processes will have diminishing returns 3 For estimation by Maximum Likelihood ML and by sienaBayes paralle
185. in your MS Word file You can then further modify the table e g change the double minus sign to the MS Word minus sign available under insert symbol and replace the dots for the t stat of the rate parameters by blanks 4 The function siena07 writes an output file which is an ASCII text file that can be read by any text editor It is called pname out where pname is the name specified in the call of sienaAlgorithmCreate This output file is divided into sections indicated by a line 1 subsections indicated by a line 2 subsubsections indicated by 3 etc For getting the main structure of the output it is convenient to have a look at the 1 marks first The primary information in the output of the estimation process consists of the fol lowing three parts 64 6 5 1 Convergence check This was discussed in Section 6 1 2 above 6 5 2 Parameter values and standard errors The next crucial part of the output is the list of estimates and standard errors Suppose that the following result was obtained on the R console Estimate Standard Convergence Error t ratio Rate parameters 0 Rate parameter 6 0742 1 0134 1 eval outdegree density 2 5341 0 1445 0 0571 2 eval reciprocity 2 1106 0 2625 0 0710 3 eval transitive triplets 0 5449 0 1781 0 0584 4 eval 3 cycles 0 0779 0 3425 0 0777 5 eval smoke1 similarity 0 4519 0 2497 0 0400 The rate parameter is the parameter called p i
186. includes user specified interactions e 2009 11 20 R forge revision 25 version number 1 0 8 The default method for estimation is conditional if there is only one dependent variable Movement of behavior variable restricted if all observed changes are in one direction In this case linear change effects removed 202 If all observed changes in a network are in one direction density effects are removed If a behavior variable only takes two values the quadratic effects are not selected by default t statistics appear on print of sienaFit object easier to use xtable method warning if behavior variables are not integers Fixed bug in editing all effects in the GUI Fixed a bug in effect creation for changing dyadic covariates Fixed a bug in returning simulated dependent variables Now fails if there are only two waves but you have a changing covariate In the GUI can just change the type 2009 11 08 R forge revision 24 version Number 1 0 7 2009 11 08 R forge revision 23 corrected bug in creation of effects data frame for multi group projects and for changing covariates added effect numbers to the Estimation screen 2009 11 08 R forge revision 22 new option to edit effects for one dependent variable at a time Model options screen layout altered slightly 2009 11 08 R forge revision 21 Fixed a bug causing crashes but not on Windows due to bad calculation of derivative matrix 2009 10 31 R forge re
187. ing of programming RSiena This was done as part of the project Adolescent Peer Social Network Dynamics and Problem Behavior funded by NIH Grant Number 1R01HD052887 01A2 Principal Investigator John M Light Oregon Research Institute For earlier work on SIENA we are grateful to NWO Netherlands Organisation for Scientific Research for their support to the project Models for the Evolution of Networks and Behavior project number 461 05 690 the integrated research program The dynamics of networks and behavior project number 401 01 550 the project Statistical methods for the joint development of individual behavior and peer networks project number 575 28 012 the project An open software system for the statistical analysis of social networks project number 405 20 20 and to the foundation ProG AMMA which all contributed to the work on SIENA Part I Minimal Intro 1 1 Giving references When using SIENA it is appreciated that you refer to this manual and to one or more relevant references of the methods implemented in the program The reference to this manual is the following Ruth M Ripley Tom A B Snijders Zs fia Boda Andr s V r s and Paulina Preciado 2014 Manual for SIENA version 4 0 version September 10 2015 Oxford University of Oxford Department of Statistics Nuffield College http www stats ox ac uk siena A tutorial is Snijders et al 2010b A basic reference for the network dynamics model is Snijder
188. inue with phase 3 63 6 5 Output Output can be obtained in several ways 1 On the R console When the sienaFit object produced by siena07 is called ans requesting just ans or print ans produces output on the R console The function summary ans produces more extensive output 2 A table in latex or html format can be produced by the xtable sienaFit method For example xtable ans file ansi htm type html produces in the working directory a html file with the ans results in tabular form The xtable package has many further options 3 In package RSienaTest the function siena table is available which serves a similar purpose but not using xtable This function writes the table to a file the default file name of the table produced is the name of the sienaFit object The choice between xtable sienaFit and siena table depends on the preference for the tables produced For importing the results of xtable or siena table into MS Word the following steps can be used Request siena table ans for some sienaFit object called ans in this example This will produce under the default settings the file ans htm in the current working directory Copy paste this into the MS Word file In MS Word then select this table but only the lines of the header and the parameters not any preceding blank line nor the footnote In the MS Word menu choose Insert Convert text to table Autofit to contents This will produce the table
189. ion Let a be the vector with the coefficients of the linear combination Then sum a ans theta is the linear combination t a ans covtheta a is the variance and sqrt t a ans covtheta a is the standard error 76 8 2 Score type tests The Wald test is based on the estimate for the parameter and thereby integrates estima tion and testing Sometimes however it can be helpful to separate these two types of statistical evaluation This is the case notably when estimation is instable e g when a model is considered with rather many parameters given the information available in the data set or when the precise value of the estimate is not determined very well as happens under the Donner Hauck phenomenon treated in the previous section The score type test gives the possibility of testing a parameter without estimating it This is done using the generalized Neyman Rao score test that is implemented for the Method of Moments estimation method in SIENA following the methods of Schweinberger 2012 For the ML estimation method following the same steps produces the Rao 1947 efficient score test Since the name of score test is associated with likelihood based analysis as in Rao 1947 the test of Schweinberger 2012 that is associated with the Method of Moments is called score type test When using the score type test some model is specified in which one or more param eters are restricted to some const
190. ip defined by the number of transitive triplets h gt 7 i that have the same covariate value for and 7 net Si68 T gt Tij Vin Zhj Ilu vj different covariate x transitive triplets diffXTransTrip defined by the number of transitive triplets i gt h gt j i that have different covariate values for i and 7 Sigg 2 22 Tij Lih Enj L Tu FO indegree popularity from same covariate sameXInPop defined by the number of incoming ties received by those to whom 7 is tied and sent by others who have the same covariate value as 1 sio 2 27 Tij Dy Thy Tu Un indegree popularity from different covariate diffXInPop defined by the number of incoming ties received by those to whom 7 is tied and sent by others who have a different covariate value than 2 spi z ar Tij oh Thj Hui Z vn outdegree activity to same covariate sameXOutAct defined by the squared number of ties to those others who have the same covariate value as z sb a X mu ui u outdegree activity to different covariate diffXOutAct defined by the squared num ber of ties to those others who have a different covariate value than 2 she x So ty Hoi Z o outdegree activity to homogeneous covariate homXOutAct defined by the sum of outgoing ties weighted by the number of outgoing ties to those with the same co variate value as alter sira 2 Xj Tij Ep Vin HU vh outdegree activity weighted by alter
191. ipt04SienaBehaviour R illustrates how to specify models for dynamics of networks and behaviour The website contains a lot of other scripts illustrating other functionalities of RSiena 2 5 Steps for looking at results Executing SIENA 1 Look at the start of the output file obtained from print01Report for general data description degrees etc to check your data input and get a general overview of the data set In this file there is a section Change in networks which contains some basic descriptives Some of these refer to the periods these are the combinations of two successive waves For example a two wave data set has one period and a three wave data sets has periods 1 2 and 2 gt 3 The Distance mentioned there is the Hamming distance between successively observed networks i e the number of tie variables that differ The Jaccard index is the Jaccard distance between the successive networks Ni Noi Nio Ni where Npk is the number of tie variables with value h in one wave and value k in the next wave The Jaccard index is a measure for stability see Snijders et al 2010b Both for the Hamming distance and the Jaccard index only those cells in the adjacency matrix are counted that have available data in the wave at the start and the wave at the end of the period concerned If Jaccard indices are very low while the average degree is not strongly increasing this indicates that the turnover in the network
192. istance 2 totAInAltDist2 defined by 1 s behavior multiplied by the total of the incoming alter averages 2 of his alters excluding the contribution from a tie i j if any sg z z zi gt tij S maximum alter effect maxA1t defined by s behavior multiplied by the maximum behavior of his alters sja z z zi max zj zj and the mean behavior ie 0 if gt i 0 minimum alter effect minAlt defined by 2 s behavior multiplied by the minimum behavior of his alters sigo z z zi min wig zj and the mean behavior i e 0 if gt zi 0 dense triads effect behDenseTriads defined by behavior multiplied by the number of dense triads in which actor 7 is located sist z z DEN I z Zi Tip Z Dj nj gt c where c is either 5 or 6 peripheral effect defined by s behavior multiplied by the number of dense triads to which actor stands in a unilateral peripheral relation s32 z z a Zi Diy nk Cig Eji 1 Eri 02 tig HL ji 2in HT pi 2jn nj 2 c where c is the same constant as in the dense triads effect for symmetric networks the unilateral condition is dropped and the effect is sper 2 2 4 Dj np 2i 1 26 1 wea I aig Dji Lin Ta Zjh Zn gt c reciprocated degree effect recipDeg Sesh z z 24 37 Tij Eji average similarity x popularity ego effect avSimPopEgo defined by the sum of centered similarity scores sim b
193. it Corrected conditional estimation for symmetric networks Now do not need to specify the variable to condition on if it is the first in sienaModel Create 2010 06 21 R forge revision 108 effects print method with no lines selected no longer gives error new argument in cludeOnly so you can print lines which are not currently included effectsDocumentation was failing due to timeDummy column New average alter effects Corrected format of error message if unlikely to finish epoch Corrected print report for multiple groups via the GUI and for 8 waves Fixed names for used defined dyadic interactions Fixed bug where SienaTimeTest dummies with RateX would not work with changing covariates 2010 06 21 R forge revision 107 RsienaTest only reinstated includeTimeDummy 2010 06 18 R forge revision 106 new version numbers 1 0 11 105 and 1 0 12 105 for RSiena and RSienaTest respectively 2010 06 18 R forge revision 105 Fixed siena01Gui bug when trying to edit the effects Problem was introduced in revision 81 2010 06 10 Updated time heterogeneity script for Tom 2010 06 08 R forge revision 102 RSienaTest only Removed includeTimeDummy 2010 06 08 R forge revision 101 RSienaTest only Fixed RateX so that it works with chang ing actor covariates as well 2010 06 08 R forge revision 100 corrected revision numbers in ChangeLog 2010 06 08 R forge revision 99 Fix to bug introduced in revision
194. ithm specification object with options for the algorithm and the function siena07 carries out the estimation If you do not want to see the graphical interface with intermediate results or if your computer has problems showing this then add the option batch TRUE as in resultsi lt siena07 algorithmi data mydata effects myeff batch TRUE If you wish to have detailed information at the console about the intermediate steps taken by the algorithm then add the option verbose TRUE as in 54 resultsi lt siena07 algorithml data mydata effects myeff verbose TRUE The estimation produces an output file in the current working directory of which the name is defined by the projname option in this example the name is trypro out To look at the information you may either look at this file which can be opened by any text editor or produce results on the R console A brief summary of the results is given in the R console by typing the name of the sienaFit object For example results1 could give a summary such as Estimates standard errors and convergence t ratios Estimate Standard Convergence Error t ratio Rate parameters 0 Rate parameter 6 0803 1 0220 1 eval outdegree density 2 5270 0 1589 0 0152 2 eval reciprocity 2 1021 0 3038 0 0039 3 eval transitive triplets 0 5470 0 1988 0 0214 4 eval 3 cycles 0 0805 0 3845 0 0369 5 eval smokel similarity 0 4400 0 2560 0 0427 Overal
195. ity effect for the same reasons as mentioned above for the sqrt measure of the popularity effect reciprocal degree related popularity effect reciPop defined by the sum of the re ciprocal degrees of the others to whom is tied set a2 yumaq where the reciprocal degree is defined by r ee T gt h Z jhZhj reciprocal degree related popularity sqrt effect reciPopSqrt defined by the sum of the square roots of the reciprocal degrees of the others to whom 7 is tied 109 29 30 31 32 33 34 35 D a where the reciprocal degree is defined as above for non directed networks the popularity and activity effects are taken together as degree effects since in degrees and out degrees are the same in this case in degree related activity effect inAct defined as the cross product of the actor s in and out degrees 5359 2 Ti T i endowment effect only likelihood based in degree related activity sqrt effect inActSqrt defined by 8730 T Ziy VZ in isolate Outdegree effect inIsDegree the additional out degree or activity effect for actors with in degree zero defined as the out degree but only if the actor has in degree zero sist x z Huy 0 yy Tij out degree related activity effect outAct defined as the squared out degree of the actor 685 a oes endowment effect only likelihood based out degree related activity sqrt effect outActSqrt
196. j counting only those for which v vj vp 126 26 27 28 mized WW X closure same V path jumping to different V X W closure jumping V jumpWWClosure G specified with interactionl W interaction2 V s126 2 Di jen Vij Win Whj Tv Un Z vj w w this refers to the closure of W W paths restricted to jump eS outside of V groups in the sense that the focal actor and the i X j mediating actor have the same value of V but the target actor has a different value mized WX X closure same V path jumping to different V h X mixed W closure jumping V jumpWXClosure specified with interactionl W interaction2 V s137 2 X jp Tij Win hj Ilu vn Z 05 w x this refers to the closure of W X paths restricted to jump e gt o outside of V groups in the sense that the focal actor and the i X j mediating actor have the same value of V but the target actor has a different value mixed WX gt X closure homogeneous on V X mixed W h closure homog V homWXClosure specified with interactionl W interaction2 V sizs 2 D jp Vij Win rj T Vi uj un w x this refers to the closure of W X paths restricted to triples Il o that are homogeneous with respect to V i X j There are two effects similar to the effects described above depending on the auxiliary variable 0 alters v average Now the alter is defined however by the other networ
197. k W Thus W alters v average yr is defined by 29 gt Wig Wi covariate alter at W distance 2 altDist2W This effect is associated with an effect parameter which can have values 1 or 2 For parameter 1 it is defined as the sum of W alters covariate average over all actors to whom 1 has a tie sing 1 y aay parameter 1 j For parameter 2 it is defined similarly but for an alters covariate average excluding ego sing z gt myin parameter 2 j 127 30 31 32 nj WihUh _W i if wy 04 gt 0 0 if tDj Wii 0 total covariate alter at W distance 2 totDist2W This effect is like the previous effect but now defined defined as the sum of W alters covariate total over all actors to whom 7 has a tie For parameter 1 it is sigo 1 y Lij Lj4 uy parameter 1 j For parameter 2 it is defined similarly but for an alters covariate total excluding ego 339 z gt Tij 254 Zi ae parameter 2 j y _W i where and Cy are as above ego alter W distance 2 covariate similarity simEgoDist2W defined as the sum of centered similarity between 7 and alters covariate average for all actors j to whom i has a tie EA sisi z Y Ej simo sim j where the similarity scores sim v are defined as _ A l W ij A sim v while A max v u is the observed range of the original covariate v i
198. ks In prepa ration Transparencies available at internet Snijders T A B and Baerveldt C 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 and Bosker R J 2012 Multilevel Analysis An Introduction to Basic and Advanced Multilevel Modeling London Sage 2nd edition Snijders T A B Koskinen J H and Schweinberger M 2010a Maximum likelihood estimation for social network dynamics Annals of Applied Statistics 4 567 588 Snijders T A B Lomi A and Torlo V 2013 A model for the multiplex dynamics of two mode and one mode networks with an application to employment preference friendship and advice Social Networks 35 265 276 Snijders T A B Pattison P E Robins G L and Handcock M S 2006 New specifications for exponential random graph models Sociological Methodology 36 99 153 Snijders T A B Steglich C E G and Schweinberger M 2007 Modeling the co evolution of networks and behavior In van Montfort K Oud H and Satorra A editors Longitudinal models in the behavioral and related sciences pages 41 71 Mahwah NJ Lawrence Erlbaum Snijders T A B van de Bunt G G and Steglich C 2010b Introduction to actor based models for network dynamics Social Networks 32 44 60 Snijders T A B and van Duijn M A J 1997 Simulation for statistical i
199. l maximum convergence ratio 0 1608 Requesting a longer summary by a command such as summary results1 will produce more information including e g the covariance correlation matrix of the estimators Convergence check The column Convergence t ratio shown above also called t statistics for deviations from targets is an indicator of convergence If some of these values are higher in absolute value than 0 1 convergence is not adequate The value Overall maximum convergence ratio is another stricter indicator of convergence For adequate convergence this value should be less than 0 25 In this example convergence is good If convergence is not adequate the estimation must be repeated Usually the best way to do this is by employing the argument prevAns in the call of siena07 Given that the earlier result was already called results1 this is done e g by resultsi lt siena07 algorithmi data mydata effects myeff prevAns results1 Further see below for more information about convergence 55 6 1 1 Initial Values The initial values can be given in three ways 1 The default if useStdInits FALSE and no prevAns parameter is given in the call of siena07 the initial values are taken from the sienaEffects object in this example called myeff Requesting myeff will show the initial values As long as no time dummies have been requested using siena TimeFix the initial values for the requested effects are i
200. lization goes by period for multi group projects period x group Therefore for this type of estimation the maximum meaningful number of parallel processes is number of waves 1 x number of groups 4 The parameters required to run all processes on one computer are fairly simple in your call to siena07 set nbrNodes to the number of processes and useCluster and 70 10 11 initC to TRUE The Model Options screen also allows you to specify the number of processes and will automatically set the other required parameters for you To use more than one machine is more complicated but it can be done by using in addition the clusterString parameter The computers need to be running incoming ssh For machines with exactly the same layout of R directories on each simply set clusterString to a character vector of the names of the machines For other cases e g using Macs alongside Linux see the documentation for the package parallel RSiena uses sockets for inter process communication On Windows sub processes are always started using R scripts On Linux and Mac there is an option available in R version 2 14 0 or later via the code interface to siena07 to ask for the sub processes to be formed by forking See the help page for details Each process needs a copy of the data in memory If there is insufficient memory available there will be no speed gain as too much time will be spent paging In each ite
201. llowing We use the example on one of the following pages where an average similarity effect on drinking is reported of beh 3 9689 where drinking has a range of r 5 1 4 For an individual all of whose friends drink more than this individual does the contribution of friends influence to the odds of an increase in drinking as compared to no change is a factor exp 3 9689 4 2 7 In this formulation the condition in the event of a ministep with respect to drinking behavior is left implicit In the same situation if hypothetically a total average similarity effect were found of 0 82 then one could say that having one additional friend who drinks more than oneself increases the odds of an increase in drinking as compared to no change by a factor exp 0 82 4 1 23 In general parameters for the total similarity effect will tend to be smaller than those for the average similarity effect because the former refer to comparisons about a single friend and the latter to comparisons about all friends 13 3 Ego alter selection tables When some variable V occurs in several effects in the model then its effects can best be understood by considering all these effects simultaneously For example if in a network dynamics model the ego alter and similarity effects of a variable V are specified then the formulae for their contribution to the evaluation function can be obtained from the components listed in Section 12 1 1 as Bego
202. lly obtained parameters should be such that the expected values of the statis tics are equal to the observed values Expected values are approximated as the averages over a lot of simulated networks Observed values are calculated from the data set These are also called the target values 2 To find these parameter values an iterative stochastic simulation algorithm is ap plied This works as follows a b In Phase 1 the sensitivity of the statistics to the parameters is roughly deter mined In Phase 2 provisional parameter values are updated iteratively this is done by simulating a network according to the provisional parameter values calculating the statistics and the deviations between these simulated statistics and the target values and making a little change the update in the parameter values that hopefully goes into the right direction A lot of such updating steps are taken each using the parameter that was produced in the preceding step Only a hopefully good update is possible because the simulated network is only a random draw from the distribution of networks and not the expected value itself In Phase 3 the final result of Phase 2 is used and it is checked if the average statistics of many simulated networks are indeed close to the target values This is reflected in the so called overall maximum convergence ratio and the t statistics for deviations from targets If some of these are too high
203. lue of the changing covariates is assumed to be valid for the period from moment tm to moment tm41 The value at tm the last moment does not play a role Constant dyadic covariates are specified using function coDyadCovar and changing dyadic covariates by varDyadCovar The mean is always subtracted from the covariates See Section 4 2 2 on centering 27 4 2 Internal data treatment 4 2 1 Interactions and dyadic transformations of covariates For actor covariates also called monadic covariates two kinds of transformations to dyadic covariates are made internally in SIENA Denote the actor covariate by v and the two actors in the dyad by i and j Suppose that the range of v i e the difference between the highest and the lowest values is given by ry The two transformations are the following 1 dyadic similarity defined by 1 v v rv and centered so the mean of this similarity variable becomes 0 note that before centering the similarity variable is 1 if the two actors have the same value and 0 if one has the highest and the other the lowest possible value the mean of the similarity variable is calculated by function sienaDataCreate and stored as the simMean attribute of mydata cCovars myvar where mydata is the name of the object created by sienaDataCreate and myvar is the name of the variable used as the argument for sienaDataCreate while the name cCovars applies for constant monadic covariates and is to be replac
204. mber of mixed X W two paths 385 So the dependent variable here is only the tie variable j in the figure above The effect is defined as Sira taj Orina Tin Why 3 18 XWX closure 2 of W c1 XWX2 h This is an elementary effect not an evaluation effect compris ing of the XWX closure of W effect only the contribution of x Ww the number of mixed X W two in stars i h j W h In other words only the i gt j tie in the figure here is the de er pendent variable The effect is defined as J sta z Tij ha Tih Wjh 19 mixed WW gt X closure X closure of W closure Siig 2 D jn Vij Win Whj 3 i this refers to the closure of W W two paths the contribution of the tie i 3 j is proportional to the number of W W two w w paths i LAW e The interpretation is that actors have the tendency to make a j and maintain X ties to those to whom they have an indirect distance 2 W tie W ties of W ties tend to become X ties 20 mixed cyclic WW gt X closure X cyclic closure of W cyClosure 3 0 s30 z D ith Tij Wjh Whi this refers to the cyclic closure of W W two paths the contri w Ww bution of the tie i j is proportional to the number of W W o o W W xX two paths j gt h gt i 1 j The interpretation is that actors have the tendency to make and maintain X ties to those from whom they receive an in direct distance 2 W tie W ties of W
205. me type evaluation endowment or creation effects Examples of the use of includelnteraction are as follows myeff lt includeInteraction myeff egoX recip interactionl c smokei myeff lt includeInteraction myeff egoX egoX interaction c smoke1 alcohol Note the interaction1 parameter this parameter is used also when defining these effects using includeEffects or setEffect In this case however two effects are defined and ac cordingly the interaction1 parameter has two components combined by the c function For effects such as recip that have no interaction1 parameter the corresponding string is just the empty string Note that the name interaction1 does not itself refer to interactions in the sense of this section Interactions between three effects are defined similarly but now the interaction1 parameter must combine three components The list of effects in Chapter 12 contains a variety of interaction effects that cannot be created in this way for example those with short names transRecTrip simRecipX avSimEgoX and covNetNet there are many more 49 5 8 2 Interaction effects for behavior dynamics For behavior dynamics interaction effects can be defined by the user for each dependent behavior variable separately as interactions of two or three actor variables again using the function includelnteraction These are interactions on the ego level in line with the actor oriented nature
206. minimal dataset suitable for analysis with SIENA consists of two observations of a 10 single network defined on the same set of nodes In this case one is able to test how the structure of the network contributes to its own evolution However depending on the data available further modeling options may be applicable Currently the implemented Stochastic Actor Oriented Models are suitable for the analysis of 1 the evolution of a directed or undirected one mode network e g friendships in a classroom Snijders 2001 2 the evolution of a two mode network e g club memberships in a classroom the first mode is constituted by the students the second mode by the clubs Koskinen and Edling 2012 3 the evolution of an individual behavior e g smoking and 4 the co evolution of one mode networks two mode networks and individual behaviors e g the joint evolution friendship and smoking or of friendship and club member ship Steglich et al 2010 Snijders et al 2013 In all these cases the data can also include covariates observed variables that influence the dynamics but of which the values are not themselves modeled In the first two cases one can assess with SIENA the ways and the extent to which changes in a given one or two mode network depend on the network structure itself and on covariates The third option modeling changes in an individual behavior on its own without reference to its embeddedness in a net
207. n section 12 1 4 below The value 6 0742 indicates that the estimated number of opportunities for change per actor note that each actor corresponds to a row in the adjacency matrix between the two observations is 6 07 rounded in view of the standard error 1 01 Note that this refers to unobserved changes and that some opportunities for change lead to the decision no change and moreover some of these changes may cancel make a new choice and then withdraw it again so the average observed number of differences per actor will be smaller than this estimated number of unobserved changes The other five parameters are the weights in the evaluation function The terms in the evaluation function in this model specification are the out degree effect defined as s 1 in Section 12 1 1 the reciprocity effect sj2 transitive triplets effect s 3 three cycles effect Si5 sex similarity effect sig Therefore the estimated evaluation function here is 2 53 si x 2 11 Si2 x 0 54 siz x 0 08 15 z 0 45 Sis3 x where again some rounding was applied in view of the standard errors The parameter estimates can be combined with the standard errors to test the parameters Testing of parameters is discussed more extensively in Chapter 8 For the rate parameter testing the hypothesis that it is 0 is meaningless because the fact that there are differences between the two observed networks implies that the rate of change must be positive The weig
208. n starting from an initial parameter value that is far from the true parameter estimate A too high value implies that the algorithm will be unstable and may be thrown off course into a region of unreasonable e g hopelessly large parameter values When using the Method of Moments the default estimation procedure it usually is unnecessary to change this In the ML case when the autocorrelations are smaller than 0 1 but thet statistics for deviations from targets are relatively small less than say 0 3 but do not all become less than 0 1 in absolute value in repeated runs of the estimation algorithm then it will be good to decrease the initial value of the gain parameter Do this by dividing it by e g a factor 2 or a factor 5 and then try again a few estimation runs 6 7 Other remarks about the estimation algorithm 6 7 1 Conditional and unconditional estimation SIENA has two methods for MoM estimation and simulation conditional and uncondi tional They differ in the stopping rule for the simulations of the network evolution In unconditional estimation the simulations of the network evolution in each time period and the co evolution of the behavioral dimensions if any are included carry on until the predetermined time length chosen as 1 0 for each time period between consecutive observation moments has elapsed In conditional estimation in each period the simulations run on until a stopping crite rion is reached that is
209. n the number of the wave minus 1 here 1 because there are supposed to be 2 waves This type of information can be found out by requesting str sim_ans sims 568 Section 4 1 2 explains how such an edgelist can be transformed to an adjacency matrix Determine number of actors normally the user will know this n lt length mydata nodeSets 1 create empty adjacency matrix adj lt matrix 0 n n Make shorter notation for edge list edges lt sim_ans sims 856 1 111 1 put edge values in desired places adjledges 1 2 lt edges 3 As an example the following commands turn this list into a list of edgelists according to the format of the sna package Butts 2008 and then calculate the maximum k core numbers in the networks This assumes that a one mode network is being analyzed 84 First define a function that extracts the desired component from the list element gives the column names required for sna edgelists and adds the attribute defining the number of nodes in the graph as required by sna make edgelist sna lt function x n x lt x 1 1 1 colnames x lt c snd rec val attr x n lt n x Apply this function to the list of simulated networks simusnas lt lapply sim_ans sims make edgelist sna 50 Define a function that calculates the largest k core number in the graph library sna max kcores lt function x max kcores x
210. n the vector myeff initialValue myeff include Changing these values is not often necessary because the parameter prevAns as explained in the next item does this behind the scenes If one does wish to change the initial values contained in the effects object this can be done using the function updateTheta which copies the estimates from earlier results contained in a sienaFit object to the effects object For a single effect the initial value can be changed by the setEffect function in which the initialValue then must be set 2 If useStdInits FALSE and the prevAns previous answer parameter is used such as in resultsi lt siena07 algorithml data mydata effects myeff prevAns results0 the initial parameter estimates are taken from the results of what is given as the prevAns parameter This must be a sienaFit object in this example it is given as results0 If the specification of the effects object used to obtain results0 was the same as myeff then not only the initial values are copied but also Phase 1 of the algorithm is skipped because information for the sensitivity of the statistics with respect to the parameters is taken from the results of Phase 3 of results0 If the specification of the effects object used to obtain results0 was not the same as myeff then for those parameters that do match the initial values are copied from results0 and Phase 1 is carried out as usual 3 If useStdInits TRUE is u
211. na binary or source file so that this is the current directory Then the pathname consists only of the filename e In R from binary for Windows install packages pathname to RSienaTest_1 1 289 zip repos NULL type binary for Mac install packages pathname to RSienaTest_1 1 289 tgz repos type binary e In R from source NULL install packages RSienaTest_1 1 289 tar gz repos NULL type source e In command com or in batch mode Windows from binary R CMD INSTALL RSienaTest_1 1 289 zip e In the terminal Mac from binary R CMD INSTALL RSienaTest_1 1 289 tgz e In command com or in batch mode Windows or in the terminal Mac from source R CMD INSTALL RSienaTest_1 1 289 tar gz e In drop down menu in R for Windows go to Packages Install package s from local zip file for Mac go to Packages amp Data Package Installer e In RStudio go to Tools Install packages Install From Package archive file zip tar gz 2 3 Using SIENA within R 1 Load data networks behavior covariates into R see Section 4 1 a Network data should be in objects of class matrix or sparse matrix edgelist b Behavioral data should be in objects of class matrix Oo Individual constant covariates should be in objects of class vector or should be in columns or rows of a matrix d Individual varying covariates should be in objects of class matrix e Dyadic covariates should be in o
212. nce or catalogue for the user to employ Stochastic Actor Oriented Models SAOM to analyze network dynamics in R The functions are presented in execution order more or less as they would be used in practice A list of useful R functions to read and prepare the data set is also included at the beginning In all cases examples on how to use these functions are provided In the syntax column when arguments of functions are followed by and a single option this is the default option The descriptions provided are suitable for beginner and intermediate R and Siena users For the advanced specifications of the functions the user should refer to the help by typing funName in the R console where funName is the name of the function We consider that the model estimation is composed by 6 stages 1 Getting started 2 Get the data the right format or check that it is in the correct format 3 Data specification 4 Model specification 5 Model estimation 6 Working with the results Tables 3 and 4 present the list of useful R functions and the list of RSiena functions in execution order respectively 169 1 pio uomnno x UI Y WO SUOIPPUNJ nJ sn lq T uordo nuou Y BIA qe reA OsTy Xn Poypo ayy Aq yoolqo PIO ayy sooejdor y pue mopurm e Sutusdo Aq X 35 qo oy SULYPO smoy sy00po xy x xU y v x 399 qo Jo UOISUQUIP y SUINIIY T3ou uup x uup wp Z ST
213. nd setEffect are only eval creat and endow In Chapter 12 almost all effects are evaluation effects and the effects that are elementary and not evaluation effects are mentioned as such h focal actor is 2 ties that lead to the closure are i gt j andi gt h but the a W 0 i J 5 1 2 Specification in SIENA The model specification is defined in SIENA by the so called effects object which formally is an object of class sienaEffects or for multiple groups as discussed in Chapter 11 of class sienaGroupEffects This object is originally created by the function getEffects and subsequently modified by the functions includeEffects and or setEffects The scripts on the SIENA website give examples An important ingredient here is the so called shortName of each effect which is used to identify it effects of covariates need in addition the name of the covariate because the shortName does not specify the covariate If there are several dependent variables networks and or behavioral variables the variable name name also is required to specify the effect The shortNames are part of the effects object For the practical use of SIENA the shortNames are important A list of effects with their shortNames can be displayed in a browser by using the function 37 effectsDocumentation For example the command cbind myeff effectName myeff type myeff shortName 1 20 gives a list of the first 20 effects in the myeff object As anothe
214. nding and adding an effect 18 1 Example adding the truncated out degree effect 18 2 Notes on effectGroups and two mode networks A List of Functions in Order of Execution B Changes compared to earlier versions C References 161 163 167 169 180 204 1 General information SIENA shorthand for Simulation Investigation for Empirical Network Analysis is a set of methods implemented in a computer program that carries out the statistical estimation of models for repeated measures of social networks according to the Stochastic Actor oriented Model SAOM of Snijders and van Duijn 1997 Snijders 2001 Snijders et al 2007 Snijders et al 2010a and Greenan 2015 also see Steglich et al 2010 A tutorial for these models is in Snijders et al 2010b A website for SIENA is maintained at http www stats ox ac uk snijders siena At this website publications tab you shall also find references to introductions in vari ous other languages as well as the file Siena_algorithms pdf which gives a sketch of the main algorithms used in RSiena The website further contains references to many pub lished examples example scripts illustrating various possibilities of the package course announcements etc This is a manual for RSiena which also may be called SIENA version 4 0 the manual is provisional in the sense that it is continually being updated taking account of updates in the package RSiena is a contributed pa
215. ned by its behavior multiplied by the average of the alter averages i of his alters excluding the contribution from a tie j i if any defined by Tih Uh i _ Logia Yh if tj gt 97 de O 27 0 if zj zji 0 also see 15 and 24 sa 2 2 aly ty E Tij and the mean behavior i e 0 if the ratio is 0 0 this is similar to avAltDist2 but now for covariate V instead of the behavior Z alter s distance two covariate total effect on behavior z totXAltDist2 defined by 1 s behavior multiplied by the total of the alter totals on V of his alters excluding the contribution from a tie j i if any dhea 21 Big Lrt 24 Dy ig eya OE this is similar to totAltDist2 but now for covariate V instead of the behavior Z 138 47 48 49 50 5l 52 average total covariate alter effect at distance 2 avTXA1tDist2 defined by 1 s behavior multiplied by the average of the alter totals on V of his alters excluding the contribution from a tie j gt i if any sto z a Zy zy z zi OE 1 mu and the mean behavior i e 0 if the ratio is 0 0 this is similar to avTA1tDist2 but now for covariate V instead of the behavior Z total average covariate alter effect at distance 2 totAXAltDist2 defined by 1 s behavior multiplied by the total of the alter averages on V of his alters excluding the contribution from a tie j gt i if any sto 2 2 14 P this i
216. negligible but also not a very strong influence Parameters of the objective function For parameters of the objective function it will be usually be possible to use some prior knowledge together with neutrality with respect to the sign of tested parameters in order not to unduly bias results In most cases the outdegree parameter is expected to be negative and the reciprocity parameter positive The researcher should consider 98 earlier studies of similar network dynamics reasonable values for the prior mean for the outdegree parameter might be 2 or 1 and for the reciprocity parameter 1 5 or 2 For homophily parameters on important attributes expressed by the simX effect which is standardized as long as these are regarded as control effects one might specify the prior mean conservatively as 0 3 or 0 5 Since many SIENA parameters are defined in such a way that they have values in the range between 1 and 1 a prior variance in the range from 0 02 to 0 5 would often be reasonable but it will be good to consider earlier studies to have a good grounding for this choice Continuing the example above if the 5 varying non rate parameters would start with an outdegree and a reciprocity parameter the prior means and prior variances could be modified e g to m7 lt c 4 5 2 1 5 0 0 0 S7 lt matrix 0 7 7 diag S7 lt c 2 2 1 0 3 0 2 0 1 0 1 11 3 6 Operation of sienaBayes In Section 11 3 4 it was alread
217. nference in dynamic network models In Conte R Hegselmann R and Terna P editors Simulating Social Phenomena pages 493 512 Springer Berlin Steglich C E G Snijders T A B and Pearson M A 2010 Dynamic networks and behavior Separating selection from influence Sociological Methodology 40 329 393 206 Steglich C E G Snijders T A B and West P 2006 Applying SIENA An illustra tive analysis of the coevolution of adolescents friendship networks taste in music and alcohol consumption Methodology 2 48 56 van de Bunt G G 1999 Friends by choice An actor oriented statistical network model for friendship networks through time Amsterdam Thesis Publishers van de Bunt G G van Duijn M A J and Snijders T A B 1999 Friendship networks through time An actor oriented statistical network model Computational and Mathematical Organization Theory 5 167 192 Veenstra R Dijkstra J K Steglich C and Van Zalk M H 2013 Network behavior dynamics Journal of Research on Adolescence 23 3 399 412 Viechtbauer W 2005 Bias and efficiency of meta analytic variance estimators in the random effects model Journal of Educational and Behavioral Statistics 30 261 293 Viechtbauer W 2010 Conducting meta analyses in R with the metafor package Journal of Statistical Software 36 3 1 48 Zeggelink E P 1994 Dynamics of structure an individual oriented approach Social Netw
218. ng convergence problems even after repeated estimations using the prevAns parameter and trying out various settings for the algorithm as suggested in the preceding sections this may have several reasons 59 e The data specification was incorrect e g because the coding was not given prop erly e The starting values were poor Try restarting from the standard initial values a certain non zero value for the density parameter and zero values for the other pa rameters or from values obtained as the estimates for a simpler model that gave no problems The initial default parameter values can be obtained by choosing the model option standard initial values e The model does not fit well in the sense that even with well chosen parameters it will not give a good representation of the data This can be the case e g when there is a large heterogeneity between the actors which is not well represented by effects of covariates The out degrees and in degrees are given in the begin of the SIENA output to be able to check whether there are outlying actors having very high in or out degrees or a deviating dynamics in their degrees Strong heterogeneity between the actors will have to be represented by suitable covariates if these are not available one may define one or a few dummy variables each representing an outlying actor and give this dummy variable an ego effect in the case of deviant out degrees and an alter effect in the case of
219. ng ini tialization phase check for large initialEstimates done only for non rate parameters e 2015 07 18 Revision 288 Changes in RSiena and RSienaTest plot sienaRl new parameter actors proportions with piechart improved hopefully effect of parameter radius changed siena table does no more produce the double minus sign in html output Changes in RSiena 180 Correction of error for two mode networks in sienaGOF Changes in RSienaTest New effects homXOutAct FFDeg BBDeg RFDeg diffXTransTrip sameXInPop and diffXInPop also added for two mode networks but they are not dyadic In names of behavior effects and statistics dropped the redundant parts behavior and beh sienaBayes new parameter nSampRates correction in use of prevBayes more efficient calculation of multivariate normal density Small changes in HowToCommit tex e 2015 05 21 and 2015 06 02 Revision 286 Changes in RSiena and RSienaTest SienaRIDynamics dropped from RSiena it still has an error retained in RSienaTest Changes in RSienaTest Correction of error for two mode networks in sienaGOF e 2015 05 20 Revision 285 Changes in RSiena and RSienaTest tmax added to sienaFit objects and tconv max mentioned in print sienaFit sienaAlgorithmCreate has new arguments n2start truncation doubleAveraging standardizeVar this leads to various changes in phase2 r Diagonalization corrected matrix transpose phase2 r
220. nged example on sienaNet help page to stop it masking data files in the package 190 Example on sienaGOF page now runs RSiena Test only profileLikelihood RSienaTest only returns its object invisibly ie it does not print when not assigned but can be assigned 2012 12 23 R forge revision 221 RSiena and RSienaTest changed version check to cope with R version 3 0 0 2012 07 05 R forge revision 219 for RSienaTest only Further changes to bayes Additional effects connected with triadic closure interacting with covariates Some networks from Chris Baerveldt s data set added as data objects N34 and HN34 2012 06 11 R forge revision 217 for RSiena Test only Preliminary updates to sienaGOF to put more power in the hands of the user user may now extract more than one dependent variable from the dataset 2012 06 07 R forge revision 216 for RSiena Test only New effects connected with isolates and with mixed WWX triadic closure in various patterns for dyadic covariates as well as multiple dependent networks Modifications to bayes seems to run OK now except that multiple groups option does not work for dyadic covariates still not documented for general use 2012 05 18 R forge revision 213 for RSienaTest only Allow observed networks to have density 0 or 1 not that it is generally advisable to use such data sets Incorporated argument simOnly in sienaModelCreate to facilita
221. nges in warning message in siena07 New effects reciPop reciAct in3Plus maxAlt minAlt transTripl transTrip2 Effect antiInIsolate2 got alias in2Plus inPop is dyadic effect except for non directed networks it is gt 2ij Op Zhj 1 egoX added as effect for non directed networks can be important for representing effects of group level covariates in multi group analyses Components IActors and expectedl added to sienaRI and print sienaRI The check for MaxDegree when running siena07 now works properly also for siena Group objects Manual introduces the term elementary effects Changes in RSienaTest 182 sienaBayes the stop caused by singularity of the precision matrix after the multi group estimation now is circumvented still a warning is printed to the screen sienaBayes option priorRatesFromData changed to values 0 1 2 with 0 former FALSE 1 former TRUE 2 robust estimation of prior for rate parameters from estimates at the end of initialization phase Correction of print summary sienaBayesFit for models with more than one dependent variable e 2014 11 19 R Forge Revision 280 Changes in RSienaTest Small changes in help pages for sienaGOF and for sienaCompositionChange New parameters nSampVarying and nSampConst in sienaBayes e 2014 11 13 R Forge Revision 279 Changes in RSiena and RSienaTest Effect AltsAvAlt renamed to avXAlt Effects object no lon
222. not all three because this leads to collinearity 130 12 1 4 Network rate function The network rate function A t lambda is defined for Model Type 1 which is the default Model Type as a product X p a g m NEA of factors depending respectively on period m actor covariates and actor position see Snijders 2001 p 383 The corresponding factors in the rate function are the following 1 The dependence on the period Rate can be represented by a simple factor net _ net An Pm for m 1 M 1 If there are only M 2 observations the basic rate parameter is called p 2 The effect of actor covariates RateX with values vp can be represented by the factor MS exp 2 an Uns h 3 The dependence on the position of the actor can be modeled as a function of the actor s out degree outRate in degree inRate and number of reciprocated re lations recipRate the reciprocated degrees Define these by Ti 5 Tij Thi gt Lyi Li r gt Tj ji j j j recalling that z 0 for all i The contribution of the out degrees to A t is a factor exp Qp Ti if the associated parameter is denoted a for some h and similarly for the contribu tions of the in degrees and the reciprocated degrees Nonlinear dependence of the exponent on out degrees can also be specified e inverse outdegree effect outRateInv Denoting again the corresponding parameter by a but always for diff
223. ntaining integer numbers The diagonal values are meaningless but must be present In the case of a two mode network which is a network with two node sets and all ties are between the first and the second node set the matrix does not have to be square as usually the number of nodes in the first set will not be equal to the number of nodes in the second set and if it would be square the diagonal still would be meaningful Although this section talks only about digraphs directed graphs for one mode networks it is also possible that all observed adjacency matrices are symmetric This will be automatically detected by SIENA and the program will then utilize methods for non directed networks The values of the ties must be 0 1 or NA not available missing or 10 or 11 for structurally determined values see below The help file for sienaDependent shows by examples how the specification can be given by sparse matrices 2 Pajek format These can be used in sienaDataCreateFromSession If the digraph data file has extension name net then the program assumes that the data file has Pajek format The file should relate to one observation only and should contain a list of vertices using the keyword Vertices together with currently a list of arcs using the keyword Arcs followed by data lines according to the Pajek rules These keywords must be in lines that contain no further characters An example of such input files is given in th
224. ntial random graph models ERGMs by Snijders et al 2006 in the parametrisation of Hunter 2007 The gwespFF ef fect is an alternative expression for transitivity This concept here is specified in an actor based way by counting configurations in the local neighbourhood of a given actor rather than in the tie oriented way of the models in the ERGM family for which the GWESP statistic was first developed The actor based gwespFF effect is defined in direct analogy to the corresponding global statistic of Hunter 2007 by n 2 GWESPFF i a Y e 1 1 e7 EPFFix 12a k 1 where EPFF for edgewise partners is the number of nodes j such that i gt j and there are exactly k other nodes h for which there is the two path i gt h gt j An equivalent way of writing this is GWESPFF i a Y ziy e 1 t se s as l 12b j 1 where the convention is used that z 0 for all j The parameter q is a tuning parameter that may range from 0 to oo The internal effect parameter is defined as 100 x a For all a it holds that GWESP 0 a 0 GWESP 1 a 1 and GWESP k a increases with k to a maximum slightly less than e For a 0 the coefficients e 1 1 e are equal to 1 for all 107 k gt 1 and for a gt co they tend to k Since we can write n 2 gt LihThjtij gt k EPik jh k 1 this implies that for a oo the regular number of transitive triplets is approached while for
225. ntioned here This is explained in Section 11 1 A difference between options 1 and 2 is that the use of structural zeros option 1 will lead to a default specification where the rate parameters are equal across networks this can be changed by making the rate dependent upon dummy actor variables that indicate the different networks whereas the multi group option yields rate parameters that are distinct across different networks In this option the assumption is made that all parameters are the same for the various networks except for the basic rate parameters and except for explicitly specified interaction effects between variables depending on the sub project and other effects Usually option 2 is preferable to option 1 3 Analyzing the different networks separately without any assumption that parame ters are the same but using the same model specification and post processing the output files by a meta analysis using siena08 This is explained in Section 11 2 4 Combining different sub projects into one multi group project as in option 2 but analyzing this by sienaBayes This is explained in Section 11 3 Here the assumption for the parameters is that all basic rate parameters may differ arbitrarily between the sub projects for the other parameters some are identical and others vary randomly across sub projects according to a multivariate normal distribution The distinction between some and others here is made by
226. o the uncertainty of the population mean 101 12 Mathematical definition of effects The list of all effects available for any data set is obtained by the command effectsDocumentation which produces a html file For a given effects object say with the name myeff the command effectsDocumentation effects myeff will give a file with all effects implemented for this effects object See effectsDocumentation for further options This chapter present the mathematical formulae for the definition of the effects Fur ther background to these formulae can be found for network dynamics in Snijders 2001 2005 Snijders et al 2010b for network and behavior dynamics in the last reference and Steglich et al 2010 and for co evolution of multiple networks including two mode net works in Snijders et al 2013 The effects are grouped into effects for modelling network evolution and effects for modelling behavioral evolution i e the dynamics of dependent actor variables Within each group of effects the effects are listed in the order in which they appear in SIENA The short name of the effect shortName as it is specified in RSiena is specified in brackets For two mode bipartite networks only a subset of the effects is meaningful since the first node set has only outgoing ties and the second only incoming for example the reciprocity effect is meaningless because there cannot be any reciprocal ties the out degree populari
227. oesn ASTVA ols ASTVA 980qI9A HSTVA U918q Xx peuors LQRUuaIs S uorjdraos T s durexri xeqyu gs IVIEN 23898 ased snotacid tuo panurguos y lqer 178 x 399 qo 1rqeu rs e SI yUoWINSIe u o 9 qreyx yurad oy 03 syUOUINSIe exo ue s ssed pue q x sse o WOI SPLIOYUL YOM reu rs 9 q683x sse 5 jo yoofqo ue soqvoin Z SHSIp TEL AW sordes sue o queyx gt qeyxeuols Co STTAN 4eydstp TTON SHsIp TIAN 031e TTAN I9GRI TTON uordeo x a qeyx peurs oqe peuors Aq poonpoid se x yoofqo geur e ST JUOUINSIe pormbol uo oy q Sorystyeys poyoodxo oy JO XIIPRUL SIUBTIVAO oy pue siojyourered Aq G SO1ISTYeIS pojoadxo Jo XIIYBUI OAT LALIOP SOJBUILISO OY JO XIIPOUI OURTIVAOD oY ILM 1941930 VdUOSIOAUOD IOJ SOIISIJBIS pue SIOII prepuegs sones Jojowuered p jeurns oy Sururejuoo q 3 e SJULIG sue reuruns x Ateos Y qeuols Teuuns 9 uorjdraos qT s durexri xXequ g IVIEN 23eIS a3ed snora ad woaz p nurguoo y a1qeL 179 B Changes compared to earlier versions This begins in reverse order at end October 2009 and only presents changes which affect the user Programmers should consult the ChangeLog file in the source code on CRAN or in the R Forge repository which contains an almost complete listing of changes e 2015 09 10 Revision 289 Changes in RSiena and RSien
228. of the model There are some restrictions on what is permitted as interactions between behavior effects Of course they should refer to the same dependent behavior variable What is permitted depends on the so called interactionType of the effects which for behavior effects can be OK or blank A further explanation is given under the heading User defined interaction effects in Section 12 2 The interactionType of the effects is shown in the list of effects displayed in a browser by using the function effectsDocumentation The behavioral effects with non OK i e blank interactionType include in particu lar all effects of which the name includes the word similarity or alternatively the short name includes the string sim The requirement for behavior interactions is that of the interacting effects all or all but one have the value OK Thus for an interaction between two effects one or both should be OK for a three effect interaction two or all three should be OK As an example suppose that we have a data set with a dependent network variable friendship and a dependent behavior variable drinkingbeh drinking behavior and we are interested whether social influence as represented by the average alter effect differs between actors depending on whether currently they drink little or much Then the commands myeff lt includeEffects myeff avAlt name drinkingbeh interactioni friendship myeff lt in
229. on and the same names of all variables but it is allowed that there are differences with respect to parameters being fixed and perhaps tested To get the same names of variables the variables must be renamed in the call of sienaAlgorithmCreate an example is in script RscriptMultipleGroups R at the StOCNET website If in some but not all groups a depen dent variable has only upward or only downward changes the automatic restriction to follow this pattern also in the simulations see Section 4 2 3 must be lifted because this would make the model specifications different This must be done already in the original construction of the datasets that then later are combined by siena08 by using allowOnly FALSE in the call of sienaDependent as mentioned in Section 4 2 3 If there are some parameters that cannot be estimated for some of the data sets e g the effect of sex in a one gender school or because of near multicollinearity these pa 90 rameters must still be included in the model for those data sets but the parameters can be fixed to 0 and perhaps tested by a score type test Each parameter in the model is treated separately in the meta analysis without taking account of the dependencies between the parameters and their estimates Denote the number of combined data sets by N If we denote a given parameter e g the coefficient of the reciprocity effect by 6 then the true parameter values for the N data sets are denoted 61 42
230. onsider replacing it by the outRateLog effect but note that this works properly only for non conditional estimation cond FALSE in sienaAlgorithmCreate 4 If you are working with a data set with more than two waves there might be unmodeled heterogeneity between the periods Try modeling the periods sepa rately 5 Set the parameter firstg in sienaAlgorithmCreate to a lower value than the default 0 2 This will make the algorithm move more slowly hopefully avoiding the problematic region in the parameter space 156 The advice would be to set firstg to 0 02 and expect the necessity to do a second estimation using the prevAns parameter in siena07 If the problem still occurs for firstg 0 02 use a smaller value but less than 0 001 probably makes no sense firstg determines the step sizes in the stochastic approximation algorithm it is mentioned in some places earlier in this manual Especially for models with additional rate effects the default value of 0 2 might be too large firstg is the initial value of parameter ay mentioned on p 393 of Snijders 2001 Error in solve default z dfra system is computationally singular reciprocal condition number 2 34809e 35 or some other very small number note that e 35 means 10 to the power 35 This can happen at the end of estimation in function siena07 when the covariance matrix is singular It means that some effects in the model are linearly related or are always 0
231. orks 16 295 333 nidar i A 2012 Impact of fixed choice design on blockmodeling outcomes Advances in Methodology amp Statistics Metodoloski zvezki 9 2 139 153 207
232. ormed to have an overall average value of 0 in other words z denotes the original input variable minus the overall mean which is given in the output file under the heading Reading dependent actor variables First there are effects that have to do only with the behavioral variable itself 1 behavioral shape effect linear a Ge z i where z denotes the value of the dependent behavior variable of actor z 2 quadratic shape effect or effect of the behavior upon itself quad where the attrac tiveness of further steps up the behavior ladder depends on where the actor is on the ladder sys x 2 27 132 Next there is a list of effects that have to do with the influence of the network on the behavior To specify such effects in RSiena using e g function includeEffects it is nec essary to specify the dependent behavior variable in the keyword name as well as the network in the keyword interactionl For example myCoEvolutionEff lt includeEffects myCoEvolutionEff name drinkingbeh avSim indeg outdeg interactioni friendship The list of these effects is the following 3 10 average similarity effect avSim defined by the average of centered similarity scores sim between 7 and the other actors 7 to whom he is tied sbeh y z te y Vij sim sim and 0 if a 0 total similarity effect totSim defined by the sum of centered similarity scores sim between and
233. other nodes h for which there is the two path i h lt j gwespFB uses EPFB counting the number of nodes j with i j and there are exactly k other nodes h for which there is the two out star i h gt j gwespBF uses EPBF z counting the number of nodes j with i j and there are exactly k other nodes h for which there is the two in star i h j gwespRR uses EPRR x counting the number of nodes j with i gt j and there are exactly k other nodes h for which there are the reciprocal ties i h j In version 1 1 251 this was changed thanks to Nynke Niezink because earlier ver sions were not quite according to what is described above The effect was earlier implemented as C1 C2 X GWESPFF i a 108 22 23 24 25 26 27 28 for values c a and c2 a not dependent on z and with positive parameters a a depending according to exp a exp a 1 Note that for the default value a log 2 corresponding to the effect parameter 69 see above a a number of unilateral peripheral relations to dense triads 8353 2 jp p Vij 1 21 16 UE E Gn HL mg Ejk Zk Ehk UK gt C where c is the same constant as in the dense triads effect for symmetric networks the unilateral condition is dropped and the definition is ses a Djak mi 1 ni 1 Eki 4 in Zh HDi Zk Zhk Die gt cha in degree related popularity effect inPop earlier call
234. ould check your new version Make sure you get no warnings or errors from the check You can also INSTALL from a tar ball and check a source tree If you have permission problems on Linux or Mac you may need to do the first install from within R so that the necessary personal library directories will be created Use install packages tarballname repos NULL after creating a tar ball Or possibly just try to install some other package within R which will create the directories for you You can unpack a tar ball by using tar xf tar ball name 160 18 Understanding and adding an effect If you wish to check the definition of an effect you can locate it in the source code and study it You may also add effects to your personalized version of RSiena If you think the effect could be useful for others too it will be appreciated if you propose it for inclusion through one of the discussion lists or directly to the maintainer of the package This section gives the outline of the procedure for adding an effect and then presents an elaborate example If you only wish to understand an effect without creating a new one then you may follow the appropriate steps of this section The main things then are to go to the Ef fectfactory cpp file find the name of the effect you are interested in and from there the function that implements it and read the code of this function The explanations here are not yet given for generic effects which allow a mor
235. parameter determines the step sizes in the parameter updates in the iterative algorithm This is the parameter called firstg in function sienaAlgorithmCreate A too low value implies that it takes very long to attain a reasonable parameter estimate when starting from an initial parameter value that is far from the true parameter estimate A too high value implies that the algorithm will be unstable and may be thrown off course into a region of unreasonable e g hopelessly large parameter values It usually is unnecessary to change this but in some cases it may be useful 4 If all this is to no avail then the conclusion may be that the model specification is incorrect for the given data set 5 Further help in interpreting output is in Section 6 5 of this manual 2 6 Getting help with problems For methodological help consult the tutorial Snijders et al 2010b or this manual The website http www stats ox ac uk snijders siena contains various further publica tions also in other languages than English that may be helpful as well as example scripts There is a users group for SIENA to exchange information and seek technical advice the address is http groups yahoo com groups stocnet For technical problems running RSiena follow the following points Help pages Study the R help page for the function you are using and that seems to give the problems This manual complements the help pages but does not replace them
236. peryur y FAYL Ft S QerIea ue ooq SI SITUTPISISN SAIOMJOU SUTPUOdSIIIO 10 SONJLA 991 9P umurxeut JO 107994 patueu e sr 99139 XIN sooeds pappaquia on p ford Jo aurea SULIJS Jojoereyp SI oumeufoid Wyo OJUO A SULQOH oy ur uomne urs uo OP 0 UOTJOUNJ SI UL 0Oeu rs Teo 0 pasn oq uo ey 3jo qo TIUILIOS L euS Y s9780 PIJEN oureufoid 9ye rOurqlrros IVeu rs gt umq uosrvV IN TINN pees ASTVA HIPuUy VN puoo Z O 3 SIY o ureupuoo Q 0uILA puo qxe a Sep ISTVA 9MHXe y qnsu 000T U ISTVA SYNUTPIS9SN 99139 XeIN UAS oueufoid So0s1eysurs uj e 6 JaqeoIQWIYALIOSTy VUQBOI UIyALIOSTY eurs S uorjdraos T s durexri xXequ g IVIEN 238IS ased snora ad woaz panurguos y a1qeL 177 penulyuog y1odai aq 0 poppe aq 09 ANUASISAUOI 10J S919S1984S OY 1OJ PONSOP st Y Jt ANUL 0 Jos quounsre ue ooq Y SI 3898 SJU ATLUIUINS oy Te osuo5 y uo syurid 41 q1qeuors AreuUINS sr x JI 9DUASISAUOD 103 so17stye3s 9 ATreuordo pue solo prepueys son ea 1999 wered pogeurgso oy Sururequoo 3189 Y SQULIA uor unj MT sue yurad Cv AOQUL y898 x urd yrgeuors gud su S21 ur 3u rogoid are nO Jr p opu ururoo ATUO sorsrr91owreuo rour urejqo 09 sue s urgu s S SI OSpo se SA IOMJIU paje nurs y st sursgsue seud ur uomne nutrs qoes Joy ABM TIV
237. poch In this case you are advised to change to unconditional simulation 85 10 Getting started The best way to get started is to download the R scripts from the SIENA website and start reading and playing with them For carrying on and getting a first acquaintance with your own running of the model the data set collected by Gerhard van de Bunt is useful this data is discussed extensively in van de Bunt 1999 van de Bunt et al 1999 and used as example also in Snijders 2001 and Snijders 2005 The data files are provided with the program and at the SIENA website The digraph data files used are the two networks vrnd32t2 dat vrnd32t4 dat The networks are coded as 0 unknown 1 best friend 2 friend 3 friendly relation 4 neutral 5 troubled relation 6 item non response 9 actor non response Recode the network so that values 1 2 and 3 are interpreted as ties for the first as well as the second network and values 6 and 9 are missing data codes NA The actor attributes are in the file vars dat Variables are respectively gender 1 F 2 M program and smoking 1 yes 2 no See the Data sets tab at the SIENA website and the references mentioned above for further information about this network and the actor attributes Create the various required objects using functions sienaDataCreate getEffects and sienaAlgorithmCreate as indicated in Chapters 4 and 6 At first leave the whole model specification a
238. port and checking that the tendencies in the dependent variable or variables upward stable downward are not too different between the sub projects The sienaTimetest function can be used for formally testing this assumption Moderate violations p values larger than 0 01 will probably be acceptable in the sense that the combined results still are a meaningful aggregate strong violations are not acceptable and should be remedied by dropping some of the sub projects or by including an interaction term Given the potentially large number of periods that can be implied by the multi group option it probably is advisable when using Method of Moments estimation to use the conditional estimation option In multi group projects individual covariates are centered by subtracting the overall mean across all groups but dyadic covariates are centered by subtracting the within group means 11 2 Meta analysis of Siena results The function siena08 is a meta analysis method for SIENA It combines estimates for a common model estimated for several data sets that must have been obtained earlier This function combines the estimates in a meta analysis or multilevel analysis according to the methods of Snijders and Baerveldt 2003 and according to a Fisher type combination of one sided p values The function siena08 takes as input the sienaFit objects produced by separate runs of siena08 These sienaFit objects must have exactly the same model specificati
239. ppose that actors 7 and h actual or potential relation partners of actor i have exactly the same network position and the same values on all variables included in the model except that for some actor variable V for which only the popularity alter effect is included in the model actor h is one unit higher than actor j vp vj 1 It can lMMore exactly the value is 7 6 the standard deviation of the Gumbel distribution see Snijders 2001 144 be seen in Section 12 1 1 that the popularity alter effect is defined as sa Y maaa The contribution to this formula made by a single tie variable i e the difference made by filling in z 1 or z 0 in this formula is just v Let us denote the weight of the V alter effect by 6 Then the difference between extending a tie to h or to j that follows from the V alter effect is By x Un vj Bk x 1 Be Thus in this situation 6 is the log odds ratio of the probability that h is chosen compared to the probability that 7 is chosen E g if currently has a tie neither to 7 nor to h and supposing that Bk 0 3 the probability for i to extend a new tie to h is e9 3 1 35 times as high as the probability for i to extend a new tie to j 13 2 Behavior The evaluation function for behavior is given by fo ye gt Bb she ax z gt k see 23 In many cases the effect has the form of a product Spe B52 i sp z z gt 34 where s9 x z is not
240. r effect at distance 2 totAXInAltDist2 de fined by 1 s behavior multiplied by the total of the incoming alter averages on V of his alters excluding the contribution from a tie gt j if any 139 spy a z ald Tij wo this is similar to totAInAltDist2 but now for covariate V instead of the behavior Z There are also a number of interaction effects between actor covariates which includes other dependent behavior variables and influence effects These have to be specified using interaction1 for the covariate and interaction2 for the network e g myCoevolutionEff lt includeEffects myCoevolutionEff avAltEgoX name smoking interactionl sex interaction2 friendship Between parentheses the functionality of the ego variant of these effects is duplicated by interaction effects created for example as follows myCoevolutionEff lt includeInteraction myCoevolutionEff effFrom avAlt name smoking interactionl c sex friendship For the alter variant this way of construction will not work because the effect statistic cannot be decomposed into a product of two ego level statistics The available effects of this type are the following 53 interaction of ego tie sender variable with average similarity avSimEgoX sia z z ui zi Xy vig simi sim and the mean behavior i e 0 if xi 0 54 interaction of ego tie sender variable with total similarity totSimEgoX s
241. r example cbind myeff effectName myeff type myeff shortName myeff type eval lists all evaluation effects in myeff 5 1 3 Mathematical specification To attach precise meaning to the intuitive explanations above the mathematical definition of the model is given as follows To keep notation simple we leave all statistical parameters out of the formulae To keep the section short we do not give a lot of explanation but refer to the mentioned literature for that purpose As explained in Snijders et al 2010b the model is a continuous time Markov chain and represents how the network and behavior has changed in small steps the so called ministeps from one observed to a later observed value Each ministep entails a change in only one tie value or one behavioral variable and is modeled as follows First consider the network dynamics At any given moment let the network be denoted x The rate function for actor i is denoted z the evaluation function is f z the creation function is c z and the endowment function is e z At any given moment let the current network be denoted z9 The time duration until the next opportunity of change is exponentially distributed with parameter A 20 gt MN 29 This means that the expected time duration is Aj 29 The probability that actor i will be the next to have an opportunity for change is ri x Aj 20 Now suppose that actor i is the one who has t
242. r these and other effects are given in Chapter 12 Here we give a more qualitative description 1 2 The out degree effect which always must be included Transitivity in two mode networks is expressed in the ij emoji first place by the number of four cycles Robins and Alexander 2004 This reflects the extent to which ac tors who make one choice in common also make other 19 T J2 choices in common The following three degree related effects may be important especially for networks where degrees are theoretically important and represent social status or other fea tures important for network dynamics and or for networks with high dispersion in in or out degrees which may be an empirical reflection of the theoretical impor tance of the degrees Include them if there are theoretica reasons for doing so but only in such cases The out degree activity effect with or without sqrt often the sqrt version which transforms the degrees in the explanatory role by the square root works better reflects tendencies to dispersion in out degrees of the actors 42 4 The in degree popularity effect again with or without sqrt with the same con siderations applying reflects tendencies to dispersion in in degrees of the column units 5 The out in degree assortativity effect where parameter 2 is the same as the sqrt version while parameter 1 is the non sqrt version reflects tendencies for ac
243. rameters in this function If there are changes in network composition see Section 4 3 3 only the unconditional estimation procedure is available If there are a lot of structurally determined values see Section 4 3 1 then unconditional estimation is preferable 6 7 2 Fixing parameters Sometimes an effect must be present in the model but its precise numerical value is not well determined E g if the network at time t would contain only reciprocated choices then the model should contain a large positive reciprocity effect but whether it has the value 3 or 5 or 10 does not make a difference This will be reflected in the estimation process by a large estimated value and a large standard error a derivative which is close to 0 and sometimes also by lack of convergence of the algorithm This type of problem also occurs in maximum likelihood estimation for logistic regression and certain other generalized linear models see Geyer and Thompson 1992 section 1 6 Albert and Anderson 1984 Hauck and Donner 1977 In such cases this effect should be fixed to some large value and not left free to be estimated This can be specified by using the setEffect function with the fix TRUE option 6 7 3 Automatic fixing of parameters If the algorithm encounters computational problems sometimes it tries to solve them automatically by fixing one or more of the parameters This will be noticeable because a parameter is reported in the output as
244. ration the main process waits until all the other processes have finished The overall speed is therefore that of the slowest process and there should be enough processors to allow them all to run at speed 71 7 Standard errors The estimation of standard errors of the MoM estimates requires the estimation of deriva tives which indicate how sensitive the expected values of the statistics see Section 6 4 are with respect to the parameters The derivatives can be estimated by two methods e finite differences method with common random numbers e score function method The finite difference method is explained briefly in Snijders 2001 the score function method was developed in Schweinberger and Snijders 2007b where also the finite differ ence method is explained The score function method is preferable because it is unbiased and demands less computation time than finite differences although it requires more iter ations in phase 3 of the estimation algorithm see Section 6 4 It is recommended to use the score function method with at least 1000 iterations default in phase 3 For published results it is recommended to have 2000 or 4000 iterations in phase 3 The method for estimating derivatives is set by the findiff parameter and the number of iterations in phase 3 by the n3 parameter both in function sienaAlgorithmCreate that creates the object with specifications for the algorithm 7 1 Multicollinearity Multicollineari
245. re two focal actors 7 all of whose friends have z 3 and i2 who has four friends two of whom with z 2 and the other two with z 4 Both actors are then drawn toward the preferred value of 3 but the difference between drinking behavior 3 on one hand and 2 and 4 on the other hand will be larger for 1 than for ig In model 41 on the other hand since the average is the same both actors would be drawn equally strongly toward the average value 3 Since the objective function for model 40 depends not generally on the average be havior of the actor s friends here we present a table only for the special case of actors all whose friends have the same behavior z For the parameters given above the behavior evaluation function then reads beh 0 3618 z Z 0 0600 z 2 3 9689 sim sim This can be calculated by R as follows Define part of evaluation function obj_b lt function zi zj bi zi z_av b2 zi z_av 2 b3 1 abs zi zj ran_v sim_av Fill in the values of the parameter estimates and the averages z_av lt 3 113 sim_av lt 0 6983 bi lt 0 3618 b2 lt 0 06 b3 lt 3 9689 ZZ lt c 1 2 3 4 5 The table is transposed zi in the columns t outer zz zz obj_b The result is the following 17 f i has no friends i e xi 0 then Zea is defined to be equal to Z 18There were errors in this table in an earlier version of the manual 153
246. re again 0 0 is taken as 0 number of distances two effect nbrDist2 defined by the number of actors to whom i is indirectly tied through at least one intermediary i e at sociometric distance 2 sire o j z 0 max in Zhi gt 0 106 19 20 21 endowment effect only likelihood based because the Method of Moments estimators for endowment effects are based on the loss associated with terminated ties and this cannot be straightforwardly applied for the number of distances two effect number of doubly achieved distances two effect nbrDist2twice defined by the number of actors to whom 7 is not directly tied and tied through twopaths via at least two intermediaries stig 2 Jj vig 0 Xp tin THz gt 2 endowment effect only likelihood based number of dense triads denseTriads defined as triads containing at least c ties ss yn Zij Big Eji Lin Zh Dj Zhj 2 ch where the indicator function I A is 1 if the condition A is fulfilled and 0 otherwise and where c is either 5 or 6 this effect is superfluous and undefined for symmetric networks five variations of the GWESP geometrically weighted edgewise shared partners ef fects gwespFF gwespBB gwespFB gwespBF gwespRR and for non directed net works the sixth version gwesp Note that there is a difference since version 1 1 251 see at the end of this item These are effects like those developed for expone
247. riates may affect network or behavior change This is defined by combinations of configurations or situations which are called effects in Stochastic Actor Oriented Models Effects can be treated as the explanatory variables of the models Effects can be structural depending on the network structure itself also called endogenous or covariate related also various combinations between structure and covariates are possible Some examples for effects e structural effects reciprocity transitivity e covariate effects sex of the tie sender sex of the receiver same sex similarity in salary e combinations average level of smoking of friends interaction between sex of the sender and reciprocity Dependent variables network evaluation creation and endowment functions As we discussed earlier SIENA is capable of analyzing and modeling the evolution of networks and behavior jointly or separately Consequently a model may have more than one dependent variable Here we introduce the ways network and behavior dependent variables can be defined in Stochastic Actor Oriented Models We start with network evolution Given two observations of a binary network a single network tie variable can follow four patterns as shown in Table 1 In Stochastic Actor Oriented Models however tie change can be defined in three ways we can model the creation of previously not exist ing ties creation the maintenance of existing ties endowment or
248. riends For drug use the situation is different Actors with v 1 or 2 prefer friends with drug use vj 1 for actors with v 3 the difference is hardly discernible but if we consider the differences even though they are tiny then they are most attracted to others with vj 4 actors with the highest drug use v 4 differentiate most strongly and are attracted most to others with also the highest drug use The differences between the results with the similarity effects and the interaction effects are minor The extra degrees of freedom of the latter model gives a slightly closer fit to the data However the differences between the two fits are not significant as can be shown e g by score type tests 13 4 Ego alter influence tables In quite a similar way as in the preceding section from the parameter estimates as pre sented in the output tables combined with the formulae for the effects we can construct tables indicating how attractive are various different values of the behavior depending on the behavior of the actor s friends The functions used to define the effects can be found in Section 12 2 1 and it must not be forgotten that all variables are internally cen tered in RSiena and the subtracted means are reported in the initial output produced by print01Report but more precision can be obtained by requesting the mean attributes of the covariates see Section 4 2 2 In the first model the estimated coefficients
249. riods where it is observed This is represented internally by a variable called uponly indicating that the dependent variable cannot decrease and a variable downonly indicating that the dependent variable cannot increase The constraints signaled by the uponly and downonly variables can be lifted by using allowOnly FALSE in the call of sienaDependent see the help file for this function If a dependent variable is only increasing or only decreasing for all periods and sien aDependent was called with allowOnly TRUE the default then two basic effects are not identified These are the outdegree effect for a dependent network variable and the linear shape effect for a dependent behavior variable these effects define the balance between the probabilities of going up and going down These effects then are dropped automat ically from the effects object If this is not desired this can be prevented by calling sienaDependent with allowOnly FALSE 4 3 Further data specification options 4 3 1 Structurally determined values It is allowed that some of the values in the digraph are structurally determined i e deterministic rather than random This is analogous to the phenomenon of structural zeros in contingency tables but in SIENA not only structural zeros but also structural ones are allowed A structural zero means that it is certain that there is no tie from actor i to actor j a structural one means that it is certain that there is a tie T
250. rsion of R and which version of RSiena you are using R Forge help list If you are a programmer then for technical questions about the RSiena code as distinct from the methodology you can send an email to rsiena helpQlists r forge r project org or post in the help forum for RSiena in R Forge You need to be a registered member of R Forge and possibly of RSiena to post to a forum but anyone can send emails at present In your message please tell us which operating system which version of R and which version of RSiena you are using 21 Part II Users manual 3 Steps of modelling The operation of the SIENA program is comprised of five main parts 1 2 3 4 5 input of basic data description see Section 4 model specification see Section 5 estimation of parameter values using stochastic simulation see Section 6 testing parameters and assessing goodness of fit see Sections 7 and 8 simulation of the model with given and fixed parameter values see Section 9 The normal operation is to start with data input then specify a model and estimate its parameters assess goodness of fit and the significance of the parameters and then possibly continue with new model specifications followed by estimation or simulation The main output of the estimation procedure is written to a text file named pname out where pname is the name specified in the call of sienaAlgorithmCreate 22 4 Input data SIEN
251. rved values Wip Wkh o Mn n D Emn 031 tm wnltm p gt 3 1150 p lt 3 Note that since this is the evaluation function for actor 7 with respect to network X only the x tie indicator in the formula corresponding to the tie i 5 j is the dependent variable here The interpretation is that actors have the tendency to make the same outgoing X choices as those k with whom they share many outgoing W ties For p 2 and p 4 the square root is taken Sia 2 Dj kiki Tij Uh y 2 h Wih Wkh ve This can be regarded as a higher order effect related to indegree popularity The differences between the centered and non centered versions amount to a multiple of the indegree popularity without inPop effect Therefore when the sharedTo effect is used it is advisable also to include the inPop effect so as to avoid misinterpretations Then there are some mixed triadic effects restricted to triples with the same or different values on a monadic covariate V 25 agreement along W leading to X for same V X from W agr x same V covNetNet i 5735 0 Lien Vij Win Win vi vj this refers to agreement of actors with respect to their W w w choices structural equivalence with respect to outgoing W 2 _ choices but only for actors and choices sharing the same value i X j of a covariate V the contribution of the tie i x j is propor tional to the number of joint W choices of others i wae
252. ry to use allowOnly FALSE in the call of sienaDependent see the help page for sienaDependent The scripts RscriptListGroups R and RscriptMultipleGroups R give further examples and explanation for creating sienaGroup objects If you have a large number of groups more than 30 try first with a smaller number of groups 10 20 If you need or wish to make a selection of groups select the one with few or no missing data and with Jaccard coefficients at least 0 30 96 11 3 4 How to choose the parameter settings for sienaBayes It may be good to have an initial try run with nwarm 5 nmain 10 nrunMHBatches 5 nImproveMH 20 for speed and silentstart FALSE for information about the initial ization phase and then print the result This will give information about the results of the initialization phase and about computing time If some of the groups have some very high estimated rate parameters you should either drop those groups or decrease the value of initgainGroupwise The new value could be e g 0 005 or 0 001 or 0 0 With the lower value of initgainGroupwise dropping the groups concerned may be unnecessary so don t drop groups too soon For normal use nwarm 100 nmain 1000 nrunMHBatches 20 nImproveMH 100 may be reasonable Computing time is roughly proportional to nmain x nrunMHBatches We still have to develop guidelines about how to choose the number of iterations If the tracelines show that the process is still quite unstable e
253. s 2001 or Snijders 2005 Basic references for the model of network behavior co evolution are Snijders et al 2007 and Steglich et al 2010 A basic reference for the Bayesian estimation is Koskinen and Snijders 2007 and for the maximum likelihood estimation Snijders et al 2010a More specific references are Schweinberger 2012 for the score type goodness of fit tests and Schweinberger and Snijders 2007b for the calculation of standard errors of the Method of Moments estimators For the model for diffusion of innovations in dynamic networks please refer to Greenan 2015 For assessing and correcting time heterogene ity and goodness of fit assement and associated model selection considerations refer to Lospinoso et al 2011 and Lospinoso 2012 2 Getting started with SIENA There may be various strategies for getting acquainted with RSiena In any case it is a good idea to study the tutorial Snijders et al 2010b Two recommended options for learning the how to are the following 1 One excellent option is to read the User s Manual from start to finish leaving aside the Programmer s Manual 2 A second option is to read this Minimal Introduction to get a sense of the rest by looking at the table of contents and then follow the references to specific sections of your interest The searchable pdf file makes it easy to look for the relevant words This Minimal Introduction explains the basics of Stochastic Actor
254. s These are then used for the simulations since they were indicated as missings NA in the data themselves they will not be used for the calculation of target statistics in the Method of Moments 4 3 3 Composition change joiners and leavers SIENA can also be used to analyze networks of which the composition changes over time because actors join or leave the network between the observations This can be done in two ways using the method of Huisman and Snijders 2003 or using structural zeros For the maximum likelihood estimation option the Huisman Snijders method is not implemented and only the structural zeros method can be used Structural zeros can specified for all elements of the tie variables toward and from actors who are absent at a given observation moment How to do this is described in subsection 4 3 1 This is straightforward and not further explained here This subsection explains the method of Huisman and Snijders 2003 also called the method of joiners and leavers which uses the information about composition change in a somewhat more efficient way Network composition change due to actors joining or leaving the network is handled separately from the treatment of missing data The data matrices must contain all actors who are part of the network at any observation time If adjacency matrices are used as data input they must therefore all have the same number of n rows each actor having a separate and fixed line in the
255. s covariate a1tX0utAct defined by the squared sum of ties weighted by alter s covariate values net veia 2 Si75 1 gt Tij vj since the covariate here is used as a weight this probably makes sense especially for non centered covariates homogeneous covariate x transitive triplets ChomXTransTrip defined by the num ber of transitive triplets i h gt j i that have the same covariate value for i j and h si z yj Tij Lih Cag I ui u Uh 116 77 transitive triplets jumping to different V jumpXTransTrip h sirs 0 jan Vij Vin nj Hvi va A 05 this refers to transitive closure restricted to jump outside of V groups in the sense that the focal actor and the mediating actor have the same value of V but the target actor has a different value J 78 covariate ego x alter egoXaltX defined by the product of i s covariate and the sum of those of his alters net Sing 2 vi gt Tij Uj 79 covariate ego x alter x reciprocity egoXaltXRecip defined by the product of 7 s covariate and the sum of those of his reciprocated alters net spo z Vj ye Tij Lji Vj 80 ego gt alter for covariate higher defined by the number of ties where 7 s covariate is larger than alter s while equality counts for half sigo 2 Do tij dsign v vj where dsign d 0 for d lt 0 0 5 for d 0 and 1 for d gt 0 81 covariate of indirect ties IndTies defined
256. s have names The length of this vector is equal to the number of dependent networks Each element of this vector must have a name which is the name of the corresponding network E g for one dependent network called mynet one could use MaxDegree c mynet 10 to restrict the maximum degree to 10 For two dependent networks called friends and advisors one could use MaxDegree c friends 6 advisors 4 51 For a single network the default value 0 is used to specify that the maximum is unbounded For multiple networks if for one network there is a bound for the maximum outdegree but for another network this should not be bounded then the value 0 will not work but one should use a bound which is at least n 1 where n is the number of actors in the network or the largest number if there are multiple groups If the MaxDegree parameter is used for data where all or almost all degrees are equal to this maximum value then it is likely that the estimation algorithm will not converge A fixed choice design for network data collection is not compatible with the free choice nature of the Stochastic Actor Oriented Model See Holland and Leinhardt 1973 for a discussion of fixed choice designs and nidar i 2012 for references to more recent literature 5 11 Goodness of fit with auxiliary statistics There is now available in RSienaTest a function sienaGOF which permits users to assess the fit of the model with respect to auxiliary
257. s in s relations where i has the mediating position ordered pairs of actors j h for which j is tied to 7 and to h while also j is tied to h which is different from the transitive triplets effect only for directed networks sig 2 jp Tji Vih Ejh this cannot be used together with the transitive triplets effect in Method of Moments estimation because of perfect collinearity of the fit statistics transitive reciprocated triplets effect transRecTrip which can be regarded as an interaction between the transitive triplets effect and reciprocity where the recipro cated tie is the tie 1 j that closes the two path i gt h gt j sir 2 jp Tij Ti Lih Zhj transitive reciprocated triplets effect type 2 transRecTrip2 another interaction between the transitive triplets effect and reciprocity where the reciprocated tie is the tie h j in the closed the two path i gt h gt j i gt j sig z J jp Tij Lih Lng Tin this represents the tendency to send ties simultaneously to pairs of actors who are 104 10 11 12 13 14 mutually linked but when outdegree activity is also included in the model it repre sents as well the tendency to send ties simultaneously to pairs of actors who are not linked to each other number of three cycles cycle3 sig z jp Tij Tjh Ehi shared popularity sharedPop net a Y sio z il different Tij Thj Vik Thk this is like a 4 cycle but in
258. s it is by default see Section 5 a constant rate function the out degree effect and the reciprocity effect Then let the program estimate the parameters using function siena07 You will see a screen with intermediate results current parameter values the differences deviation values between simulated and observed statistics these should average out to 0 if the current parameters are close to the correct estimated value and the quasi autocorrelations discussed in Section 6 It is possible to intervene in the algorithm by clicking on the appropriate buttons the algorithm may be restarted or terminated In most cases this is not necessary A little bit of patience is needed to let the machine complete its three phases When the algorithm has finished look at the results in the output file or by the print or summary function of the resulting sienaFit object Check that the overall maximum convergence ratio is small enough ideally less than 25 If not continue estimation with the prevAns option as discussed in Section 6 1 2 When satisfactory convergence has been obtained make sense of the results for example is the reciprocity parameter significant As further steps include some extra effects First candidates are the transitive triplets effect or the transitive ties effect and the 3 cycles effect see e g Section 5 you can find their shortName needed to specify them in Chapter 12 where also the mathematical specifications
259. s similar to totAA1tDist2 but now for covariate V instead of the behavior Z alter s distance two incoming covariate average effect on behavior z avXInAltDist2 defined by s behavior multiplied by the average of the incoming alter averages a of his alters excluding the contribution from a tie j i if any defined by Donzi Thj Uh i jfrtyj z gt i _ a H 4 j Tij 28 0 if 4 Tij 0 also see 25 shio z z a Xj 05 ar Oy Tij and the mean behavior i e 0 if the ratio is 0 0 this is similar to avInAltDist2 but now for covariate V instead of the behavior Z alter s distance two incoming covariate total effect on behavior z totXInAltDist2 defined by 2 s behavior multiplied by the total of the incoming alter totals on V of his alters excluding the contribution from a tie i j if any E P Bag Un a ag OF this is similar to totInAltDist2 but now for covariate V instead of the behavior Z average total incoming covariate alter effect at distance 2 avTXInAltDist2 de fined by it s behavior multiplied by the average of the incoming alter totals on V of his alters excluding the contribution from a tie gt j if any beh sbeb a 2 z Ey zi z 214 OF DO zu and the mean behavior i e 0 if the ratio is 0 0 this is similar to avTInAltDist2 but now for covariate V instead of the behavior Z total average incoming covariate alte
260. s than 0 2 and for all the individual parameters the t ratios for convergence all are less than 0 1 in absolute value convergence is reasonable when the former is less than 0 30 For published results it is suggested that estimates presented come from runs in which the overall maximum convergence ratio is less than 0 25 These bounds are indications only and are not meant as severe limitations In the example above the largest absolute value of the t ratios for convergence is equal to 0 0427 and the overall maximum convergence ratio is 0 1608 both are quite good values If convergence is not adequate the best way to continue is by making another esti mation run now carrying on from the last obtained result This is done by using this result in the prevAns previous answer parameter while taking care that useStdInits FALSE has been specified An example is resultsi lt siena07 algorithm1 data mydata effects myeff prevAns results1 In this case this second estimation run produced good results with a maximum absolute t ratio for convergence equal to 0 0777 The output file gives more extensive results viz the averages and standard deviations of the deviations from targets and the resulting t ratios End of stochastic approximation algorithm phase 3 Total of 1822 iterations Parameter estimates based on 822 iterations basic rate parameter as well as convergence diagnostics covariance and derivative matr
261. se matrices even for observation times where the actor is not a part of the network e g when the actor did not yet join or the actor already left the network The times of composition change can be given either in a data file or in a list available in the R session For networks with constant composition no entering or leaving actors this file or list is omitted and the current subsection can be disregarded If there is composition change estimation by the Method of Moments is forced to be unconditional see Section 6 7 1 For these waves where the actor is not in the network the entries of the adjacency matrix can be specified in two ways First as missing values using missing value code NA In the estimation procedure these missing values of the joiners before they joined the network are regarded as 0 entries and the missing entries of the leavers after they left the network are fixed at the last observed values This is different from the regular missing data treatment Note that in the initial data description the missing values of the joiners 33 and leavers are treated as regular missing observations This will increase the fractions of missing data and influence the initial values of the density parameter A second way is by giving the entries a regular observed code representing the absence or presence of a tie as if the actor was a part of the network In this case additional information on relations between joiners and oth
262. sed in the call of sienaAlgorithmCreate standard initial values are used These consist of some reasonable values for the rate parameters and the outdegree parameter as well as for the linear shape parameter for behavioral dependent vari ables if any and O parameters for the rest The default is useStdInits FALSE 56 6 1 2 Convergence Check When parameters have been estimated first the convergence of the algorithm must be checked This is done by looking at the t ratios for convergence and the overall maximum convergence ratio These are given in the output of the algorithm presented above This check considers the deviations between simulated values in Phase 3 see below of the statistics and their observed values the latter are called the targets Ideally these deviations should be 0 Because of the stochastic nature of the algorithm when the process has properly converged the deviations are small but not exactly equal to 0 The program calculates the averages and standard deviations of the deviations and combines these in a t ratio in this case average divided by standard deviation The overall maximum convergence ratio is the maximum value of the ratio average deviation standard deviation for any linear combination of the target values A precise definition is given in Siena_Algorithms pdf which can be downloaded from the SIENA website Convergence is excellent when the overall maximum convergence ratio is les
263. should not be too long RSiena does not work with case numbers The correspondence between cases in the different components of the data set is by the order of the rows in the data matrices For a data set with n actors each data matrix should have n rows and always the th row should correspond to the 7 th actor It is also useful to note here that in case of co evolution models those with more than one dependent networks and or behaviors data for all dependent variables must be available for the same set of time points 4 1 1 Network data For data specification by the sienaDependent function the network must be specified as a matrix or array or list of sparse matrix of triples For data specification by the graphical interface siena01Gui documented separately or by the function sienaDataCreateFromSession edge list formats are also allowed This can be either the format of the Pajek program or a raw edge list here called Siena format For large number of nodes say larger than 100 the edge list format is more efficient in use of computer memory Sparse matrices which can be used by input via sienaDependent have the same efficiency as Pajek or Siena format The three possible formats for digraph input are as follows 23 1 Adjacency matrices These can be used in sienaDependent and in sienaDataCreateFromSession In the usual case of a one mode network the adjacency matrix is given in a matrix of n rows and n columns co
264. ski 1989 if there is no earlier observed value the value 0 is imputed For the dependent behavior variables the same principle is used if there is a previous observation of the same variable then this value is imputed if there is none then the observationwise mode of the variable is imputed Missing covariate data are replaced by the variable s global mean In the course of the simulations however the imputed values of the dependent behavior variables and of the network variables are allowed to change In order to ensure a minimal impact of missing data treatment on the results of param eter estimation Method of Moments estimation and or simulation runs the calculation 32 of the target statistics used for estimation by the Method of Moments and reporting in these procedures uses only non missing data When for an actor in a given period any variable is missing that is required for calculating a contribution to such a statistic this actor in this period does not contribute to the statistic in question For network and dependent behavior variables the tie variable or the actor variable respectively must provide valid data both at the beginning and at the end of a period for being counted in the respective statistics By using the argument imputationValues in coCovar and varCovar other values i e values different from the mean that is used by default for imputation can be given for imputation of missings in monadic covariate
265. smaller a the extra contribution of a high number of intermediaries h is downweighted An often used value is a log 2 0 69 Snijders et al 2006 corresponding to an internal effect parameter of 69 myeffects lt setEffect myeffects gwespFF parameter 69 but it is worthwhile to try out different values of a to see which one gives the best fit Although the fit statistic of the GWESP effect is identical to that for transitive ties for a 0 and approximates the fit statistic for transitive triplets for large a the estimates are not the same because some other calculations are done differently The issue is that the GWESP effects are not implemented as an evaluation effect but as an elementary effect where for the change statistic only changes of the tie i gt j in 12b are considered and not of the tie i gt h Thus the GWESP effects are defined in RSiena as the elementary effects el os pQ Q iai TihThj silo aer q 1 1 e i 13 It should be noted that although the GWESP statistic is not triadic but depends on higher order configurations still it is actor oriented because only those configu rations are considered that are part of the personal network i e the set of actors immediately connected to the focal actor 7 The other types of GWESP effect are analogous with different tie orientations They are defined as follows gwespBB uses EPBB z counting the number of nodes j with 1 j and there are exactly k
266. some ex amples in this file or in the result of effectsDocumentation For covariate related effects for two mode networks see extra remarks in Sec tion 18 2 e Insert a new row in this group Copy a row that corresponds best to your new effect and modify effectName functionName shortName and more if this 161 seems necessary Perhaps your new effect is suitable in more than one group then a new row can be made for all these groups differing only in the name of the effect group e g check that there are three versions of inPop for directed non directed and bipartite two mode networks Assume our new effect has shortName newEf In some cases the new function will have extra parameters as you can see from other examples this is mostly the case if one function is being used to define more than one effect For how to deal with internal effect parameters look up a function defining an effect that has such a parameter e Build the package and install it Check from R that the new effect which has only been created nominally appears now in the effects object in RSiena If this is not the case there may be furethr changes necessary in the file effects r also see Section 18 2 4 Open the folder RSiena src model effects In an editor open the files AllEffects h and EffectFactory cpp These are C files using a C editor is convenient but not necessary Note however that you must save the files as ASCII raw text f
267. statistics of networks e g geodesic distributions that are not explicitly fit by a particular effect but are nonetheless important features of the network to represent by the probability model This can be used to check when one has followed the approach to model specification explained in Sections 5 2 to 5 6 and explained also in Snijders et al 2010b whether the end result gives a good representation also of these other statistics The sienaGOF function proposed and elaborated by Lospinoso 2012 operates basi cally by comparing the observed values at the ends of the periods with the simulated values for the ends of the periods The differences are assessed by combining the auxiliary statistics using the Mahalanobis distance The results of sienaGOF can be plotted which then produces violin plots Hintze and Nelson 1998 which present the distribution of the statistic as a combination of a box plot and a smooth approximation to the density by a kernel density estimate with the observed values superimposed The violin plots tend to become squiggly when the proba bility distribution is concentrated on a few points integers usually and as a consequence the density plot tries to approximate a discrete distribution For the associated plot func tion options center and scale are available to equalize the centers and scales of the various statistics plotted For distributions and cumulative distributions over sets of integers e
268. step changes the network state and therefore the actors are each others ever changing context Zeggelink 1994 This allows the model to represent the feedback process that is typical for network dynamics These changes are not individually observed but they are simulated what is observed is the state obtained at the next observation wave This simulation model implements the statistical model for the network dynamics The statistical procedures utilize a large number of repeated simulations of the network evolution from each wave to the next They estimate and test the parameters producing a probabilistic network evolution that could have brought these observations to follow one another To avoid misunderstandings two notes have to be made about the meaning of actor decisions and the role of Stochastic Actor Oriented Models in causal inference First the fact that SIENA models are actor oriented does not imply the assumption that the actors take decisions in any real sense It means that the changes in the network are organized so to say by the nodes in the network This aligns very well with a substan tive standpoint where the nodes have agency Snijders 1996 but it does not necessarily reflect a commitment to or belief in any particular theory of action elaborated in the scientific disciplines In fact the purpose of SIENA in this matter is to assist substan tive researchers in further developing their theories of action by e g
269. sure 2 of covariate XWX2 This is an elementary effect not an evaluation effect compris ing of the XW gt X closure of covariate effect only the contribution of the number of weighted X W two in stars 0 is h j W h In other words only the 7 j tie in the figure x here is the dependent variable The effect is defined as a sto z ig Dri Tin Wih h 0 x w j Monadic covariate effects 114 For actor dependent covariates vj recall that these are centered internally by SIENA as well as for dependent behavior variables for notational simplicity here also denoted vj these variables also are centered the following effects are available 60 61 62 63 64 65 66 67 covariate alter or covariate related popularity altX defined by the sum of the covariate over all actors to whom 7 has a tie 5360 1 gt Tij Uj covariate squared alter or squared covariate related popularity altSqX defined by the sum of the squared centered covariate over all actors to whom 7 has a tie not included if the variable has range less than 2 sgi z Jj Tij vj covariate ego or covariate related activity egoX defined by 2 s out degree weighted by his covariate value net S 62 Vi Ti covariate related similarity simX defined by the sum of centered similarity scores sim between 7 and the other actors j to whom he is tied si s e E mi simi sim
270. t al 2006 and Steglich et al 2010 We refer to any of these papers for a further description of the data The friendship network data over 3 waves are in the files s50 network1 dat s50 network2 dat and s50 network3 dat We also use the attribute data for alcohol use s50 alcohol dat as a dependent variable It can be seen from the SIENA output file using these data that the alcohol use variable assumes values from 1 to 5 with overall mean equal to v 3 113 and mean of the similarity variable sim 0 6983 Drug use is used as a changing actor variable with range 1 4 average v 1 5 and average dyadic similarity sim 0 7533 Suppose that we fit a model of network behavior co evolution to this data set with for the network evolution the effects of outdegree reciprocity transitive ties number of distances two the ego alter and similarity effects of alcohol use as well as the ego alter and similarity effects of drug use and for the behavior i e alcohol dynamics the shape effect the effect of alcohol on itself quadratic shape effect and the average similarity effect The results obtained are given in the following part of the output file Network Dynamics 1 rate constant network rate period 1 8 2357 1 6225 2 rate constant network rate period 2 5 6885 0 8434 3 eval outdegree density 2 1287 0 1565 4 eval reciprocity 2 3205 0 2132 5 eval transitive ties 0 2656 0 2025 6 eval number of a
271. t be at least two in order to analyze a data set with Stochastic Actor Oriented Models In case of modeling evolution across more than two observations in time esti mated parameter values are assumed to be equal in all periods unless time heterogeneity is specifically represented by changing parameters see Section 5 9 for further details 11 This section focuses on three related topics the type of network and behavioral data SIENA works with the meaning of explanatory variables or so called effects in Stochastic Actor Oriented Models and the different dependent variables with which SIENA captures network and behavior evolution Network data Stochastic Actor Oriented Models operate on binary networks that is on relations on a given set of actors where tie variables between actors have two states existent 1 or non existent 0 Weighted networks are not allowed but as mentioned above it is possi ble to define multiple networks representing discrete levels of relationships It is possible to specify that some ties in the network are impossible structural zeros or necessary structural ones see Section 4 3 1 for more details For the network evolution Stochas tic Actor Oriented Models how ties are being created maintained or terminated by actors Behavioral data Behavioral variables in Stochastic Actor Oriented Models can be thought of as indi cating the presence or intensity of a behavior For example b
272. t h was included at the appropriate alphabetic place In the file EffectFactory cpp after the piece referring to effectName outActSgrt the lines 163 else if effectName outTrunc t pEffect new TruncatedOutdegreeEffect pEffectInfo were inserted This refers the program when it encounters short name outTrunc to the function TruncatedOutdegreeEffect The next step was to construct this function To choose a template for TruncatedOutdegreeEffect we could make various differ ent choices here it is important to have a look at the various effects defined in Chapter 12 that depend only on the outdegree Consider the effects Outdegree ac tivity sqrt short name outActSqrt and sum of 1 out degree c short name outInv as possible examples A look in EffectFactory cpp shows that these are imple mented using the functions OutdegreeActivitySqrtEffect and InverseOutdegreeEffect respectively Therefore look at the files OutdegreeActivitySqrtEffect cpp and Inverse OutdegreeEffect cpp where these functions are defined The former defines the effect through a calculateContribution function which defines the tie flip contribution the function called A z above and tieStatistic which is the function r z when the effect can be defined as si x gt aig ri a 45 j The latter defines the effect through a calculateContribution function and an egoStatistic function which is the effect as defined
273. t is possible that conver gence has set in only later depending on the case the traceplots may give information about this If you conclude that convergence has occurred later then use this to define the nfirst parameter in the print and summary functions for sienaBayesFit object see print sienaBayesFit 99 When the procedure seems to have diverged and this occurs right from the start it is advisable to use smaller values of the parameters initgainGlobal and initgainGroupwise If divergence sets in later and is most pronounced for the rate parameters it may be ad visable to use a smaller value of reductionFactor e g 0 1 If generally the tracelines are irregular it may be good to increase nrunMHBatches but another possibility is to increase the mult parameter set in sienaAlgorithmCreate Using other packages for convergence assessment The advice of literature such as Gelman et al 2014 is to use multiple sequences produced independently preferably from overdispersed starting points for assessing convergence For example one may use 4 or 5 such sequences Function extract sienaBayes can be used to extract from these sequences the draws from the posterior distributions of the parameters of interest This function produces a three dimensional array of iterations by chains by parameters which then can be used e g in function monitor of package stan or with the help of package coda Currently there is no good way in s
274. t on the parameters bl b2 b3 and the overall average v_av Watch out for statements that take more than one line as used here in the definition of the functions obj_n The rule is that always the lines before the last must be syntactically incomplete In this case this is satisfied because the first line ends with a obj_n lt function vi vj bi vi v_av b2 vj v_av b3 vj v_av vj v_av b4 vi v_av vj v_av Now fill in the values of the parameter estimates and the averages v_av lt 3 113 OH 150 b1 lt 0 0078 b2 lt 0 1041 b3 lt 0 0141 b4 lt 0 1655 Define the value of v for which the table is to be given vv lt c 1 2 3 4 5 And calculate and display the table sel_tab lt outer vv vv obj_n sel_tab This gives the following table U x Uj 1 2 3 4 5 1 0 57 032 00 0 17 0 42 2 018 0 10 0 02 0 06 0 14 3 0 18 0 10 0 01 0 08 0 16 4 0 51 0 26 0 01 0 24 0 49 5 0 81 0 40 0 02 0 43 0 85 For drug use we obtain the formula 0 0214 v 0 0 2603 u 0 0 0249 u 0 0 1976 v 0 v 0 and the following table Ui E Uj 1 2 3 4 1 0 18 0 18 0 53 0 89 2 0 06 0 10 0 26 0 42 3 0 11 0 07 0 03 0 00 4 0 33 0 09 0 14 0 38 The fact that we are using three variables involving alter alter alter squared inter action instead of two alter and similarity leads to greater freedom in
275. tall RSiena and the other packages in the regular way from CRAN However it is advisable to have the latest version of RSiena or RSienaTest from R Forge or the SIENA website You can go to http r forge r project org R group_id 461 or to http www stats ox ac uk snijders siena siena_downloads htm and there download the appropriate version of the package appropriate for your operation system Windows Mac Unix Installation can be done in various ways by the function install packages in R via the drop down menu in the R console or in command mode which for Mac is the terminal If a binary file is available zip for Windows tgz for Mac then using the binary is recommended Installation from binary is much faster than installation from source Installation from the R Forge repository can be done as follows In these commands RSienaTest can be replaced by RSiena e for Windows install packages RSienaTest repos http R Forge R project org e for Mac the binary file code is not available on R Forge but the source code may also work 16 install packages RSienaTest repos http R Forge R project org type source If this does not work try one of the following methods Installation from a downloaded file can be done as follows assuming the root name of the file is RSienaTest_1 1 289 and filling in the correct path name It will be convenient to first navigate to the directory containing the RSie
276. tcome of the test of HY is significant at a usual level of significance i e de is thought to be positive whereas the estimate is 2 0 This poten tial inconsistency is possible because the test and the estimator in this approach are not directly related cf Snijders and Baerveldt 2003 The likelihood based method does not suffer from this problem because the maximum likelihood estimate always is contained in the confidence interval based on the profile likelihood There may be reasons to distrust the estimates which are large with also a large standard error This is known as the Donner Hauck phenomenon in logistic regression discussed in Section 6 7 2 Unfortunately it is impossible to say in general what is to be regarded as a large standard error A threshold of 4 or 5 for the standard error often is 92 reasonable for most effects if a tested parameter has a standard error larger than 4 then it is advisable to redo the analysis in a specification where this parameter only is fixed to 0 and a score test is carried out for this parameter However for some effects in any case for the average similarity effect for behavior dynamics parameters and standard errors tend to be larger and a larger threshold e g 10 is appropriate The same holds for effects of covariates with small variances less than 1 An alternative probably better for the estimation of standard errors is by using a non parametric bootstrap confidence int
277. te simulation without estimation Incorporated argument allowOnly in sienaNet to permit ignoring monotonicity in data and its consequences for upOnly and downOnly Some new effects interactions between reciprocity and transitivity 2012 03 29 R forge revision 211 Fixed bug in effectsDocumentation 2012 03 29 R forge revision 210 Altered ML code in hope of fixing intermittent ML bug Just might cause different answers 2012 03 25 R forge revision 208 fix bug in bipartite network endowment and creation effect scores Rationalise behavior network effects for symmetric networks in allEffects csv effects r partially Fix bug which caused crash creating starting values for sparse matrices with movements only in one direction 2012 03 16 2012 03 21 R forge revisions 206 207 new behavior rate effects 2012 03 07 R forge revision 205 191 Bug fix for effects AvSimEgoX totSimEgoX avAltEgoX with changing covariates Minor alterations to altDist2 simDist2 and the multi network versions Bug fix in probability in chain for symmetric networks type b models e 2012 02 29 R forge revision 204 l Fixed bugs in endowment and creation effect statistics for behavior Similarity effects Fixed bug causing occasional failure in bayes routine Fixed bug causing occasional failure in maximum likelihood with constraints Added error message if try to use maximum likelihood with composition change Fixed bug in en
278. teractions Tests Wald RSiena and Multipar RSiena added Error occurrence with message about cvalue in EvaluateTestStatistic corrected Divergent parameters in siena07 get NA for their rows and columns in the resulting covariance matrix The following changes in revision 244 were ported from RSienaTest to RSiena In siena08 also report Bonferroni combination of the two Fisher combinations In siena07 rolled back change in truncation from version 1 1 227 to the earlier pro cedure descriptives sienaGOF added Minor changes of output in siena table print siena siena07 and in error message for includeEffects Change artificial results from 999 to NA in siena07 For ML estimation added autocorrelations during phase 3 to print summary sienaFit e 2013 10 31 R Forge Revision 246 Changes in RSiena and RSienaTest New behavior objective function effects avSimAltX totSimAltX and avAltAltX to differ entiate sources of peer influence in directed networks Added effect class covarBehaviorNetObjective to effectsDocumentation R Fix of a bug that occurred in the case of on average decreasing behavior variables e 2013 16 09 R Forge Revision 245 Changes in RSienaTest 186 New structural rate effect outRateLog Duplication of outTrunc effect outTrunc2 allowing use with two different parameters In siena08 also report Bonferroni combination of the two Fisher combinations In phase2 of siena07 rolled back
279. testing the null hypothesis that component k of the parameter vector is 0 Ho k 0 the t test is based on ans theta k sqrt ans se k 4 s e 0k This can be easily calculated by hand from the RSiena results In some cases however the t statistic 4 does not have an approximate standard normal distribution under the null hypothesis so that this test is not appropriate This is the so called Donner Hauck phenomenon named after Hauck and Donner 1977 who first drew attention to this phenomenon in the case of logistic regression It is discussed also in Geyer and Thompson 1992 section 1 6 and Albert and Anderson 1984 This occurs when the data indicates that the parameter should be very large in absolute value but not how large The parameter estimate as well as the standard error then are large and the ratio 4 does not need to be large The Wald test then cannot be used for significance testing In Section 6 7 2 we proposed that in such cases it may be helpful to fix the parameter at some large value without estimating it Or when it is being estimated and the overall maximum convergence ratio is small so convergence is judged as good this estimate can be used but in these cases not its standard error One possibility that then is available to test the significance is to make a second estimation run in which the parameter is fixed at the value 0 corresponding to the null hypothesis and test this null value using
280. the calculation of the ego statistic seems correct 166 6 To complete the extension of the package by this effect it also was added to the set of effects for symmetric and bipartite networks This was done by inserting at appropriate places in the file allEffects csv the same line but now with effectGroup changed to bipartiteObjective and symmetricObjective respectively 18 2 Notes on effectGroups and two mode networks For two mode networks the difference between the two node sets implies some peculiarities Recall that effectGroups are used in the file allEffects csv and in function effects r In the function getEffects in file effects r some additional measures are taken for ef fects in effectGroup covarBipartiteEff This implies that for adding such effects it will be necessary to see whether this function also must be modified this will have to be done in function covarBipartiteEff Note it would be preferable perhaps to have separate effect classes for covariates on the first and on the second mode as done for the effect groups in the following paragraphs A different approach was taken for effectGroups covarABehaviorBipartiteObjective and covarBBehaviorBipartiteObjective the former is for covariates on the first node set the second for covariates on the second node set For effects defined for two dependent networks and one actor covariate the following effectGroups are defined e covarNetNetObjective is for effects wh
281. the curve that is fitted the top or in the rare case of a reversed pattern bottom of the attractiveness of alters is not necessarily obtained at the diagonal i e at ego s value Straightforward calculus shows us that 38 is a quadratic function and obtains its extreme value a max imum if Bsq alter is negative a minimum if it is positive the latter is in general less likely for Balter Bexa vi v Uj y 2 Bsq alter 39 If the effect sq alter of the squared alter s value is negative and the interaction effect Bexa is positive then this location of the maximum increases with ego s own value vi Of course the number given by 39 will usually not be an integer number so the actual value of vj for which attractiveness is maximized is the integer in the range of V closest to 39 16Tn earlier versions of the manual there were some differences in this and the following tables because too much rounding was used at an early stage 151 For drinking there is a weak positive effect of squared drinking alter the effect of squared drug use alter is weak negative For drinking we see that the most attractive value for egos with v 1 or 2 is no drinking vj 1 whereas for egos with v gt 3 the most attractive alters are those who drink most v 5 We also see that egos with the highest drinking behavior are those who differentiate most strongly depending on the drinking behavior of their potential f
282. the tie variable X is structurally fixed at time tm at a value 2 tm then Xx also is equal to ij tm independently of whether this tie variable is structurally fixed at time tm 1 at the same or a different value or not at all This is the direct consequence of the structural fixation On the other hand the following rule is also used If Xj is not structurally fixed at time tm but it is struc turally fixed at time tm 1 at some value x tm41 then in the course of the simulation 31 process from tm to tm 1 this tie variable can be changed as part of the process in the usual way but after the simulation is over and before the statistics are calculated it will be fixed to the value x tm 1 The target values for the algorithm of the Method of Moments estimation procedure are calculated for all observed digraphs x tm4 1 However for tie variables X that are structurally fixed at time tm the observed value jj tm 1 is replaced by the structurally fixed value 2 tm This gives the best possible correspondence between target values and simulated values in the case of changing structural fixation 4 3 2 Missing data SIENA allows that there are some missing data on network variables on covariates and on dependent action variables Missing data must be indicated by the usual missing data code for R NA Missingness of data is treated as non informative One should be aware that having many missing data can seriously impair the
283. this is corrected Separate help files for sienaTimeTest plot sienaTimeTest includeTimeDummy Bug fix to treatment of missing data in sparse format bipartite networks Change to error message if an epoch is unlikely to terminate e 2010 06 04 R forge revision 92 RSienaTest only New average alter effects Bug fix to effects object for more than two groups e 2010 05 29 R forge revision 89 RSienaTest only New option to control orthogonalization in sienaTimeTest changes to includeEffects and sienaDataCreate NB changes reverted in revision 93 e 2010 05 28 R forge revision 88 RSienaTest only Time dummies for RateX effects e 2010 05 27 R forge revision 87 RSienaTest only bug fix to plot sienaTimeTest e 2010 05 23 R forge revision 86 RSienaTest only Bug fix to plot sienaTimeTest new function includeTimeDummy e 2010 05 22 R forge revision 85 RsienaTest only fixed bug in sienaTimeTest with uncondi tional simulation e 2010 04 24 R forge revision 81 New print summary and edit methods for Siena effects objects e 2010 04 24 R forge revision 80 199 fixed bug causing crash with rate effects and bipartite networks added trap to stop conditional estimation hanging new functions INCOMPLETE for maximum likelihood and Bayesian estimation one period two waves only no missing data one dependent variable only for Bayesian model 2010 04 13 R forge revision 79 new function sienaTimeTest 2010 04 12
284. tic shape effect by default unless range is less than 2 194 Shorten behavior interaction effectnames by removing the repeated variable name Fix bug when displaying manual from siena01Gui 2011 07 23 R forge revision 163 Fix bug in effectsDocumentation reduce memory size needed for non ML non finite difference models 2011 07 02 R forge revision 161 Fix problem with bayes routine with single data object only Fix problems with getRSienaRDocumentation internal functions within internal func tions now work but still not automatically and function now runs on non Windows too 2011 06 24 R forge revision 160 behavior endowment effects are now all defined consistently as current value less previous one as in the manual 2011 06 22 2011 06 23 R forge revision 158 159 behavior interactions Minor bug fixes to correct effects object and inclusion of non requested underlying effects Replace influence interaction effects by the three options Time dummies for behavior effects 2011 06 18 R forge revision 157 Fixed minor bug in siena07 code controlling maximum size of move was incorrect if using prevAns for an exactly equivalent fit 2011 06 13 R forge revision 156 fixed bug removing density effect for bipartite networks with some only waves up or down only 2011 06 12 R forge revision 155 Fixed bug with behavior variables with values 10 or 11 the 10th value in the matrix had 10 subtracted from it
285. ties tend to become reciprocated by X ties 124 21 closure of shared incoming WW gt X X shared incoming W sharedIn Oo sio z gt Zh Tij Whi Whj this refers to shared incoming W ties contributing to the tie w W 1 x J e o i X j The following two Jaccard similarity effects also are triadic but not expressed as sums over triads 22 23 Jaccard similarity with respect to outgoing W ties effect JoutMix the Jaccard similarity with respect to outgoing W ties 8759 z gt Tij Jw out i j where 2 h Wih Z jh Wit Wi ae Wih Wjh Jw out 4 J where 0 0 is taken as 0 Jaccard similarity with respect to incoming W ties effect JinMix defined by the Jaccard similarity with respect to incoming W ties siz3 gt Tij Jw inli J where gt h Whi Why Wai 035 gt h Whi Why divin 459 where again 0 0 is taken as 0 125 Then there are effects using mixed configurations on four nodes cf sharedPop 24 shared W leading to agreement along X X shared W to agreement sharedTo 4 W k o lt se SA z Dy h kiki Tij Zkj Win Wen this refers to the closure of mixed W X three paths the w x contribution of the tie i j is proportional to the number of u mixed W X three paths Wr Z k j i X j The effect parameter p can take the values 1 2 3 and 4 The value c a constant for centering is the average of the obse
286. timation process and give information with a score type test see Section 8 2 about the significance of this excluded effect Usually this will be applied with initialValue 0 the default But sometimes it may be done with a plausible non zero value for initialValue 60 e Two or more effects are included that are almost collinear in the sense that they can both explain the same observed structures This will be seen in high absolute values of correlations between parameter estimates presented in the summary of the results object and also in the output file In this case it may be better to exclude one of these effects from the model e An effect is included that is large but of which the precise value is not well determined see above section on fixing parameters This will be seen in estimates and standard errors both being large and often in divergence of the algorithm Fix this parameter to some large value Note large here means e g more than 5 or less than 5 depending on the effect of course Another trick that may be tried is the following Sometimes one or some of the rate parameters are especially the causes of difficulties of convergence Then one may fix this parameter at a good value and estimate the rest of the parameters Suppose that this is feasible i e good convergence can be obtained provided that this rate parameter is fixed Then by trial and error one may find a fixed value for this rate parameter for which
287. ting new effects New effect groups covarABNetNetObjective co varANetNetObjective and covarBNetNetObjective See SienaSpec tex pdf section 4 9 covarNetNet Bug corrected that occurred in print01Report for a sienaGroup object where the com ponent objects have constant dyadic covariates When a statistic is not plotted in plot sienaGOF because its variance is 0 a note about this is printed to the screen Minimum and maximum of plotted region in plot sienaGOF is calculated without taking into account non plotted statistics Bug corrected with includeTimeDummy for timeDummy greater than or equal to 10 siena TimeTest r In case of collinear parameter estimates standard errors are reported as NA Arguments main and ylab dropped from plot sienaGOF they did not work and their functionality now is covered by the argument so using main and ylab as arguments now should work Thanks to David Kavaler Changes in RSienaTest sienaBayes correction in initialization of truncation rate parameters based on prior error corrected for sampling constant parameters Changes in RSiena Parameter reduceg added in sienaAlgorithmCreate for use in siena07 like in RSiena Test e 2014 12 11 R Forge Revision 282 Changes in RSiena and RSienaTest Effects cl XWX and c12 XWX corrected thanks to Christoph Stadtfeld interactionType of gwesp effects was made dyadic Some layout cha
288. ting the targets we have to add the targets to the deviations To do this repeated transposition t can be used stats lt t t sim_ans sf sim_ans targets Calculate means and covariance matrix v lt apply stats 2 mean 83 covsf lt cov stats covsf is the same as sim_ans msf Of course any other distributional properties of the generated statistics can also be ob tained by the appropriate calculations and graphical representations in R 9 1 Accessing the generated networks If one is interested in the networks generated not only in the statistics internally calcu lated then the entire networks can be accessed This is done by using the returnDeps option as follows sim_ans lt siena07 myalgorithm data mydata effects myeff returnDeps TRUE The returnDeps TRUE option attaches a list sim ans sims containing all simulated networks as edge lists to the sim_ans object This uses rather a lot of memory Since here the default n3 1000 was used sim_ans will be a list of 1000 elements e g the 568 th network generated for wave 2 is given by sim_ans sims 568 1 1 111 The numbering is as follows first the number of the simulation run here arbitrarily 568 then the number of the group as defined in Section 11 1 1 in the usual case of single group data structures then the number of the dependent variable here 1 because it is supposed that there only is a dependent network the
289. tion is zero for creation of ties and is given by a 20 k for dissolution of ties In this formula the ypt are the parameters for the endowment function The potential effects s x in this function and their formulae are the same as in the evaluation function except that not all are available as indicated in the preceding subsection For further explication consult Snijders 2001 2005 here the gratification function is used rather than the endowment function Snijders et al 2007 and Steglich et al 2010 A better term than endowment is perhaps maintenance These functions are combined in the following way For the creation of ties the objec tive function used is P x Ga 21 in other words the parameters for the evaluation and creation effects are added For the dissolution of ties on the other hand the objective function is i 0 ela 22 in other words the parameters for the evaluation and endowment effects are added There fore a model with a parameter with some value 6 for a given evaluation effect and for which there are no separate creation and endowment effects has exactly the same con sequences as a model for which this evaluation effect is excluded and that includes a creation as well as an endowment effect both with the same parameter value k 8k and Yk Br Of the three types of effect evaluation creation and endowment one therefore should use one or two
290. to diminish the collinearity between this and the density effect this is left out in later versions of SIENA sum of 1 out degree c outInv where c is some constant defined by Sigg z 1 i 0 endowment effect only likelihood based sum of 1 out degree c out degree c 1 outSqInv where c is some con stant defined by sigo z 1 ai4 0 tix c 1 endowment effect only likelihood based out out degree 1 c assortativity outOutAss which represents the differential tendency for actors with high out degrees to be tied to other actors who likewise have high out degrees 1 c 1 sigo z x Tij T u x c can be 1 or 2 the latter value is the default out in degree 1 c assortativity outInAss which represents the differential ten dency for actors with high out degrees to be tied to other actors who have high in degrees 1 1 sigilo Y ry alas c can be 1 or 2 the latter value is the default in out degree 1 c assortativity inOutAss which represents the differential ten dency for actors with high in degrees to be tied to other actors who have high out degrees 1 c_1 a Dy ry reete c can be 1 or 2 the latter value is the default in in degree 1 c assortativity inInAss which represents the differential ten dency for actors with high in degrees to be tied to other actors who likewise have high in degrees 1 c_1 Be Dyrys ey c can be 1 or 2 the latter
291. tor is unnecessarily high on the other hand computing time will be unnecessarily high The advice is to aim at values between 0 1 and 0 3 or 0 4 A practical way to proceed is as follows For initial tuning of the multiplication factor use the model that is obtained as the default after creating the effects object with very few effects included The reason for using this model is the limited computation time and easy convergence If the highest autocorrelation is more than 0 3 increase the multiplication factor e g by making it twice as large which will also lead to a twice as long computation time and estimate the model again If the highest autocorrelation is less than 0 1 then decrease the multiplication factor and estimate again Tune the multiplication factor until the highest autocorrelation is between 0 1 and 0 3 Then start with estimating the models of interest For other models the autocorrelations may change again therefore it still can be important later on to adapt the multiplication factor to keep the highest autocorrelation less than 0 4 Another parameter of the algorithm that sometimes needs tuning but less often than the multiplication factor is the Initial value of the gain parameter This determines the step sizes in the parameter updates in the iterative algorithm It influences the stability and speed of moving of the algorithm A too low value implies that it takes very long to attain a reasonable parameter estimate whe
292. tors with high out degrees to preferably be tied to column units with high in degrees 5 4 Effects for network dynamics associated with covariates For each individual covariate there are several effects which can be included in a model specification both in the network evolution part and in the behavioral evolution part should there be dependent behavior variables in the data Of course for two mode networks the covariates must be compatible with the network with respect to number of units rows columns e network rate function al the covariate s effect on the rate of network change of the actor e network evaluation creation and endowment functions 1 the covariate similarity effect which is suitable for variables measured on an interval scale or at least an ordinal scale where it is meaningful to use the absolute difference between the numerical values to express dissimilarity a positive parameter implies that actors prefer ties to others with similar values on this variable thus contributing to the network autocorrelation of this variable not by changing the variable but by changing the network for categorical variables see the same covariate effect below the effect on the actor s activity covariate ego a positive parameter will imply the tendency that actors with higher values on this covariate increase their out degrees more rapidly the effect on the actor s popularity to other actors
293. transitive closure which can be represented by the tendency toward forming closed triplets as in this figure When the first of these ties means the closing of a two path i h j while the second means forming a tie to an actor h who made the same outgoing choice to the third actor 7 a sign of structural equivalence so these are distinct processes The evaluation effect corresponding to the tendency toward forming closed triples is the transTrip effect which is composed of the two distinct elementary effects transTrip1 contributing to cre ating or maintaining the gt j tie and transTrip2 contributing to the i gt h tie see Section 12 An elementary effect is a contribution to the creation or maintenance of a tie defined directly i e without expressing it based on the change in some evaluation function This means that elementary effects are more general than evaluation effects and all effects could be represented as elementary effects For the sake of interpretation however the evaluation function formulation is used whenever possible Elementary effects can apply similarly to the creation and maintenance of a tie or they can apply exclusively to tie creation or exclusively to tie maintenance In RSiena the difference between elementary effects and evaluation effects is only in the internal programming code and the possible values of the type of effect as specified in the effects object and the functions includeEffects a
294. tribution for this effect note that eke 540 Lid La oy e s Lj4 Lyi j j This shows that given that is being updated for all j the contribution for this effect for parameter 2 can be computed as Lj40 Z j U Tip Tji where 0 0 is interpreted as 0 total covariate alter at distance 2 totDist2 This is like the previous effect but using the total instead of the average value of alter s covariate For parameter 1 it is defined as sigs z y Tij Uj40j parameter 1 j and for parameter 2 as sigs z y Eij Ej4 zj parameter 2 j x oa where 0 and ot are as above ego alter distance 2 covariate similarity simEgoDist2 defined as the sum of centered similarity between and alters covariate average for all actors 7 to whom i has a tie net r A Sig4 z Tij sim sim y j where the similarity scores sim t are defined as A los A 2 sim 0 118 85 86 87 88 e u i where A max u is the observed range of the original covariate v al isas above in effect altDist2 and sim is the mean of all similarity scores as used also for the simX effect this centering is applied since version 1 1 285 For a constant covariate mycov this mean is given by attr mydata cCovars mycov simMean covariate similarity at distance 2 simDist2 defined as the sum of centered similarity values for alters
295. ttributes allowOnly and simOnly ported from RSienaTest Improved error messages in includeEffects ported from RSienaTest sienaGOF ported from RSienaTest siena table ported from RSienaTest For RSienaTest only bayes renamed to sienaBayes and considerably changed with print option For RSiena and RSienaTest Changes to sienaGOF new use structure with extraction functions sparseMatrixExtrac tion networkExtraction behaviorExtraction allowing the testing of any dependent vari able commented out some superfluous lines The function sienaModelCreate is now called sienaAlgorithmCreate but the earlier name is still retained as an alias the class name of the object created by this function is now called sienaAlgorithm The function sienaNet is now called sienaDependent but the earlier name is still retained as an alias the class name of the object created by this function is now sienaDependent The function effectsDocumentation now has an extra argument effects if this points to an effects object all available effects in this effects object are listed with shortName with a variety of other often used characteristics Added effects some existed already in RSiena Test average exposure effect on rate xxxxxx avExposure susceptibility to av exp by indegree effect on rate xxxxxx susceptAvIn total exposure effect on rate xxxxxx totExposure infection by indegree effect on rate xxxxxx infectln infection
296. tual W choices of others i wns j 15 W leading to agreement along X X W to agreement to h siie 2 X jn Vij Wih Chg i this refers to the closure of mixed W X two paths the contri bution of the tie 3 j is proportional to the number of mixed w x W X two paths i h j ae J Note that since this is the evaluation function for actor 7 with 1 respect to network X only the z tie indicator in the formula corresponding to the tie 1 3 j is the dependent variable here The interpretation is that actors have the tendency to make the same outgoing X choices as those to whom they have a W tie 16 XWX closure of W c1 XWX sia z Dj Tij Tin Uh h 0 this refers to the closure of mixed X W two paths the contri N W S bution of the tie i gt j is proportional to the number of mixed A X W two paths i Sha j plus the number of mixed X W e two in stars i 3 h j Kh i The interpretation is the closure of X W paths if there is a tie h 5 j then ties i x jand i 2 h will tend to entrain each other The reported target statistic is multiplied by 2 There are two partial variants of this effect they can be distinguished not by the Method of Moments but only by Maximum Likelihood and Bayesian estimation 123 17 XWX closure 1 of W cl XWX1 This is an elementary effect not an evaluation effect comprising of the XWX clo sure of W effect only the contribution of the the nu
297. tween constant and varying covariates e g sex and salary Finally there are individual monadic and dyadic covariates that refer respectively to characteristics of individual actors e g sex and to attributes of pairs of actors e g living in the same neighborhood or kinship 12 Missing data and composition change Stochastic Actor Oriented Models distinguish between two types of missing values ab sence of actors from the network and random missingness The first case refers to changing composition it is possible to specify that some actors leave or join the network between two observations during the simulation process This then applies to all dependent variables networks behaviors simultaneously see Section 4 3 3 for more details In the second case missing values are treated as randomly missing see Section 4 3 2 for more de tails Stochastic Actor Oriented Models can deal with some but not too much randomly missing data as a rule of thumb more than 20 is considered to be too much With too many missing values the simulation can become unstable and also the estimated param eters may not be substantively reliable anymore And of course missing data are likely to are caused by processes that are not totally random and therefore risk to bias the resuls Explanatory variables the effects When defining Stochastic Actor Oriented Models we have to specify the exact ways in which current network structure or cova
298. tween the sub project dummies and those parameters for which there were important between network differences or option 4 where the randomness of the effects is determined by these differences When the data sets for the different networks are quite small then one might start by option 2 and use sienaTimeTest to test for which of the effects especially there is a large variation in parameter values across the sub projects next one could follow approach 4 determining the randomness of the effects by the results about this variability In all cases it is probably best to use an identical model specification for the various groups A problem that may occur especially if the groups are small is that in some of the groups the change of the dependent variable network or behavior may be upward only or downward only which by default then will be regarded by RSiena as a constraint for the simulations as mentioned in Section 4 2 3 This leads to model differences that in most cases will be undesirable Therefore it is advisable in the original construction of the datasets to use allowOnly FALSE in the call of sienaDependent 11 1 Multi group Siena analysis The multi group option glues several projects further referred to as sub projects after each other into one larger multi group project These sub projects must have the same sets of variables of all kinds that is the list of dependent networks dependent behavioral variables actor
299. ty z z 2325 02 Tja and the mean behavior i e 0 if the ratio is 0 0 total alter effect totInAlt defined by s behavior multiplied by the sum of be havior of his in alters sits 2 2 0 Zi 25 average reciprocated alter effect avRecAlt defined by 2 s behavior multiplied by the average behavior of his reciprocated alters sho 2 2 zi X Tij ji 25 X Lig Zi and 0 if the ratio is 0 0 134 20 21 22 23 24 25 total reciprocated alter effect totRecAlt defined by it s behavior multiplied by the sum of behavior of his reciprocated alters sigo z z zi Zj Tij Zi 25 average alter effect at distance 2 avAltDist2 defined by s behavior multiplied by the average of the alter averages E of his alters excluding the contribution from a tie j gt i if any defined by Tih Zh i _ nzi jh Zh if Lj Lyi gt 0 j TY Z j 24 0 if Li Tji 0 also see 15 f see mee ym and the mean behavior i e 0 if the ratio is 0 0 total alter effect at distance 2 totAltDist2 defined by 2 s behavior multiplied by the total of the alter totals of his alters excluding the contribution from a tie 7 i if any G2 D e average total alter effect at distance 2 avTAltDist2 defined by it s behavior multi plied by the average of the alter totals of his alters excluding the contribution from a tie j 1 if any sboh
300. ty effect is meaningless because it refers to incoming ties of actors with high out degrees and there are no similarity effects of actor covariates There is one additional effect for two mode networks viz the four cycle effect Some of the effects contain a number which is denoted in this section by c and called in this manual an internal effect parameter These are totally different from the statistical parameters which are the weights of the effects in the objective function These are set or modified by the setEffect function e g myeffects lt setEffect myeffects gwespFF parameter 69 12 1 Network evolution The model of network evolution consists of the model of actors decisions to establish new ties or dissolve existing ties according to evaluation creation and endowment functions and the model of the timing of these decisions according to the rate function The model and the roles played by these three functions were briefly explained in Section 5 1 For some effects the creation and endowment functions are implemented not for es timation by the Method of Moments but only by the Maximum Likelihood or Bayesian method this is indicated below by endowment effect only likelihood based 102 It may be noted that the network evaluation function was called objective function and the creation and endowment functions were called gratification function in Snijders 2001 12 1 1 Network evaluation function T
301. ty means that the matrix that is inverted to give the correlation matrix is ill conditioned Correlations between parameter estimates close to 1 are the most usual signs of this If the parameter estimates are perfectly collinear standard errors of some parameters or linear combinations of parameters being infinitely large standard errors are reported as NA the R term for not available missing This can happen depending on the data model combination e g including the covariate ego effect for a covariate with variance 0 or including some effects that are collinear for any data set such as the combination of outdegree transitive triplets outdegree activity and balance effects see Snijders 2005 or on the combination of data model and parameters when a parameter value was given or was reached where the model is not sensitive to some parameter or combination of parameters The remedy here usually is to drop some of the effects In cases with strong but not complete multicollinearity i e correlations between some parameter estimates or some of their linear combinations being close but not equal to 1 or 1 the estimated standard errors are less reliable Estimates for these correla tions are given under the heading Covariance matrix of estimates correlations below diagonal in the output file and in the summary of the estimation results see Section 6 5 3 Strong collinearity may in practice lead to large di
302. ue data code then the other covariate effects are made available When analysing multiple data sets in parallel for which the same set of effects is desired to be included it is therefore advisable to give data sets in which a given covariate has the same value for all actors one missing value in this covariate purely to make the total list of effects independent of the observed data 4 1 5 Dyadic covariates Like the digraph data also each measurement of a dyadic covariate must be contained in a separate matrix For one mode data this is a square data matrix and the diagonal values are meaningless A distinction is made between constant and changing dyadic covariates where change refers to changes over time Each constant covariate has one value for each pair of actors which is valid for all observation moments and has the role of an independent variable Changing covariates on the other hand have one such value for each period between measurement points If there are M waves i e observation moments of network data this covers M 1 periods and accordingly for specifying a single changing dyadic covariate an xn x M 1 array is needed Like is the case for monadic covariates changing dyadic covariates are assumed to have constant values from one observation moment to the next If observation moments for the network are t ta tm then the changing covariates refer to the M 1 moments t through tyy_ and the m th va
303. ue of the behavior Z also have themselves a stronger tendency toward high values on the behavior 46 6 The total alter effect expressing that actors whose alters have a higher total value of the behavior Z also have themselves a stronger tendency toward high values on the behavior 7 The indegree effect expressing that actors with a higher indegree more popular actors have a stronger tendency toward high values on the behavior 8 The outdegree effect expressing that actors with a higher outdegree more active actors have a stronger tendency toward high values on the behavior Effects 1 and 2 will practically always have to be included as control variables For dependent behavior variables with 2 categories this applies only to effect 1 When the behavior dynamics is not smooth over the observation waves meaning that the pattern of steps up and down as reported in the initial part of the output file under the heading Initial data description Dependent actor variables Changes is very irregular across the observation periods it can be important to include effects of time variables on the behavior Time variables are changing actor covariates that depend only on the observation number and not on the actors E g they could be dummy variables being 1 for one or some observations and 0 for the other observations The average similarity total similarity average alter and total effects are different spec
304. uld use the generic effect approach and not the following 18 1 Example adding the truncated out degree effect As an example we show how the truncated out degree effect short name outTrunc was added It is defined by net si x min zi 43 where c is an internal effect parameter 1 The change statistic 42 is 1 la lt c zij 0 or i lt Gey 1 Ayus 0 else 44 Note that for this effect the case for going up z 0 must be distinguished from the case for going down z 1 2 In the file allEffects csv the name of the effect group nonSymmetricObjective seems to cover the type of effect we are considering and also contains other effects such as out degree activity which are very similar to this effect The row for the out degree activity sqrt effect was copied and inserted below this row The effectName was changed to outdegree trunc the functionName to Sum of outdegrees trunc and the shortname to outTrunc The hash sign in these names will be replaced by the value of the internal effect parameter in the written output The parm column which defines the default value of the internal effect parameter was set to 5 The package was built Loading it in R and creating an RSiena data set showed that indeed the effect was there 3 The name TruncatedOutdegreeEffect was chosen for the new function In the file AllEffects h the line include Truncated0utdegreeEffec
305. ulties if it is not the same as the name of the package you are trying to build or install you can do all these things with RSienaTest also For Windows computers the following type instructions are Dos commands A con venient way to apply them are by including them in a batch file extension name bat followed by a name with pause so that the Dos window that will contain the error messages if there are any will still be there when all is over Install Installing will recreate the binary and install in your normal R library path Type R CMD INSTALL RSiena Build Building will create a tar ball Type R CMD build RSiena This may give warning messages about the line endings if you run it on Windows Do not worry unless you have created any new source files when it might remind you to set the property of eol style on them when you add them to the repository Check Checking is a process designed to ensure that packages are likely to work correctly when installed Type R CMD check RSiena_1 0 n tar gz where n is adjusted to match the tar ball name zip file To make a zip file that can be used in Windows for installing from a local zip file and therefore is easy for distribution to others type R CMD INSTALL build RSiena_1 0 n tar gz where again n is adjusted to match the tar ball name If you make a change you need to INSTALL the new version in order to test it and before you commit any changes to a repository you sh
306. unction is defined and the arrow gt indicates a further pointer thus the variable this gt pNetwork gt outDegree this gt ego refers to the outdegree of ego denoted in our mathematical formulae by in the current network in other words 2 The variable this gt 1c refers to the internal effect parameter denoted in our formu lae by c The return statement defines the function value that is returned when the function is called Armed with this knowledge we specified the change statistic implementing 44 as follows double TruncatedOutdegreeEffect calculateContribution int alter const double change 0 Current out degree int d this gt pNetwork gt outDegree this gt ego if this gt outTieExists alter After a tie withdrawal the new out degree would be d 1 and the new effect value would have decreased by 1 if d lt this gt lc if d lt this gt 1c change 1 else When introducing a new tie the new out degree would be d 1 and the new effect value would have increased by 1 if d lt this gt lc if d lt this gt 1c change 1 return change The effect statistic implementing 44 was specified as follows double TruncatedO0utdegreeEffect egoStatistic int ego const Network pNetwork Current out degree 165 int d this gt pNetwork gt outDegree this gt ego if d lt this gt 1c return d else ret
307. unities for change of the single tie variable z occur at the rate A x Aj The numerical interpretation is different from that in the first two models 5 8 Additional interaction effects It is possible for the user to define additional interaction effects for the network and the behavior The basis is provided by the initial definition by SIENA of unspecified interaction effects The interaction is defined by the columns effect1 and effect2 and for three way effects effect3 in the effects object they contain the effectNumber sequence number of the effects that are interacting The interaction effect must be included to be part of the model but the underlying effects need only be included if they are also required individually In most cases this is advisable The number of possible user defined interaction effects is limited and is set in the call of getEffects Interactions can be specified by the function includelnteraction explained in the fol lowing subsections All effects have a so called interactionType defined by the column interactionType in the effects data frame This interaction type defines what is allowed for definition of interaction effects an explanation of the background of this is given in section Statistics 48 x for MoM of Siena_Algorithms pdf For network effects the interaction type is ego dyadic or blank for behaviour effects it is OK or
308. uns in the following The MoM estimation algo rithm is based on comparing the observed network obtained from the data files to the hypothetical networks generated in the simulations Note that the estimation algorithm is of a stochastic nature so the results can vary This is of course not what you would like For well fitting combinations of data set and model the estimation results obtained in different trials will be very similar It is good to repeat the estimation process at least once for the models that are to be reported in papers or presentations to confirm that what you report is a stable result of the algorithm 6 1 The estimation function siena07 The estimation process implemented in function siena07 starts with initial values for the parameters and returns a so called sienaFit object in this example called results1 which contains the estimates and their standard errors and a lot of further information Since the estimate is iterative depending on the initial value and stochastic the results are not always completely satisfactory We shall see below how the satisfactory convergence of the algorithm can be checked and how to go on if this is not satisfactory The estimation algorithm is determined by a call of functions such as algorithmi lt sienaAlgorithmCreate projname trypro useStdInits FALSE results1 lt siena07 algorithml data mydata effects myeff The function sienaAlgorithmCreate defines an algor
309. upName and varName 157 Error in if isbipartite argument is of length zero This can happen directly when calling sienaGOF It indicates that you used a wrong name for groupName or varName See the help file for sienaGOF Solutions Use a correct groupName and varName 158 Part III Programmers manual 15 Get the source code To do something with the source code first you must get access to it In the first place it is good to know that for any R function that can be called the source code is listed by writing the function name Thus if RSiena is loaded the command sienaAlgorithmCreate will list the code for the function with this name To get insight into a package and certainly to modify or personalize it it is necessary however to get the source code of the whole package This can be done by downloading from CRAN or R Forge the tarball with extension tar gz This file can be extracted by compression decompression programs perhaps you need to do a double extraction If you do not succeed in extracting the tar ball see below for the use of RTools for this purpose This will lead to a directory structure where at some place there is a directory called RSiena and or a directory called RSienaTest which includes the source code of the package In the file structure for RSienaTest there is a directory doc which contains a lot of programmers documentation These are in the form of TFX files which can be
310. urn this gt lc 5 Having done this the package was built and installed again To be honest there first were some errors but the error messages from the compiler are quite clear and easily led to solving the errors Upon starting R and loading RSiena indeed the new effect was available For an easy check the following commands were used mynet lt sienaDependent array c s501 s502 dim c 50 50 2 mydata lt sienaDataCreate mynet myalgorithm lt sienaAlgorithmCreate projname s50_12 myeff lt getEffects mydata myeff lt setEffect myeff outTrunc parameter 3 ans lt siena07 myalgorithm data mydata effects myeff summary ans The parameter was set at 3 because the maxima of the observed out degrees in the two data sets s501 as well as 502 were 5 so the outdegree trunc effect would be highly collinear with the outdegree effect if the default parameter of 5 were used This led to good convergence To check the calculation of the statistics it was noted that the output file mentioned the target values Observed values of target statistics are 1 Number of ties 116 0000 2 Number of reciprocated ties 70 0000 3 Sum of outdegrees trunc 3 105 0000 The value of the target statistic for the new effect should be Y set e ta Y min wi t2 3 i i This can be directly calculated in R by requesting sum pmin rowSums s502 3 which indeed returns the value 105 confirming that
311. ut not skip Phase 1 of the estimation algorithm and sometimes this turns out to lead to faster convergence The following function will iterate the execution of siena07 until it has converged It can be modified to suit your further purposes The argument ansO can be employed to use an earlier existing on track estimation result if available as the initial value for the algorithm siena07ToConvergence lt function alg dat eff ansO NULL numr lt 0 ans lt siena07 alg data dat effects eff prevAns ansO the first run repeat numr lt numr 1 count number of repeated runs tm lt ans tconv max convergence indicator cat numr tm n report how far we are if tm lt 0 25 break if tm gt 8 break success divergence without much hope of returning to good parameter values if numr gt 100 break now it has lasted too long ans lt siena07 alg data dat effects eff prevAns ans if tm gt 0 25 cat Warning convergence inadequate n ans Another approach that sometimes can be helpful to obtain convergence in difficult situations is to gradually build up the model adding further effects while using the prevAns parameter to use previous estimates as starting values for the next extended model This may be more successful than estimating a complicated model right from the start 6 2 What to do if there are convergence problems If there are persisti
312. value is the default network isolate effect isolateNet the effect of ego having in degree as well as out degree zero i e being a total isolate sigi 2 z H 4i zi 0 111 45 46 47 48 49 anti isolates effect antilso the effect of wishing to connect to others who other wise would be a total isolate i e have no incoming or outgoing ties and wishing not to sever connections to others who thereby would become a total isolate sigs x D z gt 1 054 O anti in isolates effect antiInIso the effect of wishing to connect to others who otherwise would have no incoming ties and wishing not to sever connections to others who thereby would lose their last incoming connection sing D0 T z 2 1 anti in near isolates effect indegree at least 2 effect antiInIso2 in2Plus the effect of wishing to make a new connection to others who currently have an indegree equal to 1 and wishing not to sever connections to others who currently have an indegree equal to 2 Siar 0 X x y gt 2 indegree at least 3 effect in3Plus the effect of wishing to make a new connection to others who currently have an indegree equal to 2 and wishing not to sever con nections to others who currently have an indegree equal to 3 sis 0 27 T z gt 3 isolate popularity effect isolatePop the effect of being tied to actors who further are isolates the fact that such a tie does e
313. variates the values of dependent action variables are not assumed to be constant between observations Dependent behavioral variables must have nonnegative integer values e g 0 and 1 or a range of integers like 0 1 2 or 1 2 3 4 5 The number of different values should not be too high ten values is on the high side Each dependent action variable must be given in one matrix containing k M columns corresponding to the M observation moments If any values are not integers a warning will be printed on the initial report given by printO1Report and the values will be truncated towards zero A special case of behavioral data can be used for diffusion of innovations Greenan 2015 here the behavior variable representing having adopted the innovation is binary coded 0 or 1 and changes 1 gt 0 are impossible Model specifications that are especially useful for this data type are presented in Section 12 2 4 4 1 4 Individual covariates Individual i e actor bound or monadic variables are defined by the functions coCovar in the case they are constant over time and varCovar if they are changing over time Each constant actor covariate has one value per actor valid for all observation moments and has the role of an independent variable Changing variables can change between observation moments then they are called changing individual covariates and have the role of independent variables Changing individual covariates are assume
314. ven in the later part of the runs possibilities are to increase nrunMHBatches but also to increase the mult parameter in sien aAlgorithmCreate Increasing these will for both of them lead to a proportional increase in computing time If multiple processors are available which most computers have nowadays you can make more speed by setting the nbrNodes parameter to a value larger than 1 Since parallelization goes by period x group it is nice but not necessary to have a value for nbrNodes that is a divisor of the number of periods multiplied by the number of groups higher values are meaningless Do not use such a high value for nbrNodes that your computer gets too hot or overworked For Windows machines this can be monitored by opening the Task Manager you will find how to do this by right clicking on the bottom toolbar 11 3 5 Prior distributions More research is needed for advice about prior distributions Especially for small numbers of groups the priors may have a strong influence The prior mean and prior variance need to be given for the vector of parameters that are randomly varying between the groups These are the rate parameters and the parameters specified with random TRUE in the call of setEffect The list and order of the randomly varying effects except for the rate parameters is shown by requesting myeff myeff randomEffects amp myeff include if the effects object is called myeff The prior mean priorMu
315. vision 17 version Number 1 0 6 xtable method to create lAT Xtables from the estimation results object added support for bipartite networks structural zeros and 1 s processing checked and amended use more sophisticated random number generator unless parallel testing with siena3 203 C References Albert A and Anderson J A 1984 On the existence of the maximum likelihood estimates in logistic regression models Biometrika 71 1 10 An W 2015 Multilevel meta network analysis with application to studying network dynamics of network interventions Social Networks 43 48 56 Bather J 1989 Stochastic approximation A generalisation of the Robbins Monro procedure In Mandl P and Huskov M editors Proceedings of the fourth Prague sympostum on asymptotic statistics pages 13 27 Charles University Prague Block P 2015 Reciprocity transitivity and the mysterious three cycle Social Networks 40 163 173 Butts C 2008 Social network analysis with sna Journal of Statistical Software 24 6 Cheadle J E Stevens M Williams D T and Goosby B J 2013 The differential contributions of teen drinking homophily to new and existing friendships An empirical assessment of assortative and proximity selection mechanisms Social Science Research 42 1297 1310 Cochran W G 1954 The combination of estimates from different experiments Bio metrics 10 101 129 Davison A C and Hinkley D V 1997
316. wed by a sienaTimeTest and specify those effects as randomly varying for which the time heterogeneity is largest according to the groupwise results misspecification if it would be erroneously assumed that the effect is fixed across groups would this affect the parameter estimates of primary interest About this we have little general knowledge it can be tried out by running estima tions for different specifications of this part of the model amount of information which specification will use the information in the data most efficiently Here finally we do have an answer Assuming that an effect is fixed across groups will give a smaller uncertainty posterior standard deviation interpreted as stan dard error in the estimated parameter than assuming it varies randomly cf Sec tion 11 3 8 This will be the more so as the number of groups is smaller Therefore for the coefficients for which there is no strong prior knowledge that they are variable across groups and which are tested as a primary issue for answering the research question from the point of view of statistical power it is advisable to specify that they are fixed 11 3 3 How to enter your data in sienaBayes See the example at the bottom of the sienaBayes help page for how a sienaGroup object can be created and used If some but not all of the Siena data objects combined in the sienaGroup have periods where changes are only upward or only downward it will be necessa
317. ween independent groups o o 8 6 Testing time heterogeneity in parameters o o 000000000 ee Simulation 9 1 Accessing the generated networks aoaaa 9 2 Conditional and unconditional simulation 72 72 73 74 74 76 77 78 79 80 80 81 10 Getting started 86 101 Model choice s puk 244449 88 6 bebe bee w W u W Oh SU S bbe Q Q h k a ES 87 11 Multilevel network analysis 88 11 1 Multi group Siena analysis sa sore t e w e p us w w w e ee 89 11 2 Meta analysis of Siena results a a a s wu q amp Q a ee Sus a 90 11 2 1 Meta analysis directed at the mean and variance of the parameters 91 11 2 2 Meta analysis directed at testing the parameters 93 11 2 3 Contrast between the two kinds of meta analysis 94 11 3 Random coefficient multilevel Siena analysis aaa 94 11 3 1 Which data sets to use for sienaBayes 95 11 32 Model apeciica tod placa a a A eS 96 11 3 3 How to enter your data in sienaBayes 96 11 3 4 How to choose the parameter settings for sienaBayes 97 113 5 Prior dlstribltl0Bs 6 44524 542 reso 97 11 3 6 Operation of sienaBayes u s p cu c purwa ku s w ea C P A Ua 99 11 3 7 Assessing convergence soaa esa ss s a 99 11 3 8 Interpreting results of sienaBayes o e s s r r e s 100 12 Formulas for effects 102 1
318. whether the parameter is positive or negative These are the Bayesian versions of estimates standard errors confidence intervals and p values The functions simpleBayesTest and multipleBayesTest are available for testing pa rameters see the help page for these functions To compute further properties of the sample of the posterior the components ThinParameters ThinPosteriorMu ThinPosteriorEta and ThinPosteriorSigma of the sienaBayesFit object as mentioned in the help page may be useful It should be noted that the out files produced by sienaBayes are produced somewhere 100 in the initial phase of the project and not meant to be informative for final results They may be disregarded When comparing results for specifications that differ with respect to specifying the effects as fixed or varying across groups it will be noted that posterior standard deviations for the means are larger when specifying the effects as randomly varying as compared to specifying them as fixed This is natural and it is associated with a difference in interpretation Specifying the effect as randomly varying implies that there also is an important step of generalization from the observed groups to the population of groups The between group variance then is a priori unknown and one is estimating a mean parameter from a sample of N groups usually N is not very large and the uncertainty about the between group differences will contribute considerably t
319. work is rarely used For this type of data numerous alternative longitudinal modeling techniques exist Accordingly the fourth model type has been becoming widely used Analyzing the joint evolution of networks and behavior allows researchers to address questions related to selection and influence processes for example whether smokers tend to become friends with each other or friends tend to become similar in their smoking habits The strength of the SIENA co evolution models is that one can simultaneously take into account the impact of network structure on network evolution the actual level of a behavior on be havior change the network structure on behavior change and the actual level of behavior on network evolution Besides network and behavior co evolution this class of Stochastic Actor Oriented Models also allow for the joint analysis of multiple networks e g friend ship and advice friendship and dislike or all three of them and the analysis of ordered multiple networks where the presence of a tie in one network presumes the existence of a tie in the other network like in the case of friendships and best friend relations 2 1 2 Data variables and effects Now that we have discussed some core features of Stochastic Actor Oriented Models and introduced the different implemented model types we turn our attention still just pre senting an outline to data types and the specification of a model In general the number of waves mus
320. xist will give the other actor an in degree of 1 sio T 2 Do tij H243 1 054 0 Note that perhaps this effect is of limited use as other third actors might increase the indegree of j to more than 1 and then the ex isolate does not contribute any more to s evaluation of the network the three effects above anti isolates anti in isolates and anti in near isolates may be more useful instead Note that the network isolate effect expresses the tendency for ego to be an isolate not sending ties if ego has indegree 0 whereas the in isolate and isolate popularity effect express the tendency for ego to connect to others who without this connection would have an indegree of 0 or be total isolates respectively Thus in modeling the number of isolates for the network isolate effect the agency is in the isolate see the 7 in the formula whereas for the various anti isolates and the isolate popularity effects the agency is in others connecting or not to the isolate see the j in the formulaee Dyadic covariate effects The effects for a dyadic covariate wij are 50 covariate centered main effect X sigo z Do Tij wig W where is the mean value of wij 112 5l 52 53 54 covariate centered x reciprocity XRecip net Sisi 2 2 Pig X ji Wij 00 Various different ways can be modeled in which a triadic combination can be made between the dyadic covariate an
321. y suggested to start with a run with very low values of the sample size settings for the MCMC procedure When the procedure has made a good start but the MCMC sample seems too short you can make a prolonged analysis using the prevBayes option and then combine the earlier with the later results using glueBayes This is illustrated in the example on the help page During operation of sienaBayes partial results of the function are now and then stored as objects named z in files with the name PartialBayesResult RData see the help page This is for the case that the computer or R stops inadvertently during the long computations These are sienaBayesFit objects and therefore can be used in the print and summary functions they also can be used for the prevBayes option to continue estimation 11 3 7 Assessing convergence You can visually inspect convergence by looking at the tracelines of the various param eters These can be plotted by the functions in BayesPlots r available from the Siena website In many cases the tracelines for the rate parameters already tell the story about convergence The file BayesPlots r contains a variety of plotting functions that can be used to obtain trace plots and posterior density plots The parameters nwarm and nmain in the call of sienaBayes only imply that an ex tra improveMH step is made between the warming and the main iterations there are no other differences between the warming and main iterations I
322. yi Li r gt Tj ji J j j recalling that z 0 for all i The contribution of the out degrees to the rate function is a factor exp Qp Ti if the associated parameter is denoted p for some h and similarly for the contribu tions of the in degrees and the reciprocated degrees For the analysis of diffusion of innovations which is applicable if the behavior variable is a non decreasing variable with values 0 and 1 there are various contagion effects that render a model that would reduce to a proportional hazards model if the network were constant see Greenan 2015 This holds if they are part of the rate function but not if they are included in the evaluation function This also holds for effects depending on actor covariates For all these effects the rate function is multiplied by exp an ain 2 if the associated parameter is denoted o for some h and the effect is a z 142 average exposure effect avExposure defined as the proportion of i s alters who have adopted the innovation jaa jtij G 12 y gt Tij total exposure effect totExposure defined as the number of i s alters who have adopted the innovation n aj y D 25245 j 1 infection by indegree effect infectIn defined as the sum of indegrees of s alters who are also adopters of the innovation n aia y y ZjLijt j j 1 infection by outdegree effect infectOut defined as the sum of outdegrees of
323. ying dyadic covariates as mydata dyvCovars Since smoke1 is a constant covariate and alcohol a changing covariate their means can be requested by attr mydata cCovars smokel mean attr mydata vCovars alcohol mean and the centered values for e g the variable alcohol by nydata vCovars alcohol The mean of the similarity variable is stored as the simMean attribute and is obtained by e g attr mydatafcCovarsfsmokel simMean The formula for balance is a kind of dissimilarity between rows of the adjacency matrix The mean dissimilarity is subtracted in this formula having been calculated according to a formula given in Chapter 12 It is also reported in the output and available for the first dependent variable as attr mydata depvars 1 balmean Instead of 1 you can request a different number or the name of the variable 29 4 2 3 Monotonic dependent variables In some data sets a dependent variable only increases or only decreases For a network this means that ties can be created but not terminated or the other way around This may be the case for all periods a period is defined by the two consecutive observation waves at its start and end points or just in some of the periods RSiena will note when a dependent variable only increases or only decreases in any given period and mention this in the output file generated by printO1Report This constraint then is also respected in the simulations in the pe
324. ysis you wish to add time dummy terms this may be done via The dummy t is always zero so that period w is arbitrarily considered the reference period 81 myeff lt includeTimeDummy myeff recip balance timeDummy 2 ans3 lt siena07 myalgorithm data mydata effects myeff batch TRUE and testing again tt3 lt sienaTimeTest ans3 and so on See Lospinoso 2010 for a walkthrough of the model selection process for time dummy terms 82 9 Simulation The simulation option simulates the network evolution for fixed parameter values This is meaningful e g for theoretical exploration of the model for goodness of fit assessment and for studying the sensitivity of the model to parameters Simulations are produced by the siena07 function also used for parameter estimation but by calling it in such a way that only Phase 3 is carried out see section 6 4 This is done by requesting nsub 0 in the model specification in function sienaAlgorithmCreate By also requesting simOnly TRUE the calculation of standard errors which usually is not meaningful when simulating without estimating is suppressed sim_model lt sienaAlgorithmCreate projname sim_model cond FALSE useStdInits FALSE nsub O simOnly TRUE sim_ans lt siena07 sim_model data mydata effects myeff Mostly it is more meaningful to do this for non conditional simulation hence cond FALSE and a two wave data set so that t

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