USER MANUAL - University of Melbourne
Contents
1. OO This graph contains vertices 14 arc 24 reciprocity 2 AinS 2 00 17 62500 AoutS 2 00 15 25000 AT T 2 00 6 50000 A2P T 2 00 40 50000 member interaction 6 gender interaction 2 member sender 11 gender sender 7 member receiver 13 gender receiver 12 Digraph Density 0 13187 In degree Distribution range 0 n 1 4243010000000 0 Standard deviation of in degree distribution 1 435697 Skewness of in degree distribution 0 508356 Out degree Distribution range 0 n 1 2 6 1 4 1 0 0 0 0 0 0 0 0 9 Standard deviation of out degree distribution 1 220572 Skewness of out degree distribution 0 322264 Corr Coef between in and out degree distributions 0 238744 23 Mean degree 1 71429 Global Clustering Coefficients Cto 0 18421 Cti 0 195217 Ctm 0 16279 Ccm 0 20930 AKC T 0 16049 AKC D 0 20000 AKC U 0 13953 AKC C 0 20988 Geodesic Distribution range 1 n 1 inf Note geodesic shortest path between two nodes The geodesic distribution is not based on semi paths 24 32 29 20 500000000 72 Quartiles of the geodesic distribution Note Quartiles equal to the number of nodes refer to infinite geodesics 2 4 14 14 Triad Census 300 210 120C 120D 120U 201 111D 111U 030T 030C 102 13 021D 10 021C 20 021U 12 012 130 003 164 OO2. Resource Geographic o 09 Homophily Contagion OQ 39 among partners Parameters for Binary Attributes o Ob 9 Parameters for Continuous Attributes o Oc 9 4 Parameters for Categorical Attributes oO Osame 243
3. Attr Edge Attr S21 Attr S22 Attr T 1 Attr T2 Attr Absolute difference between two actor attributes i99 Directed Graphs Parameters Without Actor Attributes Arc Reciprocity O 0O sink 99 source 9 In 2 star Out 2 star m In 3 star ES Out 3 star Pa 2 path T a 6 4 x LS 5 L i C Transitive Triad Cyclic Triad To Pa T4 x isolate Alt out star Alt in star AinS Aout ofc Alt in 1 out star 1 in alt out star Ain10utS om 1inAoutS Alt in alt out star AinAoutS AT T AT C 0 gt A2P T yox A2P U SER A2P D 34 Parameters with Actor Attributes e actors with attribute actors with or without attribute Attr attribute name Attr Interaction oe Attr Sender Attr Sender missing Attr Receiver Attr Receiver EO missing Attr Interaction 64 e6 Attr Activity reciprocity reciprocity Attr in 2 star Attr 2 path Attr out 2 star Parameters for Continuous Attributes Attr Sender O Attr Receiver ee e usc Attr Receiver Attr Sender missing missing Attr Bum o Attr Difference Attr Sum fosse 0 reciprocity Attr Difference d Attr Product reciprocity reciprocity Attr in 2 star Attr 2 path Attr out 2 star ae P
4. and Mark S Handcock Goodness of fit of social network models Journal of the American Statistical Association In Press Philippa E Pattison and Garry L Robins Neighborhood based models for social networks Social Methodology 32 301 337 2002 Philippa E Pattison and Garry L Robins Building models for social space Neighbourhood based models for social networks and affiliation structures Mathematics and Social Sciences 42 168 11 29 2004 Philippa E Pattison and Stanley Wasserman Logit models and logistic regression for social networks ii multivariate relations Brithish Journal of Mathematical and Statistical Psychology 52 169 194 1999 Herbert Robbins and Sutton Monro A stochastic approximation method The Annals of Mathematical Statistics 22 3 400 407 Sep 1951 Garry L Robins and Philippa E Pattison Models and Methods in Social Network Analysis Interdependencies and Social Processes Generalized Dependence Structures Cambridge University Press 2005 Garry L Robins Philippa E Pattison Yuval Kalish and Dean Lusher An introduction to exponential random graph p models for social networks Social Networks Special Edition 29 173 191 2007 Garry L Robins Philippa E Pattison and Stanley Wasserman Logit models and logistic regressio for social networks iii valued relations Psychometrika 6A 3 371 394 Sep 1999 Garry L Robins Philippa E Pattison and Jodie Woolcock Small an
5. simulation session name txt id arc recip in2star out2star in3star out3star uktri 1000 16 3 6 5 0 0 0 00 2000 2 3 4 0 1 2 00 3000 4 5 3 0 1 00 4000 14 2 32 0 0 0 00 5000 15 2 4 4 0 0 3 00 6000 15 143 1 0 1 00 97000 18 2 6 7 0 1 3 00 98000 13 12 10 0 0 00 990001714500 0 00 10000019 45600 1 00 24 parameter session name txt Simulation result for digraph with 14 of vertices Parameter Values of arc 1 50000 reciprocity 1 20000 2 in star 1 30000 2 out star 1 20000 3 in star 1 10000 3 out star 1 30000 AT U 2 00 1 50000 Proposed 1000000 digraphs Samples are picked up at 1 per 1000 digraphs Accepted 127343 proposed digraphs estimation session name txt STOCHASTIC ESTIMATION FOR NETWORK example ESTIMATION SETTINGS Number of sub phases in estimation phase 2 5 starting a value in estimation phase 2 0 010000 Multiplication factor for estimation phase 2 10 Number of steps in final simulation phase 3 500 Number of estimation runs 10 STOCHASTIC APPROXIMATION RUN 1 original statistics 24 000000 2 000000 17 625000 15 250000 6 500000 40 500000 starting parameters 2 902123 0 200148 0 546233 0 013692 0 046386 0 143345 Phasel started with the following setup a 0 010000 num of steps 25 num of iterations in each step 224 378698 kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkxkkk mean statistics in phasel 22 880000 1 760000 16 556250 14 147500 5 880000 37 625
6. 004 6 049 0 041 9 801 0 284 9 674 0 182 5 091 0 503 0 041 16 830 8 679 0 170 8 644 0 120 0 042 12 376 12 187 7 982 0 088 0 071 0 157 10 689 2 458 0 043 1 417 0 005 2 902 0 021 0 025 3 821 0 045 3 445 0 039 1 0 393 0 060 1 139 1 107 0 0 0 100 0 655 0 927 0 242 0 248 0 619 313 295 346 073 633 0 092 845 0 126 2322 428 639 0 017 089 OO 275 490 270 528 163 079 066 072 096 070 077 064 093 0 0 9 O 28 100 0 094 019 0 526 293 0 258 233 219 144 643 124 441 036 683 Note geodesic shortest path between two nodes The geodesic distribution is not based on semi paths FIRST QUARTILES Median of sample G25s 2 Interquartile range 1 Observed first quartile geodesic 2 in model samples 0 00 of graphs have lower G25 in model samples 27 50 of graphs have higher G25 SECOND QUARTILES Median of sample G50s 4 Interquartile range 11 Observed median geodesic 4 in model samples 36 80 of graphs have lower G50 in model samples 48 40 of graphs have higher G50 THIRD QUARTILES Median of sample G75s 14 Interquartile range 0 Observed first quartile geodesic 14 in model samples 14 00 of graphs have lower G75 in model samples 0 00 of graphs have higher G75 GOF on Triad Census Triad observ
7. member receiver gender receiver member interaction reciprocity gender interaction reciprocity 2 742 1 311 0 566 0 685 0 824 1 596 30 125 30 500 20 750 6 737 6 736 6 656 6 678 6 697 6 708 6 667 6 500 29 000 31 000 19 500 26 500 11 7 13 12 17 646 15 500 17 646 15 500 665 469 608 577 627 612 579 6 690 41 202 18 975 22 538 doa 6 2 10 940 7 055 12 828 12 135 member activity reciprocity gender activity reciprocity member in2star gender in2star member path2 gender path2 member out2star gender out2star 15 16 18 13 7 3 Std Dev in degree dist Skew in degree dist Std Dev out degree dist Skew out degree dist CorrCoef in out degree dists Global Global Global Global Global Global Global Global Clustering Clustering Clustering Clustering Clustering Clustering Clustering Clustering Cto Ctr Ctm Ccm AKC T AKC D AKC U AKC C ACCEPTANCE RATE 0 2624 11 970 11 759 17 830 12 390 6 453 2 338 1 436 0 508 I 22I 0 322 0 184 0 152 0 163 0 209 0 160 0 200 0 140 0 210 SAMPLE GEODESIC DISTRIBUTION 27 346 28 742 18 188 0 051 0 323 0 075 0 148 0 012 0 099 0 036 4 602 30 089 31 870 20 756 27 572 5 895 1 993 2 243 2 1 391 058 408 505 2215 600 239 166 138 2152 147 152 166 137 146 5 961 0 004 6 049 0 041 5 961 0
8. screen shots for BPNet with user instructions aside Simulation Simulation Estimation Goodness of Fit The same as in PNet Session Name and Folder need to be specified first and output files will have file names ending with session name and they will be located in the session folder Simulation Estimation Goodness of Fit Actors A 0 i Acktors P Starting Density 0 0 1 0 Numbers of actors A and P are the number of nodes in set A and set P Simulations can be started with a random bipartite networks with specified density Select Structural Parameters Structural parameters can be selected by clicking on the check boxes The details of the network configurations can be found in Appendix B Structural Parameter Selection Markov Parameters High Order Parameters 12 sp lambda value 1 2 0 K Ca lambda value lt Parameter values for simulations can be specified during parameter selection The default values are Os Select Actor Attribute Parameters Actor Attribute Parameters A Binary Select Paramet v Continuous select Paramet Conti Select P t v Categorica select Paramet Cat ical Select P t Actor Attribute Parameters Binary Select Paramet Continuous 1 Select Paramet Categorical Select Paramet Actor Attribute Parameters A amp P Actor attribute parameters are sele
9. the current session for simulation estimation goodness of fit or approximate Bayesian goodness of fit This name will be used for the names of the output files All output files will have file names that end with the Session Name you provided here E g if you have a session name MySession under simulation you will have an output file named simulation MySession txt Session Folder All program output files will be located in the Session Folder selected here You can browse through your system and select the folder by clicking on the Browse button Simulation Estimation Goodness of fit and Approximate Bayesian goodness of fit each has its own tab with similar structures Under each tab several settings need to be specified to configure your p model Simulation Simulation Setup To correctly configure simulation you need to specify several settings Number of Number of Actors Starting Graph Density 0 0 1 0 Actors Select Network Type Type in the Non directed Network Maximum Degree For Each Actor number of actors In the Directed Network Maximum Gut Degree For Each Actor network Starting Graph Density Type in the starting density of a random graph in the simulation that used to generate the starting simulation network Type in a floating point number between 0 0 and 1 0 select Network Type Models for directed and non directed networks can be simulated Choose the network type here If you hav
10. 0 20 75 18 188 5 091 0 503 A2P DU 2 00 20 756 7 982 0 157 3 7 member interaction 65 895 2 458 0 043 gender interaction reciprocity O 0 06 0 242 0 248 30 0 089 0 126 0 322 0 1 Skew in degree dist 0 508 0 555 0 49 0 094 0 019 Skew out degree dist 0 332 0 6 0 528 0 526 0 258 0 233 0 219 0 144 0 643 0 16 0 152 0 07 0 124 0 441 0 036 194 Appendix B Model Parameter Description Non directed Graphs Parameters Without Actor Attributes Edge L Isolate 2 Star S5 3 Star 93 Triangle Alt Triangle AT Alt Star AS Alt 2 Path A2P 2 riangle 12 Bow Tie 3 Path 4 Cycle 1 Edge Triangle 2 Edge Triangle 1 ET 2 ET Alt Edge Triangle AET 4 Clique 5 Clique 6 Clique 7 Clique BRING A Alt Clique AC Parameters with Actor Attributes e actors with attribute O actors with or without attribute Attr attribute name Attr interaction Attr T3u Attr activity Attr T2U gt l TAD A D Do e CZ AN 8 VES LORS SES P X Ni Attr T1u i Attr O3u Attr O2au Attr O2bu Attr O1 au Attr O1bu Parameters for Continuous Attributes Attr Sum e Attr difference Attr interaction 6 Parameters for Categorical Attributes Attr Matching e 3 Attr Mismatch Parameters for Dyadic Attributes Dyadic covariate
11. 000 END PHASE1 parameter 2 902123 0 200148 0 546233 0 013692 0 046386 0 143345 Phase 2 started Subphase 0 started with a valued 0 010000 Subphase 0 has gone up to 213 steps Parameter after Subphase 0 2 90351 0 33987 20 55254 0 01341 0 03369 0 12749 Subphase 1 started with a valued 0 010000 Subphase 1 has gone up to 233 steps Parameter after Subphase 1 2 86694 0 26247 0 54200 0 01491 0 04047 0 12810 25 Subphase 2 started with a valued 0 005000 Subphase 4 started with a valued 0 001250 Subphase 4 has gone up to 725 steps Parameter after Subphase 4 2 90684 0 20529 0 55291 0 00977 0 04367 0 14037 END PHASE2 parameter 2 906837 0 205294 0 552914 0 009773 0 043674 0 140375 Phase3 started with the following setup num of steps 500 num of iterations in each step 224 378698 e e oe oe ec e AG x x xA kx kx X mean statistics in phase3 24 616000 2 096000 18 135141 15 876000 6 834750 42 064875 Estimation Result for Network SUMMARY parameter standard error t statistics NOTE t statistics observation sample mean standard error effects estimates stderr t ratio arc 2 906837 0 98133 0 08919 reciprocity 0 205294 0 81794 0 05820 AinS 2 00 0 552914 0 52603 0 06192 AoutS 2 00 0 009773 0 59406 0 07868 AT T 2 00 0 043674 0 51150 0 06069 A2P T 2 00 0 140375 0 19825 0 07173 Estimated Covaria
12. 25 25 id Sea IM E E AA 27 32 32 34 36 39 42 Introduction PNet is a program for statistical analysis of exponential random graph 5 models ERGMs It has three major functionalities Simulation Simulating network distributions with specified model parameter values Estimation Estimating specified ERGM parameters for a given network Goodness of Fit Testing the goodness of fit of a specified model to a given network with a particular set of parameters Acknowledgements PNet contains code and ideas from many people We would like to thank the following people for contributing to this program Carter Butts Galina Daraganova Steve M Goodreau Mark S Handcock Nicholas Harrigan David Hunter Tasuku Igarashi Johan Koskinen Dean Lusher Martina Morris Ken Sharpe Tom A B Snijders Christian E G Steglich Lei Xing Yu Zhao System Requirements Operating Microsoft Windows operating systems system Software Microsoft NET framework version 1 1 Java TM 2 platform standard edition 5 04 The Software required is freely available from Microsoft and Sun s web site Microsoft www microsoft com Under Download search for NET Framework Version 1 1 Redistributable Package JAVA TM 2 Platform Standard Edition 6 0 http ava sun com javase downloads index sp oetup PNet PNet consists of two components a user interface developed in Java PNet jar and a simulation estimati
13. Binary Attributes e actors with attribute o actors with or without attribute Attr attribute name Attr RA Attr RP Attr TSCA Attr TSCP 39 n EN Li EU To TSOA1 Attr TSOA2 C4A1 C4A2 RAC Attr TSCAC TSOACS TSOACD gies 5 TSOP p B TSOP2 CAP1 CON a C E Attr _C4P2 Continuous Attributes RPC TSCPC ce TSOPCS TSOPCD 40 nus Ber vise V M ee Attr CAACS CAPCS Attr C4ACD Attr CAPCD Attr RAPC BH o Categorical Attributes Attr 2path match A 2path match P Attr 2path mismatch A 4cycle match A smio 4cycle match P Wim Attr 2path mismatch P Attr 4cycle mismatch A 4cycle mismatch P IPNet Graph Statistics Denotes actors with attribute O Denotes actors with or without attribute Attribute Density Star2 Contagion Partner Activity 1 3 Setting matrix Setting Homophily Distance matrix Remoteness Remoteness to partners oOb oOc o 9 AD A 9 Activity eo gt otar3 Two Path Equivalence Partner
14. PNet Program for the Simulation and Estimation of Exponential Random Graph p Models USER MANUAL Peng Wang Garry Robins Philippa Pattison Department of Psychology school of Behavioural Science University of Melbourne Australia september 2009 Table of Content Introduction Acknowledgements System Requirements Setup PNet Update PNet Using PNet Start PNet Simulation Simulation Setup Simulation Output Estimation Estimation Setup Estimation Options Estimation Output Goodness of Fit Goodness of Fit Setup Goodness of Fit Output Approximate Bayesian goodness of fit PNet Extensions BPNet Introduction Simulation Estimation Goodness of Fit References Appendix A Sample Files Sample Input Files Sample Output Files start statistics Session name txt end statistics session name txt and sample statistics session name txt simulation session name txt parameter session name txt estimation session name txt covariance session name txt gof session name txt Appendix B Model Parameter Description Non directed Graphs Directed Graphs XPNet Graph Statistics BPNet Graph Statistics IPNet Graph Statistics OQ N N N me N U m NNN i A t m SY f SB Ah N N N M aW m bM O6 24
15. arameters for Categorical Attributes Attr Matching 9 Attr Mismatch ae eve Attr Mismatch Attr Matching reciprocity reciprocity Parameters for Dyadic Attributes Dyadic covariate gt Attr Arc gt 25 Aili ATE XPNet Graph Statistics Parameters for two nondirected networks A and B Network A Network B EdgeAB 2 StarAB 3 Star AAB 3 Star ABB 2 TriangleAAB TriangleABB Binary Attributes Rab oO Rbab Oo Continuous Attributes SumAB Curae DifferenceAB CEE Categorical attributes SamecategoyAB Diff category AB 36 Parameters for two directed networks A and B Network A ArcAB ReciprocityAAB ReciprocityAABB In 2 StarAB Mixed 2 StarAB In 3 Star AAB In 3 Star ABB T ABB T AAB T ABA DD AR QU joy Network B ReciprocityAB ReciprocityABB Out 2 StarAB Out 3 Star AAB Out 3 Star ABB T BAA T BBA T BAB D gt pepe C AAB Mrs Mrb Mrom Msum Msumm Same cate arcAB Same cate reciAB C ABB Binary Attributes 5 o o Mrr Mrm Continuous Attributes OnE Mdiff Mdiffm Categorical attributes o o 38 Diff cate arcAB Diff cate reciAB BPNet Graph Statistics set P set A E EH Sp2 gt Sa2 Sp3 Pu 989 L3 C4 K Sp JE K Sa K Cp K Ca
16. cted by click on the check boxes and type in the number of attributes for a particular type binary continuous or categorical Available parameters will show up after clicking the Select Parameters button Using continuous attribute as an example attribute file name must be specified and parameters and their values can then be selected The attribute file format are the same as in PNet where attribute names are separated using as the first line then the attributes listed in space or tab separated columns Attribute file format examples are listed in Appendix A oince two sets of actors are involved in BPNet separate attribute files are required for parameters involving only one set of actors either A or P For interaction actor attribute effects the attribute file should list attributes for nodes 15 in set A first then followed by attributes for nodes in set P Putting them in the other order will produce wrong modeling results Continuous Attribute Parameter Selection A Continuous Attribute File A Documents ContAELr ExE RAc 1 RAc 2 5 1 TscAc 2 _ TsoAcs 1 C Tsoacs 2 TsoAcd 1 TsoAcd 2 C C4Acs 1 C4Ace2 CdAcdi 0 C4Acd 2 0 8 Simulation Options Simulation options are similar to PNet No conditions Fix graph density where we can fix the graph density or USE structural zero files to fix part of the Structu
17. d other worlds Global network structures from local processes American Journal of Sociology 110 4 894 936 Jan 2005 Garry L Robins Tom A B Snijders Peng Wang Mark Handcock and Philippa E Pattison Recent developments in exponential random graph p models for social networks Social Networks Special Edition 29 192 215 2007 John Skovretz and Katherine Faust Logit models for affiliation networks Sociological Methodology 29 253 280 1999 19 Tom A B Snijders Markov Chain Monte Carlo estimation of exponential random graph models Journal of Social Structure 3 2 2002 Tom A B Snijders Peter Boer Evelien Zeggelink Mark Huisman and Christian Steglich Siena Simulation investigation for empirical network analysis 2001 Tom A B Snijders Philippa E Pattison Garry L Robins and Mark Handcock New specifications for exponential random graph models Sociological Methodology 36 99 153 2006 Christian Steglich and Tom A B Snijders Dyanmic networks and behavior Separating selection from influence In Press Stanley Wasserman and Katherine Faust Social Network Analysis Cambridge University Press 1994 stanley Wasserman and Philippa E Pattison Logit models and logistic regression for social networks an introduction to markov graphs and p Psychometrika 6 3 401 425 Sep 1996 otanley Wasserman and Garry L Robins Models and Methods in Social Network Analysis An Intro
18. duction to Random Graphs Dependence Graphs and Cambridge University Press 2005 20 Appendix A Sample Files Sample Input Files Sample network or dyadic sample structural zero file attribute file The file contains a binary matrix Network files or dyadic attribute where 1 indicates changeable ties setting files contain the observed or and 0 indicates fixed ties Applying covariate network of interest in the this structural zero file example will adjacency matrix format fix all the tie variables related to node 2 and 5 Also ties between 0000000000000 0 node 1 and 13 node 1 and 14 are 0000000000000 0 also fixed 00001000001100 0 0 1 4509 3 121719151 0 0 00010000000000 00000000000000 00101001000000 140 0 01 0 1 1 00001000000000 1 0 130 0 1 1 1 1 1 1 T 1 1 00001000111000 0000000000000 0 00000000000001 10 1100111117141 00000001101000 10 1 1 0 1 0 11 1 11 1 1 00000000000001 1400 1 1 0 1 1 0111 1 1 1 00000000100000 1 0 T 1 0 1 1 1 0 1 00000001000000 ac mre 1 0 12 0 1 1 110 1 1 150 71917501 1 1 1 1 01 1 1 150 155 041 151 191 1501 1 0 I1 170 1 1 II t 1 0 1 1 0110111111110 97 Attribute file formate e Each column represents an attribute e Each row corresponds to the same row as in the adjacency matrix e Attribute names should be listed in the first line delimited by s o Note that attribute names should not start with numbers
19. e a model that having constraint on the maximum number of ties that an actor can have you should also specify it here by clicking on the checkbox and type in the maximum degree Select Structural Parameters Click on the Structural Select Structural Parameters Parameters Checkbox to enable the selection button Structural Parameters 18 8 8 112110 182 1 21002 2 2125190 E ARS cR Select Parameters Markov Parameters Mew Parameters button structural parameter dialog Edge 24 80 By clicking the appears Select parameters for your simulation Manah model and specify their values and lambda values if they are higher order parameters The Clear All button will deselect all parameters and reset their values to It will also reset lambda to the default value of 2 0 The Select All button will select all parameters Finish the structural parameter selection by clicking on the OK button Select Dyadic Attribute Parameters Select the Select Dyadic Attribute Parameters dyadic Dyadic Attributes Number of attributes 7 attribute parameters if you have one or more fixed setting network as network covariates By clicking on the Browse button a file open dialog appears select the Covariate network file and click on OK The dyadic attribute file is a plain text file having the dyadic attributes listed in the adjacency matrix format DyadicAttribute Paramete
20. e default value is 500 steps Maximum number of estimation runs As default the program will perform 1 run of estimation and quit Multiple runs can be performed one after the other each run uses the parameter values from the end of the previous run A better parameter estimate may be obtained as the new estimation may start with a better set of parameter values The program will stop once the model has converged or the maximum number of estimation runs has reached Do GOF model convergence PNet can perform automatic goodness of fit test once the model under estimation has converged The GOF output file will be located in the session folder Update After first estimation run the update button will be enabled It is used when you want to start next estimation run with previous estimated parameters so that you may start form a better set of parameters Note PNet will always load the previous estimation session Please do NOT use update if the session name session folder or network file has been changed Estimation Output File Output start_statistics_graph txt This file contains the starting graph with graph statistics estimation graph txt Estimation result shows starting parameter values starting graph statistics and parameter updates through Phase 2 of the estimation The final estimates and estimated covariance matrix are shown at bottom of the file covariance graph txt It contains the estimated covar
21. e same way as in Simulation By setting up the maximum degree the model is conditional on the maximum degree of each actor otructural Covariate and different kind of Actor Attribute parameters can be selected as in Simulation See detailed parameter description in Appendix B otarting parameter values can be specified as well at the parameter selection dialog If parameter values are not specified all starting parameter values are set to 0 0 except the edge or arc parameter which is calculated based on the density of the network Estimation Options Fix out degree distribution For Directed networks only this option will estimate conditional models such that the out degree distribution will be fixed trough out the estimation Fix the graph density Fix the density of the graph i e the number of arcs edges in the network does not change through the entire simulation Note as the number of arcs edges has been fixed the arc edge parameter is not estimable and it should not be selected for estimation Fix the graph density By fixing the graph density the number of arcs edges will not change during estimation Fixing graph density may help convergence for parameter estimation especially for large networks Note as the number of arcs edges has been fixed the arc edge parameter should not be selected for estimation Structural O File By applying structural 0 file part of the network under estimation can be
22. ed mean stddev t ratio 300 0 0 014 0 133 0 105 210 0 0 273 0 636 0 429 120C 1 0 905 1 138 0 083 120D 0 0 504 0 800 0 630 120U 2 0 372 0 693 2 350 201 0 0 603 1 198 0 503 111D 6 5 020 3 855 0 254 1111 2 4 061 3 415 0 603 030T 2 3 656 2 788 0 594 030 2 1 210 1 327 0 596 102 13 12 100 8 607 0 105 021D 10 9 375 4 749 0 132 021C 20 20 389 8 096 0 048 021U 12 11 845 4 778 0 032 012 130 129 376 16 257 0 038 003 164 164 297 29 134 0 010 Mahalanobis distance 7 168743 51 390873 50 simulated samples have smaller Mahalanobis distances than the observed network effects observed mean stddev t ratio arc 24 135 4 888 0 028 2 063 1 467 0 043 23 997 9 764 0 102 20 436 9 849 0 146 15 866 12 423 0 231 99 3 out star 8 12 216 11 91 0 354 43 605 18 853 0 032 AoutS 2 00 15 25 6 049 0 041 T1 01 0 014 0 133 0 105 32 11 0 90 a 0 0n 220 0 o 1 0 1 5 0 918 1 694 0 542 moa EI 6 8 665 Luc e 5 6 1 ee eee AT U 2 00 0 70 e 6 678 4 577 0 148 TD 2 6 75 6 697 4 627 0 012 6 5 8 5 AT TD 2 00 6 75 AT TDU 2 00 6 5 6 69 4 602 0 041 A2P T 2 00 41 202 16 83 0 042 A2P D 2 00 18 975 8 679 A2P TU 2 00 31 31 87 12 187 0 071 K L star 2 0
23. ends on the size of the network and number of parameter values burn in can vary largely The larger the network or the more parameter involved the longer burn in is needed K statistics tend to have longer burn in Number of iterations Type in the number of iterations after burn in for the simulation Number of samples to pickup Type in the number of sample graph statistics should be picked up in the simulation Click on the start button the simulation starts PNet will notify you once the simulation finished Simulation Output File Output start statistics session txt This file contains the starting graph with selected statistics simulation graph sps or simulation digraph sps This file contains the SPSS script to plot the scatter plot and histogram of the simulated graph statistics using SPSS version 12 0 and above simulation graph txt or simulation digraph txt This file contains the list of sample statistics collected during the simulation Using the SPSS script file you can plot the statistics as scatter plots and histograms parameter graph txt or parameter digraph txt Showing parameter values used in simulation Estimation Estimation Setup To correctly setup an estimation run several settings need to be configured Same as in Simulation Session Name and Number of Actors should be provided Network File can be selected by clicking on the Browse Button Network Type is selected th
24. fixed The file should contain a binary matrix where 1 indicates the corresponding tie in the network is NOT fixed 0 otherwise Please check Appendix A for the format of the structural zero file Number of Sub phases Estimation Options Each sub phase refines the parameter values C Fix out degree distribution C Fix graph density but more sub phases do not LR guarantee Number of Subphases 5 convergence The 5 default value is 5 If Gaining Factor a value a good set of starting parameter cot LEE values is available NE Number of Iterations in Phase 3 500 small number of sub phases may Max Number of Estimation Runs help reduce time required for the Do model convergence estimation No conditions Gaining Factor a value The a value is halved after each sub phase The default a value is 0 01 omaller a value may be used if a good set of starting parameter values is available Multiplication Factor The larger the multiplication factor the longer the estimation but it may help convergence especially for some large networks The default value is 10 Set it to the number of parameters may be helpful and K statistics tends to need factor values bigger than 20 e g 20 to 100 Number of steps in phase 3 In phase 3 the program simulates network graphs using estimated parameters from phase2 and produce t statistics according to the simulation and observation Th
25. goodness of fit for the specified model for all available graph statistics Approximate Bayesian goodness of fit In terms of program setup the difference between approximate Bayesian goodness of fit and Goodness of fit described in previous section is that approximate Bayesian goodness of fit requires the estimated covariance matrix as part of the input The covariance file is a text file containing the estimated covariance matrix only One may use the covariance file generated from the immediate previous estimation session or one can copy the estimated covariance matrix from the estimation result file and past it into a new text file Covariance File Browse As covariance matrix is only regards to the model estimates pleas ONLY select parameters that are included in the model in the parameter selection panels Other options for Approximate Bayesian goodness of fit are identical to the settings in Goodness of fit described in previous section PNet Extensions BPNet Introduction BPNet is a program designed for exponential random graph models for bipartite networks where network ties are only defined between two sets of actors The network statistics include both structural and configurations involving actor attributes The general setup and use of the program is similar to PNet It has a Java user interface and C simulation engine Modifications are made to accompany features of bipartite networks Following are
26. iance matrix by itself and it can be used as the covariance file in Approximate Bayesian goodness of fit Goodness of Fit Goodness of Fit Setup Most settings for Goodness of Fit is the same as in Simulation except the observed network and parameter values are required The observed network file can be specified as in Estimation Make sure that all parameters are selected you may do this by using the select all button in the parameter selection panel The parameter values from your model should also be specified You can type in the parameter values as in simulations or you can use the Update button Note Update button will only work once all parameters have been selected you may use select all button in parameter selection panels It always loads parameters from immediate previous estimation session Please only use update button immediately after a successful estimation Goodness of Fit Output File Output start statistics graph txt This file contains the observed graph and graph statistics simulation graph sps This file contains the SPSS script to plot the scatter plot and histogram of the simulated graph statistics using SPSS version 15 0 and above accept graph txt Showing the ratio of accepted simulation tie changes within each simulation intervals between every two sample graphs gof graph txt Goodness of fit file contains the original or observed statistics for the given network graph and
27. nce Matrix 0 963005 0 009254 0 318091 0 384405 0 264326 0 107297 0 009254 0 669034 0 027916 0 058325 0 007124 0 001399 0 318091 0 027916 0 276712 0 073059 0 151908 0 009170 0 384405 0 058325 0 073059 0 352912 0 136727 0 002928 0 264326 0 007124 0 151908 0 136727 0 261629 0 038435 0 107297 0 001399 0 009170 0 002928 0 038435 0 039304 effects estimates stderr t ratio arc 2 906837 0 98133 0 08919 0 205294 0 81794 0 0582 Ains 2 00 0 552914 0 52603 0 06192 AoutS 2 00 0 009773 0 59406 0 07868 AT T 2 00 0 043674 0 5115 0 06069 A2P T 2 00 0 140375 0 19825 0 07173 covariance session name txt 0 963005 0 009254 0 318091 0 384405 0 264326 0 107297 0 009254 0 669034 0 027916 0 058325 0 007124 0 001399 0 318091 0 027916 0 276712 0 073059 0 151908 0 009170 0 384405 0 058325 0 073059 0 352912 0 136727 0 002928 0 264326 0 007124 0 151908 0 136727 0 261629 0 038435 0 107297 0 001399 0 009170 0 002928 0 038435 0 039304 26 session name txt GOODNESS OF FIT Parameter Values arc 1 19735 reciprocity 0 28248 2 in star 0 00000 Isolates 0 00000 AinS 2 00 0 61944 AoutS 2 00 0 92446 AinS 2 00 0 00000 K L star 2 00 0 00000 AT T 2 00 0 02294 AT TDU 2 00 0 00000 A2P T 2 00 0 21751 A2P D 2 00 0 00000 A2P TDU 2 00 0 00000 member interaction 0 39270 gender interaction 1 01727 member sende
28. on engine pnet dll developed in C to achieve good performance Before installing PNet make sure you system meet the specified system requirements as described Copy the PNet jar and pnet dll into the same folder you can then start the program by double clicking on the PNet jar icon Note that PNet jar and pnet dll files must be located in the same folder for the Java interface PNet jar to call the library functions in pnet dll Update PNet Newer version of PNet will be available and can be downloaded from www sna unimelb edu au pnet pnet html Please replace your current PNet jar and pnet dll files and update the Java runtime environment to finish the update Using PNet To setup a simulation estimation or goodness of fit you will need to choose the relevant options from the user interface and specify several program settings The program requires input files and produces text file output Samples of input files and output files can be found in Appendix A Start PNet PNet can be started from the Windows Start menu under Program Files PNet At the top of PNet main window both Session Name and Session Folder are required for the output file names and location He Heb Session Mame MySession Session Folder curments PNet simulation Simulation Estimation Goodness of fit Bayes goodness of Fit rene tins 66 Session Name Provide a name for
29. r 1 12695 gender sender 1 33001 member receiver 0 18683 gender receiver 0 49272 gender out2star 0 00000 Simulated 1000000 digraphs Statistic samples are picked up at 1 per 1000 digraphs Accepted 262407 proposed digraphs observation sample mean standard error t statistic t statistics observation sample mean standard deviation effects observed mean stddev t ratio arc 24 24 135 4 888 0 028 reciprocity 2 2 063 1 467 0 043 2 in star 23 23 997 9 764 0 102 2 out star 19 20 436 9 849 0 146 3 in star 13 15 866 12 423 11 231 3 out star 8 12 216 11 910 0 354 path2 43 43 605 18 853 0 032 0 0 014 0 133 0 105 T2 0 0 357 1 109 0 322 T3 1 1 535 2 261 0 237 T4 0 0 819 1 266 0 647 T5 2 0 687 1 231 1 067 T6 0 0 918 1 694 0 542 T7 7 9 042 8 190 0 249 T8 7 7 819 7 847 0 104 030 7 7 216 5 313 0 041 T10 030C 3 2 416 2 082 0 280 Sink 0 1 430 1 101 1 299 f e Source Isolates AinS 2 00 Aouts 2 00 AinS 2 00 Aouts 2 00 2 2 17 625 15 250 17 625 15 250 K 1 star 2 00 1 L star 2 00 K L star 2 00 AT T 2 00 AT C 2 00 AT D 2 00 AT U 2 00 AT TD 2 00 6 AT TU 2 00 6 AT DU 2 00 6 AT TDU 2 00 6 8 y 6 500 500 000 000 750 250 500 A2P T 2 00 40 500 A2P D 2 00 17 500 A2P U 2 00 21 500 A2P TD 2 00 A2P TU 2 00 A2P DU 2 00 A2P TDU 2 00 member interaction gender interaction member sender gender sender
30. r selection v Covarate Edge 1 0 Covariate Edge 2 C Covariate s21 1 0 71 Covariate 521 2 _ Covariate 522 1 Covariate 522 2 Covariate T1 2 continuous Et E covariate network Ext My Recent B mynet txt Documents 7 Desktop File name covariate network txt Open Cancel Files of type All Files Select Actor Attribute Parameter Actor attribute Parameters are used in social selection models You may have three different types of attributes Binary Continuous and Categorical The can be selected in a similar manner The number of attributes should be specified before select the actual parameters Attribute files should also be specified similar to the way how dyadic attribute file is specified Please check Appendix A for attribute file format Seleck Actor Attribute Parameters Actor Attribute Parameters Binary Attributes Number of attributes Select Parameters Continuous Attributes Number of attributes Select Parameters Categorical Attriubtes Mumber of attributes Select Parameters Continuous selection Continuous Attribute File s example continuos txt C Procuct 2 855888289 Simulation Options Fix out degree distribution Directed networks only this option will make simulated samples having identical out degree distribution Fix the graph density Fix the density of
31. ral 0 File network and treat them as exogenous Sample graphs degree distributions and clustering coefficients can be collected in _ Pick up sample graph Files separate output files Pick up sample degree distribution Burn in number of ite rations and number of samples to pick up are the same as in Pick up sample clustering coefficient Burn in 100000 Number of Iterations 1000000 Number of samples to pick up 1000 PNet 16 Estimation Ackors A Actors P Network File Documents mynet txt The Network File is text file with a binary rectangular matrix The number of rows for the matrix should be the same as the number of Actors A and the number of columns is the number of Actors P Note putting the number of actors in the other order will produce wrong modeling results Other settings for estimation are the same as in PNet Goodness of Fit Goodness of fit settings are the same as in simulation except the network file needs to be specified in the same way as in estimation References A Baddeley and J Moller Nearest neighbour markov point processes and random sets nternational Statistical Review 57 89 121 1989 Peter Bore Mark Hujsman Tom A B Snijders Christian Steglich Lotte Wichers and Evelien Zeggelink StOCNET An open software system for the advanced statistical analysis of social networks Groningen ICS SciencePlus http stat gamma
32. rug nl stocnet 2003 P Erd s and A Renyi On the evolution of random graphs Publications of the Mathematical Institute of the Hungarian Academy of Science 5 17 61 1960 Ove Frank and David Strauss Markov graphs Journal of the American Statistical Association 81 832 842 Sep 1986 Charles J Geyer and Elizabeth A Thompson Constrained Monte Carlo maximum likelihood for dependent data Journal of the Royal Statistical Society Series B Methodological 54 3 657 699 1992 Steven M Goodreau Advances in exponential random graph p models applied to a large social network Social Networks Special Edition 29 231 248 2007 Mark S Handcock Assessing degeneracy in statistical models of social Networks working paper no 39 Center for Statistics and the Social sciences University of Washington 2003 Mark S Handcock David R Hunter Carter T Butts Steven M Goodreau and Martina Morris statnet An R package for the Statistical Modeling of Social Networks Funding support from NIH grants RO1DA012831 and R01HD041877 URL http www csde washington edu statnet 2003 Paul W Holland and Samuel Leinhardt An exponential family of probability distributions for directed graphs Journal of the American Statistical Association 6 3 3 33 50 Mar 1981 David R Hunter Curved exponential family models for social networks Social Networks Special Edition 29 216 230 2007 David R Hunter Steven M Goodreau
33. the graph i e the number of arcs edges in the network does not change through the entire simulation Note as the number of arcs edges has been fixed the arc edge parameter should not be selected for simulation Structural 0 File Structural zeros refers to the indicators for tie variables that are fixed through the simulation One may fix part of the network by applying a structural zero file to the simulation The file should contain a binary adjacency matrix with the same number of rows columns as in the number of actors In the matrix 1 indicates the corresponding tie in the network is NOT fixed O otherwise Please check Appendix A for structural zero file format Pick up Sample graph Files Sample degree distribution Sample geodesic distribution and Sample clustering coefficient If selected the corresponding samples will set to be part of the program output in separate files Burn in Simulation Options No conditions Fix out degree distribution C3 Fix graph density cuments PMet simulation Pick up sample graph files Structural 0 File Pick up sample degree distribution Pick up sample geodesic distribution Pick up sample clustering coefficient Burn in Number of Iterations Number of samples to pick up Burn in is the starting period of a simulation during which the network is evolving and getting adapted to the specified parameter values Dep
34. to meet the SPSS script requirements for variable names oample binary actor attribute sample categorical actor file attribute file member gender department club 1 1 1 1 1 1 3 2 0 1 2 3 1 0 3 2 1 1 1 3 0 0 2 1 1 0 1 2 0 0 3 1 1 3 l 1 0 3 3 0 1 2 2 0 0 3 0 1 1 1 1 0 1 2 sample continuous actor attribute file income age performance 23 34 42 23 H oo orOoOoOOrRrrRFOOF eN UF UF W w UI PEO sample Output Files e Estimation and goodness of fit output files are tab delimited to easy creating tables in excel Following are examples of output files and excel tables where applicable start statistics session name txt end_statistics session name txt and sample statistics session name txt vertices 14 matrix 0 0 OO 9 965 56 2 1 O O 3 011 2 2 oOo
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