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USER MANUAL - University of Melbourne

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1. MAIN USER INTERFACE File Number of nodes Simulation GOF Estimation A 0 Simulation Estimation GOF Bayesian estimation Output files Attribute file Browse _ Sample networks Sample degree distributions Model specification Generate GCD A X Wwo mode Indude Directed Fixed Fixdensity Starting density 0000 2 Burn in 100000 Network file Browse Iterations 1000000 Structural zero file Browse Samples 1000 Missing indicators Browse Attribute Dyadic covariates Binary 0 Continous 0 Attribute file Attribute file 4h 4 Categorical 0 Attribute file 4 L Dyadic 0 Attribute file MPNet treats a two level network as a combination of two within level one mode networks labelled as network A and B and a two mode meso level network labelled as X The overall 7 two level network is labelled as network M in the MPNet output files This means that you may have two distinct node sets Na and Ng in which case A is the network directed or undirected among the nodes in Na is the network directed or undirected among the nodes in Ng and is the bipartite network of ties between nodes in and nodes in Ng The top left section of the user interface specifies the number of nodes involved in the levels A and i e the number of node
2. 1 240 Structural zero files Part of a network can be treated as exogenous especially in the cases of ERGM estimations where in some observed networks it makes empirical sense to fix part of the network and estimate the structural features of the rest of the network given the fixed part To fix or forbid the creation or deletion of some of the network ties one can apply structural zero files in MPNet For network of size n the structural zero file contains an n by n adjacency matrix of 1 0 indicators where 1 indicates the network tie is NOT fixed and 0 otherwise Please check Appendix A for structural zero file format Missing indicators MPNet can estimate ERGM with missing network data following Koskinen et al 2013 It is only used under Bayesian estimations More detailed description can be found in the Bayesian estimation section of this user manual Network file Browse tructural zero file O Users Peng Documents MP Net rowse 5 file C Users Peng D tsMPNet B Select parameters Missing indicators Browse Attribute Dyadic covariates Nodal attributes such as gender age performance etc can be used as covariates in ERGMs t
3. Stara 200 E 00000 Star4A 2 00 0 0000 starsA 2 00 0 0000 TriangleA 2 00 0 0000 Cycle4A 2 00 0 0000 IsolatesA 2 00 0 0000 4 SI SI SI SI IST II IsolateEdgesA lt 200 E 0 0000 200 141 1 0280 2 00 0 0000 2 00 0 0600 lt lt lt 200 41 0 2094 ____ Other GOF settings are the same as in Simulations At the end of the GOF simulation MPNet will calculate t ratios for all included graph statistics For configurations that are already included in the model t ratios smaller than 0 1 in absolute value reconfirm the model is converged if there is a discrepancy between the estimation convergence statistics and the GOF t ratios you may have to increase the ratio of the number of iterations to the number of 127 samples See more detailed discussions in Koskinen and Snijders 2012 Chapter 12 of the book on ERGMs For other statistics t ratios smaller than 2 0 in absolute values suggest adequate fit to that particular graph feature T ratios greater than 2 0 standard deviation units from the mean indicate poor fit to the data on that particular graph feature Besides the same sets of output files as in Simulation session MPNet will generate a GOF result file namely MySession_gof txt It contains a tab delimited table where the first column lists the configurations included in the GOF
4. Exponential random graph models for multilevel networks Social Networks 35 1 96 115 Wang P Robins G Pattison P amp Lazega E under review Social selection models for multilevel networks Wang P Sharpe K Robins G L amp Pattison P E 2009 Exponential random graph models for affiliation networks Social Networks 31 1 12 25 Wasserman S and Pattison P 1996 Logit models and logistic regressions for social networks l an introduction to Markov graphs and p Psychometrika 61 3 401 425 231 APPENDIX A SAMPLE FILES SAMPLE INPUT FILES Sample network file 9 77 0 0 8 0 4 3 01 0 0 0 0 0 0 Network files contain the observed 0009014021000 0 Strength network in the adjacency matrix format O 15 07 02 OFO 50 09 60 0000000000000 0 0000000030000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0090 OE 02000902 0 LO OR 0000110009001 00 0300000510000 0 0001000000000 0 06000001000700 00101001000000 00700100710080 00001000000000 00001000111000 00000000000001 Sample structural zero file 0 0 0 0 0 0 0 1 1 0 1 0 0 0 00000000000001 The contains a binary matrix where 1 0000000010000 0 indicates changeable ties and 0 indicates G 970 090 970 170 070 00 0 fixed ties Applying this structural zero 0 0 0 0 0 1 0 0 0 1 0 0 0 0 file example will fix all the tie variables related to node 2 and 5 Ties between node 1 and 13 node 1 and 14 are also Sample dyadic attribu
5. option The missing indicator file has the same format as the network file i e an adjacency matrix of 1s and Os where 1s indicate ties that are part of the missing data and Os indicate non missing ties The missing indicator file can be specified under Model specification tabs by ticking the Missing indicators check box and clicking on the Browse button Model specification A B Include Directed X two mode AX B Fxed Fix density Network file C Users Peng Documents MPNet A txt Structural zero file Missing indicators Peng Documents MPNet missing bt starting density Browse Browse Browse 0000 4 Select parameters It is advisable to start estimation with Scaled identity matrix but if a short estimation round yields reasonable preliminary estimates better performance of the algorithm may be had from using Combined simulation in the options under Bayesian estimation 28 Simulation GOF Estimation Parameter burn in 500 Proposal scaling Multiplication factor MCMC Sample size estimation runs 1 ak Do at converence 500 Generate at convergence Bayesian estimation options Maximum lag SACF 100 Scaled identity matrix 9 Combined simulation Nonconditional simulation Covariance file The output of Bayesian missing data estimation is the same as in B
6. amp X Label Configuration Configuration L3AXBin L3AXBout L3AXBpath L3BXApath C4AXBentrainment C4AXBexchange C4AXBexchangeAreciprocity C4AXBexchangeBreciprocity C4AXBreciprocity C4AXBexchangeBreciprocity AinASXAinBS AoutASXAoutBS AinASXAoutBS AoutASXAinBS 40 NON DIRECTED ONE MODE SOCIAL SELECTION MODELS WITH BINARY ATTRIBUTES Configuration Configuration ActivityA InteractionA ActivityB mer InteractionB TwoPath100A TwoPath010A TwoPath100B TwoPath010B TwoPath110A TwoPath101A TwoPath110B TwoPath101B TwoPath111A Triangle1A TwoPath111B Triangle1B Triangle2A Triangle3A Triangle2B Triangle3B TWO MODE SOCIAL SELECTION MODELS WITH BINARY ATTRIBUTES X2StarA010 X2StarBO10 X2StarA100 X2StarB100 X2StarA101 X2StarB101 SAT X4CycleA1 X4CycleB1 X4CycleA2 X4CycleB2 NON DIRECTED ONE MODE SOCIAL SELECTION MODELS WITH CONTINUOUS ATTRIBUTES Configuration Configuration ActivityA SumA ActivityB SumB DifferenceA ProductA DifferenceB ProductB TWO MODE SOCIAL SELECTION MODELS WITH CONTINUOUS ATTRIBUTES gt ec X2StarA oe X2StarB X2StarASum X2StarBSum 4 20 X2StarADifference X2StarBDifference ONE AND TWO MODE SOCIAL SELECTION MODELS WITH CATEGORICAL ATTRIBUTES MatchA MismatchA ma OO we MismatchA mes OO X2StarAMatch X2StarBMatch X2StarAMismatch X2StarBMismatch X4CycleAMatch X4C
7. box to include the one mode network A in this simulation session Network A can be directed or non directed Tick the Directed check box if we are simulating a directed network Network A can also be treated as a fixed covariate in two level network models Click the Fixed check box if we want to treat network A as fixed covariate We can also simulate or estimate conditional models by ticking the Fix density check box which will force the network density to be fixed i e addition or deletion of network ties are not possible under such condition This option is useful in investigating properties of ERGM parameters and for estimation below when unconditional model convergence is hard to reach The starting density between 0 and 1 is the density of a random network generated by MPNet as the starting graph in the simulation With fixed density this will be the density of all simulated graphs If the density of the graph is not fixed the value here will not affect the longer term result of the simulation Click on the Select parameters button to specify the model effects parameters and graph statistics to be collected during the simulation A parameter selection dialog will show up with a list of implemented ERGM configurations for user selection e The include column is a list of check boxes where if ticked the corresponding graph statistics will be included in the simulation The Fixed
8. button will start the simulation Once the simulation finished MPNet will open the simulated graph statistics output file using your default text editor You can find all the output files in the session folder i e where the MPNet session setting file is allocated More detailed descriptions of the output files are in the next section SIMULATION OUTPUT MPNet will generate several output files upon finishing simulating the specified model Some of the output files are optional depending on the simulation settings described above Here is a list of possible output files and their content information Note that depending on the simulation settings not all output file listed below would appear MySession Network O txt is the initial or starting Level A graph for the simulation In a simulation session it will be a random graph with the user specified density i e the starting density It contains the adjacency matrix for the network and graph statistics such as density mean degree standard deviation and skewness of the degree distribution and global clustering coefficient For directed graphs the output file will list statistics for in and out degree distributions separately This file can be read by Pajek for visualization The nodes will be plotted as blue squares 2413 MySession Network A 1001000 txt is the 1 001 000 simulated graph in the simulation The output file name depends on the number of interactions and samples and
9. it ends with the last simulated network id It has the same format as MySession_Network_A_0 txt MySession Network O txt is the initial or starting Level B graph which follows the same format as MySession Network O txt The nodes will be plotted as red circles in Pajek When only a unipartite graph distribution is simulated i e the Include box is not ticked for network B this output will not appear MySession Network X O txt is the initial or starting meso level two mode graph which list the two mode network in edge list format followed by some two mode graph statistics Level A nodes will be plotted as blue squares and level B nodes as red circles When the Include box is not ticked for network X this output will not appear MySession Network M O txt contains the overall multilevel network in edge list format If the Sample networks option is selected under the Simulation GOF tab sample network files following the same format as described above will be generated by MPNet MySession clu is a Pajek cluster or partition file where the partitions are defined based on the levels Nodes in level A are in partition 0 and level B nodes are in partition 1 One may use the cluster file to plot the meso or the overall two level network in layers under Pajek Again this requires the Include box to be ticked for network B MySession_sim txt is the file opened by MPNet at the end of simulation which contains the sel
10. simulation the second column contains the counts of the configurations in the observed network the third column contains the means of the simulated graph statistic distribution the third column has the standard deviations the fourth column shows the t ratios and the last column shows signs for t ratios that are greater than 2 0 in absolute values indicating poor fit to the corresponding Statistics Below is an example output for a GOF test of a one mode network A Besides the user selected configurations MPNet also includes some global network measurements as part of the output including the standard deviation and skewness of the degree distributions and the global clustering coefficient The Mahalanobis distance shown at the end of the file is an overall heuristic measure of model GOF taking into account the covariance of the included statistics Smaller Mahalanobis distances indicate better fit to the dat Wang et al 2009 Mahalanobis distance should not be tested with standard chi squared statistics in this context it is an indicative measure If two models have the same configurations in the GOF output then the one with the lower Mahalanobis distance is a better fit Configuration Observed Mean StdDev t ratio EdgeA 22 22 39 3 98 0 09 Star2A 71 65 84 24 58 0 21 Star3A 62 59 14 36 77 0 07 Star4A 30 36 16 35 31 0 17 Star5A 8 15 68 24 14 0 31 TriangleA 7 5 33 3 65 0 45 Cycle4A 16 10 78 9 47 0 55 IsolatesA 2 0 32 0 59 28
11. to specify the attribute file and click on the Select button to select corresponding attribute configurations The attribute names specified in the attribute files will be loaded into the parameter selection dialog The parameter selection dialog follows the same format as the ERGM parameter selection dialog ST a age DifferenceA age ProductA FERIAS 5 o mena DifferenceA nce ProductA Reset to Os Exlude 8 0 SIMULATION OPTIONS Simulation GOF Estimation Output files Sample networks Sample degree distributions Generate GCD Burn in 100000 lterations 1000000 Samples 1000 The output files options enable us to pick sample graph matrices and sample degree distributions as tab delimited files for further analysis using other software such as SPSS or R Tick the Sample networks option will let the program generate each sample graph in adjacency matrix format together with some graph statistics such as degree distributions and global clustering coefficient etc The sample files are readable by the Pajek program for the ease of visualizing the simulated samples Be careful about the size of the sample 242 Samples if you check this box because it can take a long time for the computer to write out for instance 1000 files Tick the Sample degree distri
12. 4 IsolateEdgesA 0 0 02 0 15 0 15 ASA 46 56 43 62 12 82 0 22 ATA 17 75 13 64 8 13 0 50 A2PA 57 12 56 06 17 34 0 06 AETA 33 62 24 39 19 15 0 48 stddev_degreeA 2 51 2 22 0 33 0 87 skew_degreeA 1 06 1 30 0 15 1 60 clusteringA 0 29 0 22 0 09 0 77 Mahalanobis distance 193 24 BAYESIAN ESTIMATION MPNet implements a version of the Bayesian estimation algorithm proposed by Camio and Friel 2009 as specified in Koskinen et al 2013 Instead of obtaining the point estimates as in MCMCMLE the Bayesian estimation generates the posterior distributions of the model parameters In lieu of MLEs and standard errors point estimates and measures of uncertainty are calculated as averages and standards errors of this distribution respectively The approximations of Phase 3 are thus not necessary However as the posterior is generated using an iterative MCMC algorithm it is important to assess mixing i e how well the algorithm samples from the posterior D Simulation Estimation GOF 6 Bayesian estimation Attribute file Browse Select Bayesian estimation from the main user interface the Bayesian estimation options will be enabled The same as in Estimation network data input file and model parameter selections can be specified under the Model specification tabs The setting options for Bayesian estimations are different from Estimations as shown on the right side of the user interface BAYESIAN ESTIMA
13. MPNet Program for the Simulation and Estimation of p Exponential Random Graph Models for Multilevel Networks USER MANUAL Peng Wang Garry Robins Philippa Pattison Johan Koskinen Melbourne School of Psychological Sciences The University of Melbourne Australia June 2014 Table of Content Introduction Acknowledgements System Requirements Setup MPNet MPNet sessions Start MPNet MPNet main user interface Simulating one mode networks Simulation Options Simulation Output Simulating two mode networks Simulating two level networks Estimation Estimating ERGMs for one mode networks Estimating ERGMs for two mode networks Estimating ERGMs for combined one and two mode networks Estimating ERGMs for two level networks Estimating ERGMs with nodal attributes as covariates Kstimating conditional ERGMs Options for the estimation algorithm Kstimation Output Goodness of Fit Goodness of Fit Setup Goodness of Fit Output 12 13 14 15 17 17 18 19 19 19 20 20 21 22 23 24 Bayesian estimation Bayesian estimation settings Bayesian estimation outputs Bayesian estimations with missing network data References Appendix A Sample Files Sample Input Files Appendix B Model Configurations Non directed one mode networks A amp B Bipartite networks X Directed one mode networks A amp B Non directed one and two mode interactions A amp X or B amp X Directed on
14. PNet in the user specified folder and all MPNet output for this session will appear in this folder All MPNet output files will have file names that end with the session file 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 L lt Documents MPNet Search MPNet Organize New folder Date moditied 4 OneDrive No items match your search ag Homegroup File name Save as type PNet file pnet v Hide Folders Save Cancel The MySession pnet file records all session settings in the most recent session and allows the user to reload the session after closing the program The MPNet main user interface will appear once we saved the session file To load a previouse session click on Load a previous session button when start up MPNet A open file dialog will apperar and ask for an MPNet session file L6 Documents MPNet Search MPNet 9 Organize New folder 3 im e Date modified Type i This Desktop Documents h Downloads Music amp Pictures v MySession pnet 19 05 2014 11 52 File File name MySession pnet PNet file pnet Select a session file and click on Open will load the previouse session settings into the MPNet main user interface
15. RTITE NETWORKS X EdgeA baron EdgeB Star2A 2 Star2B Star3A Star3B Star4A Star4B Star5A Star5B TriangleA Cycle4A Cycle4B C IsolatesA IsolatesB IsolateEdgesA IsolateEdgesB uu WwW XStar3B X3Path 2 LES 1 124 DIRECTED ONE MODE NETWORKS A amp B ArcB ReciprocityB In2StarA Out2StarA Z lt 5 xe In3StarA Out3StarA In3StarB Out3StarB TwoPathA Transitive TriadA TwoPathB Transitive TriadB Sy in Cyclic TriadA 1 Cyclic TriadB 7X T1B T2A T3A cu e T4A T5A T4B T5B T6A T6B T8A T8B AinSA AoutSA AinSA2AinSB AoutSA2 AinSB2 AoutSB AoutSB2 AinAoutSA AinAoutSB NON DIRECTED ONE AND TWO MODE INTERACTIONS A amp X OR B amp X abe Star2AX RN Star2BX a 13 2 A 20 bk _ i StarAXAA StarAXAB i TriangleXAX TriangleXBX L3XAX L3XBX ATXAX ATXBX EXTA EXTB 22177 DIRECTED ONE AND TWO MODE INTERACTIONS A amp X OR B amp X 1 2121 Eo p PE A AAinS1X ABinS1X AAoutS1X ABoutS1X TXAXarc TXBXarc A TXAXreciprocity TXBXreciprocity A 38 ATXAXreciprocity ATXBXreciprocity L3XAXreciprocity L3XBXreciprocity NON DIRECTED CROSS LEVEL INTERACTIONS A B amp X 2 AC4AXB all 39 DIRECTED CROSS LEVEL INTERACTIONS A B
16. TION SETTINGS Simulation GOF Estimation Parameter burn in 500 Proposal scaling 0 010 Multiplication factor 30 MCMC Sample size 10000 estimation runs 1 ak Do GOF converence 500 Generate at convergence Bayesian estimation options Maximum lag SACF 100 8 Scaled identity matrix Combined simulation Nonconditional simulation 1 Covariance file Sg Ini Parameter burn in similar to burn in for simulations the starting parameters may be considered extreme from the posterior parameter distribution The burn in will discard the specified number of parameter updates at the beginning of the estimation Proposal scaling similar to a values in maximum likelihood estimations MLEs the proposal scaling or step size constant Tierney 1994 is a multiplier for the sizes of parameter updates Greater scaling will cover greater range for parameter proposals however greater scaling may also reduce the number of accepted parameter proposals as part of the posterior The proposal distribution in the Metropolis algorithm is 0 5 where 9 is the current value S c 1 gt and gt is some estimate of the matrix of the posterior distribution In this expression c is the proposal scaling Multiplication factor is the same as in MLEs and determines the number of iterations to be simulated in order to generate
17. XAXDiffReciprocity TXBXDiffReciprocity L3XAXSumArc L3XAXDiffArc L3XAXSumReciprocity L3XBXSumArc L3XBXDiffArc L3XBXSumReciprocity 46 L3XAXDiffReciprocity C4AXBSumEntrainmentA C4AXBSumExchangeA C4AXBSumReciprocityA C4AXBDiffEntrainmentA C4AXBDiffExchangeA C4AXBDiffReciprocityA 247 L3XBXDiffReciprocity CAAXBSumEntrainmentB CAAXBSumexchangeB C4AXBSumReciprocityB C4AXBDiffEntrainmentB C4AXBDiffexchangeB C4AXBDiffReciprocityB DIRECTED CROSS LEVEL SOCIAL SELECTION MODELS WITH CATEGORICAL ATTRIBUTES MismatchB MatchReciprocityB MismatchReciprocityB TXAXMatchArc TXBXMatchArc TXAXMismatchArc TXBXMismatchArc MatchA MatchB MatchReciprocityA u TXAXMatchReciprocity TXBXMatchReciprocity TXAXMismatchReciprocity TXBXMismatchReciprocity L3XAXMatchArc L3XBXMatchArc L3XAXMismatchArc L3XBXMismatchArc L3XAXMatchReciprocity L3XBXMatchReciprocity L3XAXMismatchReciprocity L3XBXMismatchReciprocity 48 C4AXBMatchEntrainmentA C4AXBMatchExchangeA C4AXBMatchReciprocityA C4AXBMismatchEntrainmentA C4AXBMismatchExchangeA C4AXBMismatchReciprocityA 49 CAAXBMatchEntrainmentB CAAXBMatchexchangeB C4AXBMatchReciprocityB C4AXBMismatchEntrainmentB C4AXBMismatchexchangeB C4AXBMismatchReciprocityB APPENDIX C R UTILITY FUNCTIONS FOR MPNET READING IN SIMULATED NETWORKS The function readPNetStatistics lets you read ina simulated network i
18. a network given a proposed parameter The multiplication factor generally speaking should be about three times as large as for the non Bayesian algorithm MCMC Sample size is the number of parameter proposals If all parameter proposals are accepted the posterior will contain this number of parameter sets Note that achieving 10095 acceptance of proposed parameter values are not the goal of the estimation Acceptance of all proposals suggesting the resulting posterior may only cover part of the actual posterior and a greater proposal scaling may be reguired The larger the MCMC Sample size the better the precision of the posterior mean and standard deviation given a fixed acceptance rate Max estimation runs Do GOF at convergence and Generate GCD at convergence they are not applicable in Bayesian estimations Maximum lag SACF determines the largest lag distance for which the sample autocorrelation function for the estimated posterior is In order for the effective sample size ESS to be reliable the autocorrelation at the Maximum lag has to be sufficiently close to zero as a rule of thumb smaller than 0 05 in absolute value The lag at which the SACF value is approximately zero is gives the number of parameter draws you need to discard in between every successive parameter value that you base your posterior inference on For example if the SACF at lag 100 is approximately zero then you need an MCNC sample size of 100 000 to ge
19. arameter estimate greater than twice the size of the estimated standard errors as significant and they are indicated by The variance covariance matrix of the estimated parameters is listed at the end of the estimation output This may be useful for Bayesian estimations described below GOODNESS OF FIT Once a converged ERGM is obtained the model goodness of fit GOF can be tested by comparing simulated graph statistics of the estimated model against the network that has been modelled The graph statistics are not limited to the ones that are already included in 2995 the model but also a greater range of configurations representing the network structure Click on the GOF radio button to specify a model GOF session Simulation Estimation 9 GOF Bayesian estimation Attribute file Browse Most settings for Goodness of Fit are the same as in Simulation except the observed network and parameter values are required The observed network file can be specified the same as in Estimation The parameter values can be typed under the corresponding model parameter selection dialog or by using the Update button if the GOF session is for the most recently converged model under Estimation During model parameter selection click on the Select button will include all implemented statistics in the GOF simulation Effects Include Value EdgeA 2 00 3 3993 5 Star2A 2 00 0 0000
20. ation of ESS here is based only on lags up to and including the max lag Increasing the proposal scaling will decrease the SACF If you use scaled identity and the SACF differs a lot between parameters change to option Covariance file Acceptance rate 0 38 Estimation results Effects Lambda PostMean _ Stddev EdgeA 2 2 513 1 173 ASA 2 0 4911 0 492 2 0 0097 0 25 2 2 0 0568 0 317 Covariance matrix 1 3752 0 3789 0 0932 0 1083 2277 0 3789 0 0932 0 1083 SACF Effect EdgeA ASA ATA A2PA 0 2423 0 0467 0 0736 10 0 993 0 976 0 888 0 953 0 0467 0 0624 0 0139 30 0 98 0 935 0 711 0 882 0 0736 0 0139 0 1004 50 0 969 0 895 0 572 0 824 70 0 96 0 86 0 466 0 779 90 0 951 0 825 0 378 0 73 55 100 51 55 82 60 BAYESIAN ESTIMATIONS WITH MISSING NETWORK DATA Following Koskinen et al 2013 MPNet implements Bayesian estimations with missing network ties The assumption is that we have the information about which network ties are missing and the missing ties follow the same social processes as the observed part of the network The current implementation of MPNet can only estimate models for one mode networks A Future release will extend the method to two mode and two level networks The estimation settings mostly follows settings under Bayesian estimation except it requires a missing indicator file and the use of the Combined simulation estimation
21. ayesian estimations without missing data 29 REFERENCES Caimo A amp Friel N 2011 Bayesian inference for exponential random graph models Social Networks 33 1 41 55 Daraganova G Robins G Auto logistic actor attribute models 2013 In Lusher D Koskinen J amp Robins G eds Exponential Random Graph Models for Social Networks Theories Methods and Applications New York Cambridge University Press Erd s P amp R nyi A 1976 On the evolution of random graphs Selected Papers of Alfr d R nyi vol 2 482 525 Frank O amp Strauss D 1986 Markov graphs Journal of the American Statistical association 81 395 832 842 Handcock S Robins G Snijders T A Moody J 8 Besag J 2003 Assessing degeneracy in statistical models of social networks Vol 39 Working paper Handcock M S Hunter D Butts C T Goodreau S M amp Morris M 2003 statnet An R package for the Statistical Modeling of Social Networks Web page http www csde washington edu statnet Holland P W amp Leinhardt S 1981 An exponential family of probability distributions for directed graphs Journal of the american Statistical association 6 373 33 50 Hunter D 2007 Curved exponential family models for social networks Social networks 29 2 216 230 Koskinen J H Robins G L amp Pattison P E 2010 Analysing exponential random grap
22. bution option to allow MPNet generating degree distributions of simulated samples in tab delimited output together with the standard deviations and skewness of the degree distributions The Generate GCD option will be implemented in a future release It is only used in model estimation or GOF testing with generalized Cook s distances GCDs for each node as a measure of how extreme or important each node is in contributing towards the network structure see Koskinen et al 2013 for more details Burn in is the first period of a simulation during which the simulation move towards the desired graph distribution implied by the specified parameter values Depending on the size of the network and number of parameter values the required burn in can vary a lot The larger the network or the more parameters the longer burn in is needed Examination of the output files can indicate whether the simulation has reached a consistent state and the burn in is sufficient For instance the number of edges in a stationary graph distribution should vary consistently around a mean and not be consistently increasing or decreasing The Iterations box contains the number of proposed simulation updates after burn in Samples expresses the number of graphs sampled from the simulation Note that the number of iterations between graph samples is calculated as the division between the number of iterations and the number of samples to pick up Clicking on the Start
23. column is not implemented yet which is designed for explore model properties when certain effect is fixed Please ignore for now The column provides the weighting parameter for the alternating statistics introduced by Snijders et al 2006 They are not in use for other statistics e The Value column specifies parameter values for included effects Here a Markov model is specified with EdgeA 2 Star2A 0 5 Star3A 0 3 and TriangleA 1 0 We may include other graph statistics but leave the parameter values at 0 for MPNet to generate the corresponding graph statistic distributions There are several buttons at the bottom of the parameter selection dialog e Clear All will unselect all included configurations and set their parameter values to 0 e Select All will select all available parameters implemented under the current dialog Reset to Os will set all parameter values to 0 Exclude 0 05 will unselect all statistics with parameter values as Os The Select and Exclude 9 0 buttons become particularly useful for model GOF testing Click on OK to finalize the parameter selection ASA me 2 2 EES x EM
24. e and two mode interactions amp X or amp X Non directed cross level interactions A B amp X Directed cross level interactions A B amp X Non directed one mode social selection models with binary attributes Two mode social selection models with binary attributes Non directed one mode social selection models with continuous attributes Two mode Social selection models with continuous attributes One and two mode social selection models with categorical attributes Directed one mode social selection models with binary attributes Directed cross level social selection models with binary attributes Directed one mode social selection models with continuous attributes Directed cross level social selection models with continuous attributes Directed cross level social selection models with categorical attributes Appendix C I utility functions for mpnet reading in simulated networks reading in simulated statistics 25 25 27 28 30 32 32 34 34 34 35 37 38 39 40 41 41 42 42 43 44 44 45 46 48 50 50 50 INTRODUCTION MPNet is a program for statistical analysis of exponential random graph models ERGMs for multilevel networks It has three major functionalities Simulation Simulating network distributions with specified model parameter values Estimation Estimating specified ERGM parameters for a given network using Markov Chain Mote Carlo Maximum like
25. e corresponding tabs The statistics involving network ties from different networks can be selected under the A X tab pe Model specification A B X two mode A and X A B and X Structure Structure structure Binary Binary Binary Continuous Continuous Continuous LI Categorical Categorical Categorical Attribute covariates Binary 0 F Attribute file Continuous 0 S Attribute file Categorical 0 7 Attribute file Click on the Structure buttons to open the corresponding parameter selection dialogs with configurations representing interactions among ties across the levels Using A and X as an example i Effects Include Star2AX StarAAT1X StarAX1A StarAXAA TriangleXAX L3XAX ATXAX YT Select All Reset to 05 Exlude 9 0 The dialog shares the same format as parameter selection dialogues for one or two mode network simulations estimations For multilevel social selection models MPNet require attribute files before the user can select attribute parameters The attribute file format follows the format as described in the sectio
26. e format of a raw adjacency matrix The number of rows and columns of the matrix must be the same as the number of nodes specified Please refer to the Appendices for an example network file ESTIMATING ERGMS FOR ONE MODE NETWORKS Model specification X two mode Include Directed Fixed Fix density Starting density 0000 2 Network file C Users Peng Documents MPNet A txt Browse Structural zero file Browse Select parameters _ Missing indicators Browse To estimate models for one mode networks only inclusion of network A is required Tick the Directed option if the network is directed For estimations of models conditioning on the density of the network tick the Fix density option Click on Select parameters to open the parameter selection dialog 24772 Effects Include Fred Value EdgeA 2 00 100000 2 200 0 0000 Star3A 200 0 0000 Star4A 200 l 00000 StaroA 200 0 0000 Tria ngleA 200 0 0000 Cycle4A 200 0 0000 IsolatesA 200 0 0000 DIBIBIBIBEBIUEBLIEBIIEL lsolateEdgesA 2 00 0 0000 ASA 2 00 0 0000 ASA2 2 00 10 0000 2 00 0 0000 200 00000 C C a La La IS lt I LI 5 Clear All Select Al
27. ected graph statistics The statistics are listed in columns separated by tabs MySession spss sps is an SPSS script to plot the scatter plot and histogram of the simulated graph statistics using SPSS version 12 0 and above It will read in the statistics in MySession sim txt If the Sample degree distributions option is ticked under the Simulation GOF tab the degrees of each node will be listed as tab delimited columns in the output files MySession_degreeA txt MySession degreeB txt and MySession degreeX txt MySession model txt lists the parameter statistic names the lambda values and the parameter values used in the simulation SIMULATING TWO MODE NETWORKS To simulate two mode networks we need to specify the number of nodes in each modes A and B e g to simulate a 16 by 12 bipartite network 244 The under Model specifications click on X two mode tab tick the Include check box make sure only network X is included Inclusion of A or B networks will simulate the corresponding one mode networks together with the two mode network Model specification A B Include Fixed Fixdensity Noisolates Starting density 0 000 Network file Browse Select Structural zero file Browse parameters Missing indicators Browse Most of the model specification settings are the same as in one mode networks A or B except there is one more option as No
28. ession as described previously MySession model txt contains the model specification during the estimation session and the starting parameter values MySession update txt contains the model specification during the estimation session and the most recent parameter estimates MPNet uses this file for updating parameter values when the Update button is clicked MySession est txt contains all parameter estimates throughout the entire estimation session i e any estimation runs under this session name will be appended towards the bottom of this file The most recent estimates are listed at the end of the file The Estimation results section of the output lists the effect names parameter estimates estimated standard errors t ratio for convergence test and sample autocorrelation functions SACF for a reliability check They are listed in tab delimited columns which you may copy and paste into table format e g In Excel Here is an example output Effects Lambda Parameter Stderr t ratio EdgeA 2 3 3993 1421 0 092 0 065 ASA 2 1 028 0 505 0 078 0 064 ATA 2 0 06 0 249 0 069 0 077 2 2 0 2094 0 251 0 071 0 061 When all t ratios in the estimated model have absolute values smaller than 0 1 we consider the model is well converged SACFs smaller than 0 4 indicates there are sufficient distances between simulated samples during the estimation hence the model is more reliable We consider the absolute value of a p
29. h Y amp Lusher D 2007 An introduction to exponential random graph p models for social networks Social networks 29 2 173 191 Robins G Snijders T Wang P Handcock M amp Pattison P 2007 Recent developments in exponential random graph i p lt i gt models for social networks Social networks 29 2 192 215 Robins G Elliott P amp Pattison P 2001 Network models for social selection processes Social Networks 23 1 1 30 Robins G L Pattison P amp Elliott P 20010 Network models for social influence processes Psychometrika 66 161 190 Robins G Pattison P amp Wang P 2009 Closure connectivity and degree distributions exponential random graph p models for directed social networks Social Networks 31 105 117 Snijders T A 2002 Markov chain Monte Carlo estimation of exponential random graph models Journal of Social Structure 3 2 1 40 Snijders T A Pattison P E Robins G L amp Handcock M S 2006 New specifications for exponential random graph models Sociological methodology 36 1 99 153 Snijders T A Van de Bunt G G amp Steglich C E 2010 Introduction to stochastic actor based models for network dynamics Social networks 32 1 44 60 Tierney L 1994 Markov Chains for Exploring Posterior Distributions The Annals of Statistics 22 4 1701 1728 Wang P Robins G Pattison P amp Lazega E 2013
30. h file name e g MySession_varcov txt If this estimate of gt is close to the true posterior variance covariance matrix the proposal scaling c should be in the range of 0 5 to 4 BAYESIAN ESTIMATION OUTPUTS Bayesian estimation summarize the estimation results in two file MySession posterior bayesian txt contains the estimated posterior It has p tab delimited columns for models with p parameters each column contains the accepted parameter values in the posterior with parameter names on the first row The posterior can be plotted by software such as R Excel etc Plotting the parameter draws across iterations gives a quick indication of whether the algorithm performs well If there is drift better initial values and a longer burn in may be needed If the parameters move slowly there is great autocorrelation between different values a larger proposal scaling is needed MySession est bayesian txt As shown in the example below the output summarizes the parameter posterior distributions in terms of means and standard deviation followed by the covariance matrix of the parameters Since there is no convergence test for Bayesian estimation the reliability of the generated posterior is indicated by the sample autocorrelation functions SACFs for different lags up to the user defined maximum lag The maximum lag should be set to the lag for which SACF is approximately zero then the effective sample size ESS can be trusted the calcul
31. h p star models with missing data using Bayesian data augmentation Statistical Methodology 7 3 366 384 Koskinen d H Robins G L Wang Pa and Pattison P E 2013 Bayesian analysis for partially observed network data missing ties attributes and actors Social Networks vol 35 4 514 527 Koskinen J H amp Snijders T A 2012 Simulation Estimation and Goodness of Fit In Lusher D Koskinen J amp Robins G Eds Exponential Random Graph Models for Social Networks Theory Methods and Applications Cambridge University Press Lusher D Koskinen J amp Robins G Eds 201 2 Exponential Random Graph Models for Social Networks Theory Methods and Applications Cambridge University Press Pattison P amp Robins G 2002 Neighborhood based models for social networks Sociological Methodology 32 1 301 337 Pattison P amp Robins G 2004 Building models for social space neighourhood based models for social networks and affiliation structures Math matiques et sciences humaines Mathematics and social sciences 168 Pattison P amp Wasserman S 1999 Logit models and logistic regressions for social networks II Multivariate relations British Journal of Mathematical and Statistical Psychology 52 2 169 193 30 Robbins H amp Monro S 1951 A stochastic approximation method The annals of mathematical Statistics 400 407 Robins G Pattison P Kalis
32. isolates Ticking such option in simulations or estimations will ensure all nodes in the bipartite network to have a degree at least 1 Similar to one mode attribute files the bipartite attribute covariate files contains attribute values in tab delimited columns with attribute headers in the first row However as two sets of nodes are involved attribute values should be listed for A nodes first followed by B nodes For attribute that are only applicable to one set of nodes 05 should be used for the other set of nodes and only relevant graph statistics or parameters should be selected during simulation or estimation For example a 16 people A by 12 club B bipartite graph with the gender as binary attribute for people the binary attribute file should start with gender as header followed by a column of 28 attribute values where the first 16 is defined by the gender of people the rest 12 should be listed as Os Other simulation settings and output files are very similar to the setting and outputs in simulations for one mode networks as described in the previous section SIMULATING TWO LEVEL NETWORKS Simulating two level networks will require the number of nodes in both levels A and B and the inclusion of all three networks A B and X by ticking the Include check boxes under each of the tabs A B and X under model specifications The within A and B and meso level X model parameters statistics can be selected under th
33. l 2009 2013 as shown in the Appendices 18 Model specification A B a Include Freed Fix density No isolates Starting density 0 000 5 Network file C Users Peng Documents MPNet X tt Browse Structural zero file parameters Missing indicators Browse ESTIMATING ERGMS FOR COMBINED ONE AND TWO MODE NETWORKS Estimating ERGMs for a combined one and two model networks require inclusion of network A X and their corresponding network files The within one or two mode network effects are the same as in separate models for network A or B The interaction effects between network A and X can be selected under the A X B tab by ticking the check box next to the Structure button under A and The interaction configurations can be selected by click on the Structure button and they follow the specifications proposed in Wang et al 2013 See the appendices for a list of configurations Model specification X two mode A and X A B and X Structure L Structure Binary Binary Binary LI L Continuous Continuous L Continuous LI L Categorical Categorical Categorical ESTIMATING ERGMS FOR TWO LEVEL NETWORKS ERGMs for two level networks require network files for all networks A B and X The possible within and meso level model configurations follow the same specifications as in models for individual one or two mode networks The interaction effect
34. l Reset to Os Exlude 0 Select the effects to be included in the model under estimation by ticking the check boxes under the Include column The Value column contains the starting parameter values If we leave all parameters at 0s MPNet will start estimation with an Edge or Arc parameter calculated based on the density of the network Note that if we are estimating a model conditioning on the density of the network please do not select Edge or Arc parameter The model specificantion implemented in MPNet follows the Markov Frank and Strauss 1986 and the social circuit Snijders et al 2006 Robins et al 2009 assumptions Some higher order configurations are also implemented based on Pattision and Snijders 2013 Please refer to the Appendices for a list of implemented model configurations ESTIMATING ERGMS FOR TWO MODE NETWORKS To estimate ERGMs for two mode networks we need to specify the number of nodes in set A and set B Then only include network X under the Model specification tabs The network file is a n by m rectangular matrix if we have n nodes in set A and m nodes in set B Possible conditional ERGMs including fixing the density of the network the Fix density option or enforce nodes to have degrees at least 1 the No isolates option Click on the Select parameters button to open the parameter selection dialog The implemented two mode configurations follows the model specifications proposed in Wang et a
35. lihood estimation Snijders 2002 or Bayesian approximation algorithms with and without missing data Caimo and Friel 2011 Koskinen et al 2011 2013 Goodness of Fit Testing the goodness of fit of a specified model to a given network with a particular set of parameters MPNet is capable of modelling one mode and bipartite networks This documentation will illustrate how to model one mode networks bipartite networks then two level networks which are combinations of one and two mode networks The model specifications largely follow Wang et al 2013 The whole list of ERGM specifications implemented in MPNet is summarized in the Appendices For a description of ERGMs and their applications see Lusher D Koskinen J amp Robins G 2013 Exponential random graph models for social networks Theory methods and applications Cambridge University Press ACKNOWLEDGEMENTS MPNet contains code and ideas from many contributors We would like to thank the following people for contributing to this program Emmanuel Lazega Galina Daraganova Dean Lusher Tom A B Snijders Lei Xing and Yu Zhao SYSTEM REQUIREMENTS Operating system Microsoft Windows or Macintosh with Windows parallels Software Microsoft NET Framework Version 4 0 The Software required is freely available from Microsoft web site http www microsoft com en au download details aspx id 17851 MPNet can be made to run native in Macintosh environmen
36. n R readPNetStatistics lt function filename impordata lt scan filename what character quiet TRUE n as numeric impordata grep vertices impordata 1 1 impordata zmpordata l grep matrirx impordata c4l grep matrix impordata tnil An 27271 AdjMatrax matrix as n umeric aimpordata n n byrow T return AdjMatrix If your session is called mytest and you file with _Network_A_ iteration txt appended for iteration 1001000 it would be called mytest_Network_A_1001000 txt in your current directory check it using dir read it into using SimADJ lt readPNetStatistics mytest Network 1001000 txt You can wrap this function to read in all or part of the simulated networks simply done by using the command paste The resulting variable is of the matrix class and sna or network can be used to plot the network or calculate summary statistics READING IN SIMULATED STATISTICS If your session is called mytest the output from MPNet appended as sim txt i e mytest sim txt will be a normal text file that you can read into using read table output lt read table mytest_sim txt header TRUE Each row of the data frame will contain the statistics count for a sample point in the estimation If you are simulating the unimodal A network and are saving the number of edges the number of edges across simulations can be plotted using plo
37. n for simulating two mode networks i e tab delimited columns with headers in the 246 first row and attribute values from nodes of type A followed by nodes of type B using 0 as values for attributes that do not apply to either types of nodes Other simulation settings and simulation output files are similar to simulations for one or two mode networks as described in previous sections ESTIMATION Estimating ERGM parameters under MPNet require the user to specify the network data to be modelled the ERGM specification and some estimation options MPNet implements Markov Chain Monte Carlo Maximum Likelihood estimation algorithm as proposed by Snijders 2002 based on the Robbins Monro procedure 1951 MPNet can model one A or two mode X networks a combination of one and two mode networks A and X and two level networks A B and X To estimate a model start MPNet and provide a session name for a new session Select the Estimation radio button You may also continue from a previous session Note that in contrast to PNet you may change data set and specifications in an active or saved session O Simulation 9 Estimation GOF Bayesian estimation Attribute file Browse Upon selecting the Estimation option the Network File text box is enabled under the Model specification tabs for user to specify the network data Click on the Browse button to specify the network file which has th
38. n under the tabs for the corresponding networks and make sure no parameters are selected for fixed networks Model specification A B X two mode AXB Include Directed Fixed Fix density Starting density 0000 2 Network file C Users Peng Documents MPNeft A txt Browse Structural zero file Browse Select parameters Missing indicators rowse OPTIONS FOR THE ESTIMATION ALGORITHM The MCMCMLE algorithm has several customizable settings or options modifying which may help model convergence Simulation GOF Estimation Subphases 5 Gaining factor 0 010 Multiplication factor 10 Iterations in phase 3 500 Max estimation runs 1 m Mun Do GOF at converence 500 Generate GCD at convergence 20 Subphases Each sub phase refines the parameter values but more sub phases do not guarantee convergence The default value is 5 If a good set of starting parameter values is available a smaller number of sub phases may help reduce time required for the estimation Gaining Factor is a multiplier that affects the sizes of parameter updates It is halved after each sub phase to refine the parameter values as the model converges The default a value is 0 01 Smaller a values may be used if a good set of starting parameter values is available Multiplication Factor is a multiplier that determines the number of simulation itera
39. o form social selection models SSMs Robins et al 2001 Attributes or measurements on the tie variables or dyads e g distance strength can be treated as covariate under ERGMs MPNet can handle binary continuous categorical nodal attributes as well as dyadic attributes for network ties as covariates for ERGMs Attribute Dyadic covariates Binary 2 Attribute file C Users Peng Do Continous 3 7 Attribute file C Users Peng Do Categorical 2 Attribute file C Users Peng Do Dyadic 2 gt Attribute file C Users Peng Do Tick the corresponding types of attribute check boxes to enable attribute covariates Following the check boxes enter the number of attributes to be included in the simulation or estimation The covariate values are stored in Attribute files for binary continuous and categorical attribute tab delimited text files where the first row of the file contains the names of the attributes e g gender age etc and each column contains the attribute values in the same order as the nodes listed in the network matrices The number of columns must be the same as the number of attributes specified on the MPNet interface or MPNet will provide an error message Attribute files for dyadic attribute are valued adjacency matrices start with the attribute name then stack one upon another depending on the number of such attributes See example attribute file formats in the Appendices Click on the Browse button
40. ous run An improved parameter estimate may be obtained as the new estimation may start with a set of parameter values closer to convergence MPNet will stop and ignore the subsequent estimation runs as soon as the model is converged otherwise the maximum number of estimation runs will be performed Do GOF at convergence PNet can perform a goodness of fit GOF examination once the model under estimation has converged The GOF output file will be located in the session folder See detailed description of the GOF test in the next section Click on Start button to start the estimation Upon completion of the estimation MPNet will show you whether the model has converged or not and open the estimated model with the default text editor After first estimation run the Update button will be enabled It is used when you want to start the next estimation run with previous estimated parameters so that you may start the new estimation from a better set of parameter values ESTIMATION OUTPUT SOT For a MPNet estimation session with session name MySession MPNet will generate the following output MySession Network O txt MySession Network B O txt MySession Network X O txt and MySession Network M O txt are the networks that have been modelled in adjacency matrix format for networks A and B and edge list format for networks X and the overall two level network M The content of the files are the same as output from a simulation s
41. s among the networks A B and X can be selected by the Structure buttons for the corresponding interactions under the A X B tab The implemented model configurations follow Wang et al 2013 and they are listed in the Appendices ESTIMATING ERGMS WITH NODAL ATTRIBUTES AS COVARIATES 19 MPNet can model network structures with nodal attributes as covariates The attribute file inputs are the same as described in the Simulation section Note that separate attribute files are required for each of the networks under the Model specification tabs The attribute file format for the interactions among networks A B and X are the same as attribute file for bipartite network X i e columns of attribute values starting with attribute names then attribute values for A nodes then B nodes with Os represent attribute values that do not apply to either set of nodes ESTIMATING CONDITIONAL ERGMS Besides using nodal attributes as covariates we may also treat one or more of the three networks involved in the two level network as fixed and exogenous The research question is then about how one given network affects the structures of the other networks For example how club membership fixed two mode network X may affect friendship one mode network A or vice versa Snijders and Van Duijn 2002 has a detailed discussions on conditional estimations for ERGMs with covariates To fix one or more networks as covariates tick the Fixed optio
42. s in Na and respectively The top middle section specifies the functions the current session is performing i e ERGM simulation ERGM estimation test ERGM goodness of fit GOF or Bayesian estimation The tabbed panel on the right specifies function specific settings such as setting for a simulation section including the number of simulation burn ins number of simulation iterations and number of sample networks etc The bottom left tabbed panels are interfaces designed for specifying network data involved in an MPNet session The following section uses an example to demonstrate how to use MPNet to simulate one mode networks SIMULATING ONE MODE NETWORKS Simulating one mode networks in MPNet will only involve network A i e all data settings are under the network A tab The following settings or information are required for simulations Number of nodes A 30 Number of nodes Type in the number of actors in the one mode network A 9 Simulation Estimation GOF Bayesian estimation Attribute file Browse Select Simulation radio button to perform model simulation Model specification A B X two mode AXB Include Directed Fixed Fix density Starting density 02 2 Network file Browse Structural zero file Browse select parameters Missing indicators Browse Under the Model specification tabs select network A and click on the Include check
43. t outputSEdgeA 50
44. t 1000 independent draws from the posterior distribution If the SACF at lag 100 is greater than say 0 4 you need to modify the parameter proposals by increasing the proposal scaling There are several possible matrices we may apply to Bayesian estimation which is used for determining the direction of parameter updates There are four options approximating 2 which is used to set the proposal variance covariance matrix through S c V 1 p X Scaled identity matrix An identity matrix that implies no preferred direction of updates The directions of updates are solely based on the difference statistics between the observed graph and the simulated samples Combined simulation only applicable for Bayesian estimations with missing data as in Koskinen et al 2013 See more detailed instructions in the next section 2 26 Nonconditional simulation the differences between the observed graph and the simulated samples are refined by a covariance matrix generated based on a simulation with the starting parameters This is an analogous procedure to the one employed in Phase 1 of the non Bayesian estimation Covariance file A user defined covariance matrices of the parameters are used to refine the direction of parameter updates The covariance file is a p by p matrix if there are p parameters in the model Such covariance file may be obtained based on previous estimations of the same model MPNet generates such files at the end of estimations wit
45. t either by following James Hollways instructions on http www jameshollway com mpnet for mac or by downloading his bottled version from http www jameshollway com mpnet for mac mpnet SETUP MPNET MPNet exe is an Windows executable program available from PNet website at www sna unimelb edu au pnet pnet html New versions of MPNet will be available from the PNet website To update MPNet simply download the most recent version and discard the early versions MPNET SESSIONS Simulations and Estimations of ERGMs under MPNet are organized by sessions A session typically consists of the following steps 1 network data specifications 2 ERGM specifications 3 simulation or estimation runs 4 analyzing and interpreting the simulation estimation outputs MPNet keeps track of session setting in a PNet session file e g session pnet which contains all settings such as network data and model specifications in the most recent MPNet session Users can start a new session or load a previous session when start up MPNet START MPNET Double click on the MPNet exe program to start the program with the option of beginning a new session or load a previous session Start a new session To start a new session click on the Start a new session button A file saving dialog will appear and ask for a MPNet session file name Specify a session name e g MySession and click on Save the MySession pnet file will be created by M
46. te file fixed Dyadic attribute files contain the values of 00110111111100 network ties as covariate in the adjacency 00000000000000 matrix format with headers as attribute 10010111111111 names Multiple dyadic attributes are 10100111111111 listed in the same file each with separate 9 00 0 9 0 0 0 0 0 0 0 0 9 headers L 0 ICI Q O I I 1 1 I 1 1 I 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 I I I 1 I Note Examples here omitted some values Ua a o MEN in the matrices 1011011110111X1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 10 11 50 21 I II I I I Disbins 10110111111101 01507040050090 2220 0000000000000 0 232 Attribute file format Attribute names should be listed in the first line delimited by tabs Note that attribute names should not start with numbers to meet the SPSS script requirements for variable names Each column represents an attribute Each row corresponds to the same row as in the adjacency matrix Sample binary attribute file Sample categorical 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 2 3 1 1 3 1 1 0 3 3 0 1 2 2 0 0 3 2 0 1 1 1 1 0 1 2 Sample continuous attribute file Income age performance 1 0 23 2 1 1 34 6 1 1 42 5 0 5 23 4 0 3 24 1 1 1 19 1 1 5 38 2 0 2 49 1 0 1 58 1 0 2 47 2 1 0 24 3 0 2 36 2 0 1 19 4 0 5 20 3 APPENDIX B MODEL CONFIGURATIONS NON DIRECTED ONE MODE NETWORKS A amp B BIPA
47. tions between network samples during estimations other factors including the size and the density of the network The larger the multiplication factor the greater the distances between network samples and hence the smaller the auto correlations between samples which may yield a more reliable model Networks with greater number of nodes may require greater multiplication factors to achieve model convergence However greater multiplication factor will also result in longer estimation time The default value is 10 but for directed networks and larger networks a larger multiplication factor is generally needed It is rare that estimation requires a larger multiplication factor than 100 If the SACF see OUTPUT below is greater than 0 4 you will need to increase the multiplication factor Iterations in phase 3 In phase 3 MPNet simulates network graphs using estimated parameters obtained from phase 2 and produces t statistics based on comparisons between the simulated graph distribution and the observed graph statistics The default value is 500 samples Note that the number of simulation updates between samples is the same as in the estimation which is determined by the network size network density and the multiplication factor Max estimation runs As default the program will perform one estimation and stop Multiple estimations runs in sequence can be performed such that each new run uses the parameter values obtained from the end of the previ
48. ycleBMatch 43 X4CycleAMismatch X4CycleBMismatch DIRECTED ONE MODE SOCIAL SELECTION MODELS WITH BINARY ATTRIBUTES Configuration Configuration SenderA ReceiverA SenderB ReceiverB InteractionA ActivityReciprocityA 1 wM S InteractionB ActivityReciprocityB InteractionReciprocityA In2Star010A InteractionReciprocityB In2Star010B 1 Out2Star010A Mix2Star010A Out2Star010B 53 S Mixed2Star010B 1 A DIRECTED CROSS LEVEL SOCIAL SELECTION MODELS WITH BINARY ATTRIBUTES Configuration Configuration L3AXBSenderAB L3ASXBRpath C4AXBentrainmentA C4AXBentrainmentB C4AXBexchangeA C4AXBexchangeB CAAXBAReciprocityA C4AXBAReciprocityB DIRECTED ONE MODE SOCIAL SELECTION MODELS WITH CONTINUOUS ATTRIBUTES Label Configuration Configuration SenderA ReceiverA SenderB ReceiverB SumA DifferenceA SumB DifferenceB E ProductA SumReciprocityA M ProductB SumReciprocityB DifferenceReciprocityA ProductReciprocityA DifferenceReciprocityB O ProductReciprocityB 4 Mixed2StarA E L Mixed2StarB o a In2StarA 3 Out2StarA 4 In2StarB a Out2StarB e _ 45 DIRECTED CROSS LEVEL SOCIAL SELECTION MODELS WITH CONTINUOUS ATTRIBUTES Configuration Configuration Star2AXSender EE Star2BXSender Star2AXReceiver Star2BXReceiver TXAXSumArc TXAXDiffArc TXAXSumReciprocity TXBXSumArc TXBXSumReciprocity T

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