András Vörös
Department of Social Statistics, University of Manchester
SOST71032 Social Network AnalysisAssignment
Introduction to Exponential Random Graph Models (ERGMs)
Model extensions
 Simulation
 With a given network size and ERGM parameters, we can simulate networks (draw from our
ERGM distribution)
 This is supported by the popular software packages
 Good input for further analyses
 Goodness of Fit (GoF)
 Does our (converged) model provide a good representation of the observed network?
 Structurally isomorph networks have the same probability → no R2 (cf. tie prediction)
 “Fit”: how similar are simulated networks to the observed in different (not explicitly modeled)
structural characteristics (e.g. shortest paths, number of components, etc.)
 Multiple GoF tests may be performed
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Analyses options beyond estimation with ERGMs
 Basic model: directed, binary, uniplex
 Undirected model (Lusher et al. 2013, Chapter 8)
 Multiplex model (Lusher et al. 2013, Chapter 10)
 Bi-partite/two-mode model (Lusher et al. 2013, Chapter 10)
 Autologistic Actor Attribute Model, ALAAM (Daraganova & Robins 2013)
 Multi-level network model (Wang et al. 2013)
 Weighted/valued model (Krivitsky 2012)
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ERGM extensions
 Longitudinal models
 discrete time – TERGM (Hanneke et al. 2010), STERGM (Krivitsky & Handcock 2014)
 continuous time – LERGM = tie-flip model (Snijders & Koskinen 2013)
 Egocentric model (Crossley et al. 2015)
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ERGM extensions
 As you can see from the numerous extensions, there few limitations on the type
of networks you can analyze
 Typically complete networks, though solutions for egonets exist
 Network size: from a few actors to several thousands (technical limitations)
 Missing data:
 network data is sensitive to missings
 software can handle missing data
 up to 20% may be ok, especially if it’s really random
 Assumption: ties form from local processes!
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What kind of data can you use for an ERGM?
 R: statnet / ergm package
 https://statnet.org/
 MPNet
 http://www.melnet.org.au/pnet
 To get help: manuals, socnet and statnet mailing lists
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Software and getting help
 In principle, your ERGMs should work on several thousands of nodes (currently,
limit of 2K nodes in MPNet, more in statnet)
 However, it gets difficult to obtain convergence – partly specification, partly
algorithmic issues
 Some proposed solutions
 Componentwise ERGMs: conditional marginalization (Snijders 2010)
 Meta-analysis of snowball samples (Pattison et al. 2013; Stivala et al. 2016)
 Auxiliary parameter MCMC (Byshkin et al. 2017)
 This is under strong development in the statistical network modeling community
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ERGM on large networks
 Lusher, D., Koskinen, J., & Robins, G. (2013).
Exponential random graph models for social
networks: Theory, methods and applications.
Cambridge University Press
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Suggested readings
 Robins, G., Pattison, P., Kalish, Y., & Lusher, D. (2007). An introduction to
exponential random graph (p*) models for social networks. Social Networks, 29,
173-191.
 Robins, G.L., Snijders, T.A.B., Wang, P., Handcock, M., & Pattison, P. (2007).
Recent developments in exponential random graph (p*) models for social
networks. Social Networks, 29, 192-215.
 Robins, G., Lewis, J. M. and Wang, P. (2012) Statistical Network Analysis for
Analyzing Policy Networks. Policy Studies Journal, 40, 375–401.
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Suggested readings
 Byshkin, M., Stivala, A., Mira, A., Krause, R., Robins, G., & Lomi, A. (2016). Auxiliary parameter MCMC for exponential random graph
models. Journal of Statistical Physics, 165(4), 740-754.
 Crossley, N., Bellotti, E., Edwards, G., Everett, M. G., Koskinen, J., & Tranmer, M. (2015). Social network analysis for ego-nets: Social
network analysis for actor-centred networks. Sage.
 Daraganova and Robins (2013) Autologistic Actor Attribute Models. Chapter 9 in Lusher et al. 2013.
 Hanneke, S., Fu, W., & Xing, E. P. (2010). Discrete temporal models of social networks. Electronic Journal of Statistics, 4, 585-605.
 Krivitsky, P. N. (2012). Exponential-family random graph models for valued networks. Electronic Journal of Statistics, 6, 1100.
 Krivitsky, P. N., & Handcock, M. S. (2014). A separable model for dynamic networks. Journal of the Royal Statistical Society: Series B
(Statistical Methodology), 76(1), 29-46.
 Pattison, P., Robins, G., Snijders, T. & Wang, P. (2013). Conditional estimatation of exponential random graph models from snowball and
other sampling designs. Journal of Mathematical Psychology, 57, 284-296.
 Stivala, A., Koskinen, J., Rolls, D., Wang, P., & Robins, G. (2016). Snowball sampling for estimating exponential random graph models for
large networks. Social Networks, 47, 167-188.
 Snijders and Koskinen (2013) Longitudinal models. Chapter 11 in Lusher et al. 2013.
 Snijders, T. A. B. (2010). Conditional Marginalization for Exponential Random Graph Models. The Journal of Mathematical Sociology, 34:4,
239-252.
 Wang, P., Robins, G., Pattison, P., & Lazega, E. (2013). Exponential random graph modules for multilevel networks. Social Networks,
35(1), 96-115.
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References