Role Analysis in Networks Using Mixtures of Exponential Random Graph Models

Abstract

A novel and flexible framework for investigating the roles of actors within a network is introduced. Particular interest is in roles as defined by local network connectivity patterns, identified using the ego-networks extracted from the network. A mixture of Exponential-family Random Graph Models is developed for these ego-networks in order to cluster the nodes into roles. We refer to this model as the ego-ERGM. An Expectation-Maximization algorithm is developed to infer the unobserved cluster assignments and to estimate the mixture model parameters using a maximum pseudo-likelihood approximation. The flexibility and utility of the method are demonstrated on examples of simulated and real networks.

Modeling Unobserved Heterogeneity in Social Networks with the Frailty Exponential Random Graph Model

“…Currently, likelihood-based inference is provided by Markov chain Monte Carlo Maximum Likelihood (MCMC-MLE) algorithms (Corander, Dahmström, and Dahmström 1998; Crouch, Wasserman, and Trachtenberg 1998; Besag 2000; Handcock 2000; Snijders 2002) as well as pseudolikelihood procedures (Strauss and Ikeda 1990; Wasserman and Pattison 1996), though there are important objections to the latter (Besag 2000; Snijders 2002). Important to the analysis of social processes, many extensions to the ERGM have allowed for role analysis (Salter-Townshend and Brendan Murphy 2015) and the consideration of egocentrically sampled network data (Krivitsky, Handcock, and Morris 2011). In addition, this family of models is developing to consider longitudinal or dynamic networks in the form of temporal ERGMs (TERGMs) (Hanneke and Xing 2007; Hanneke, Fu, and Xing 2010; Desmarais and Cranmer 2010; Cranmer and Desmarais 2011) and separable temporal ERGMs (STERGMs) (Krivitsky and Handcock 2014; Christenson and Box-Steffensmeier 2016).…”

Diagnosing Multicollinearity in Exponential Random Graph Models

“…These practical limitations do not subvert the issue that multicollinearity in ERGM can yield similar estimation problems as in any statistical model: skewed regression coefficients and biased standard errors. Moreover, unique collinearity-type problems arise when using ERGM (Snijders et al 2006;Dekker, Krakhardt, and Snijders 2007;Salter-Townshend and Murphy 2015). First, the reliance of dyadic dependent ERGMs on Markov Chain Monte Carlo (MCMC) maximum likelihood estimation (MLE) means that highly collinear estimates may result in multiple models from which the best fitted model cannot be determined (Chandrasekhar and Jackson 2014).…”

“…Multicollinearity may be particularly difficult to detect with the inclusion of dyadic dependent terms (Snijders et al 2004;Salter-Townshend and Murphy 2015). This is because endogenous network statistics largely depend on the network's density, which functions equivalently to the intercept in OLS regression (Robins et al 2007;Faust 2007;Lusher et al 2013).…”

Diagnosing Multicollinearity in Exponential Random Graph Models

“…First, highly collinear models may have multiple solutions to the likelihood function. In such cases, a single ERGM specification may result in multiple models from which the best fitted model cannot be determined (Hunter et al 2008;Salter-Townshend and Murphy 2015). Second, variance estimates calculated through Markov Chain Monte Carlo (MCMC) maximum likelihood estimation (MLE) may be unstable when collinearity exists.…”