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We extend the well-known and widely used Exponential Random Graph Model(ERGM) by including nodal random effects to compensate for heterogeneity in thenodes of a network. The Bayesian framework for ERGMs proposed by Caimo andFriel (2011) yields the basis of our modelling algorithm. A central question innetwork models is the question of model selection and following the Bayesianparadigm we focus on estimating Bayes factors. To do so we develop anapproximate but feasible calculation of the Bayes factor which allows one topursue model selection. Two data examples and a small simulation studyillustrate our mixed model approach and the corresponding model selection.

Bayesian Exponential Random Graph Models with Nodal Random Effects