Exponential random graph (p∗p∗) models for affiliation networks

Recent advances in Exponential Random Graph Models (ERGMs), or p∗p∗ models, include new specifications that give a much better chance of model convergence for large networks compared with the traditional Markov models. Simulation based MCMC maximum likelihood estimation techniques have been developed to replace the pseudolikelihood method. To date most work on ERGMs has focused on one-mode networks, with little done in the case of affiliation networks with two or more types of nodes. This paper proposes ERGMs for two-mode affiliation networks drawing on the recent advances for one-mode networks, including new two-mode specifications. We investigate features of the models by simulation, and compared the goodness of fit results obtained using the maximum likelihood and pseudolikelihood approaches. We introduce a new approach to goodness of fit for network models, using a heuristic based on Mahalanobis distance. The classic Southern Women data and Australian Interlocking Director data are used as examples to show that the ERGM with the newly specified statistics is a powerful tool for statistical analysis of affiliation networks.