Exponential random graph models for affiliation networks

Statistical modeling of social networks as complex systems has always been and remains a challenge for social scientists. Exponential family models give us a convenient way of expressing local network structures that have sufficient statistics for their corresponding parameters. This kind of model, known as Exponential Random Graph Models (ERGMs), or p∗ models, have been developed since the 1980s. However, due to the difficulty of dealing with the intractable normalizing constant, pseudo-likelihood estimation methods have been applied in most studies. Recently, simulation based MCMC maximum likelihood estimation techniques have been developed. Furthermore, current advances in the ERGM provides a much better chance of model convergence for large networks compared with the traditional Markov models. To date most work on ERGMs has focused on one-mode networks, and little has been done on applying maximum likelihood estimation in the case of affiliation networks with two or more modes. This paper considers the application of MCMC maximum likelihood estimation to affiliation networks. Similar techniques have been applied to affiliation networks as in the latest specification for one-mode networks. We investigated features of the model by simulation, and compared the goodness of fit results obtained using the maximum likelihood and pseudolikelihood approaches. Examples used in this paper show that the ERGM with the newly specified statistics is a powerful tool for statistical analysis of affiliation networks.