Bilinear Mixed-Effects Models for Affiliation Networks

An affiliation network is a particular kind of two-mode social network that consists of a set of ‘actors’ and a set of ‘events’ where ties indicate an actor’s participation in an event. While event affiliations are fundamental in defining the social identity of individuals, statistical methods for studying affiliation networks are less well developed than methods for studying one-mode, or actor-actor, networks. One way to analyze affiliation networks is to consider one-mode network matrices that are derived from an affiliation network, but this approach may lead to the loss of important structural features of the data. The most comprehensive approach is to study both actors and events simultaneously. In this paper, we extend the bilinear mixed-effects model developed for one-mode networks to affiliation networks by considering dependence patterns in the interactions between actors and events. We describe a Markov chain Monte Carlo algorithm for Bayesian inference and illustrate the proposed methodology through an analysis of extracurricular activity participation data.