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An affiliation network is a particular type of two-mode social network thatconsists of a set of `actors' and a set of `events' where ties indicate anactor's participation in an event. Although networks describe a variety ofconsequential social structures, statistical methods for studying affiliationnetworks are less well developed than methods for studying one-mode, oractor-actor, networks. One way to analyze affiliation networks is to considerone-mode network matrices that are derived from an affiliation network, butthis approach may lead to the loss of important structural features of thedata. The most comprehensive approach is to study both actors and eventssimultaneously. In this paper, we extend the bilinear mixed-effects model, atype of latent space model developed for one-mode networks, to the affiliationnetwork setting by considering the dependence patterns in the interactionsbetween actors and events and describe a Markov chain Monte Carlo algorithm forBayesian inference. We use our model to explore patterns in extracurricularactivity membership of students in a racially-diverse high school in aMidwestern metropolitan area. Using techniques from spatial point patternanalysis, we show how our model can provide insight into patterns of racialsegregation in the voluntary extracurricular activity participation profiles ofadolescents.

Bilinear Mixed-Effects Models for Affiliation Networks