Catherine Calder, The Ohio State University
An affiliation network is a particular type 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. Methods for the analysis of affiliation networks are particularly useful for studying patterns of segregation and integration in social structures characterized by both people and potentially shared activities (e.g., parties, corporate board memberships, church attendance, etc.) 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. Statistical methods for studying affiliation networks, however, are less well developed than methods for studying one-mode, or actor-actor, networks. In this talk, I will describe a bilinear generalized mixed-effects model, which contains interacting random effects representing common activity pattern profiles and shared patterns of participation in these profiles. I will demonstrate how the proposed model is able to capture forth-order dependence, a common feature of affiliation networks, and describe a Markov chain Monte Carlo algorithm for Bayesian inference. I then will use the model to explore patterns in extracurricular activity membership of students in a racially-diverse high school in a Midwestern metropolitan area. Using techniques from spatial point pattern analysis, I will show how our model can provide insight into patterns of racial segregation in the voluntary extracurricular activity participation profiles of adolescents. This talk is based on joint work with Yanan Jia and Chris Browning.