Bilinear Mixed Effects Models for Dyadic Data

This article discusses the use of a symmetric multiplicative interaction effect to capture certain types of third-order dependence patterns often present in social networks and other dyadic datasets. Such an effect, along with standard linear fixed and random effects, is incorporated into a generalized linear model, and a Markov chain Monte Carlo algorithm is provided for Bayesian estimation and inference. In an example analysis of international relations data, accounting for such patterns improves model fit and predictive performance.