  Under the sociological theory of homophily, people who are similar to one
another are more likely to interact with one another. Marketers often have
access to data on interactions among customers from which, with homophily as a
guiding principle, inferences could be made about the underlying similarities.
However, larger networks face a quadratic explosion in the number of potential
interactions that need to be modeled. This scalability problem renders
probability models of social interactions computationally infeasible for all
but the smallest networks. In this paper we develop a probabilistic framework
for modeling customer interactions that is both grounded in the theory of
homophily, and is flexible enough to account for random variation in who
interacts with whom. In particular, we present a novel Bayesian nonparametric
approach, using Dirichlet processes, to moderate the scalability problems that
marketing researchers encounter when working with networked data. We find that
this framework is a powerful way to draw insights into latent similarities of
customers, and we discuss how marketers can apply these insights to
segmentation and targeting activities.
