Explaining Preference Heterogeneity with Mixed Membership Modeling

Abstract

Choice models produce part-worth estimates that tell us what product attributes individuals prefer. However, to understand the drivers of these preferences we need to model consumer heterogeneity by specifying covariates that explain cross-sectional variation in the part-worths. In this paper we demonstrate a way to generate covariates for the upper level of a hierarchical Bayesian choice model that lead to an improvement in explaining preference heterogeneity. The covariates are uncovered by augmenting the choice model with a grade of membership model. We find improvement in model fit and inference using the covariates generated with the proposed model over competing models using standard discrete covariates. This paper provides an important step in a continued synthesis between mixed membership models, which include models for text analysis and more traditional discrete multivariate data, and marketing models.