Bayesian inference on group differences in multivariate categorical data

TL;DR

This paper introduces a Bayesian methodology for testing group differences in multivariate categorical data, combining flexibility, efficiency, and tractability, with applications to election polls and other fields.

Contribution

It proposes a novel Bayesian model using group-dependent mixtures of tensor factorizations for flexible, scalable analysis of multivariate categorical group differences.

Findings

Improved accuracy in detecting group differences in simulations.

Effective application to US election poll data.

Enhanced computational efficiency over existing methods.

Abstract

Multivariate categorical data are common in many fields. We are motivated by election polls studies assessing evidence of changes in voters opinions with their candidates preferences in the 2016 United States Presidential primaries or caucuses. Similar goals arise routinely in several applications, but current literature lacks a general methodology which combines flexibility, efficiency, and tractability in testing for group differences in multivariate categorical data at different---potentially complex---scales. We address this goal by leveraging a Bayesian representation which factorizes the joint probability mass function for the group variable and the multivariate categorical data as the product of the marginal probabilities for the groups, and the conditional probability mass function of the multivariate categorical data, given the group membership. To enhance flexibility, we define the conditional probability mass function of the multivariate categorical data via a group-dependent mixture of tensor factorizations, thus facilitating dimensionality reduction and borrowing of information, while providing tractable procedures for computation, and accurate tests assessing global and local group differences. We compare our methods with popular competitors, and discuss improved performance in simulations and in American election polls studies.