Bayesian Mixture Models With Focused Clustering for Mixed Ordinal and Nominal Data

TL;DR

This paper introduces a focused mixture model for mixed ordinal and nominal data that allows tailored modeling of variable groups, improving handling of missing data and capturing variable associations.

Contribution

The paper proposes a novel mixture model that separates variables into focus and remainder groups, enabling customized sub-models and better handling of missing data.

Findings

Improved modeling of mixed data with missing values.

Effective capture of associations among variables.

Application to political survey data demonstrates practical utility.

Abstract

In some contexts, mixture models can fit certain variables well at the expense of others in ways beyond the analyst's control. For example, when the data include some variables with non-trivial amounts of missing values, the mixture model may fit the marginal distributions of the nearly and fully complete variables at the expense of the variables with high fractions of missing data. Motivated by this setting, we present a mixture model for mixed ordinal and nominal data that splits variables into two groups, focus variables and remainder variables. The model allows the analyst to specify a rich sub-model for the focus variables and a simpler sub-model for remainder variables, yet still capture associations among the variables. Using simulations, we illustrate advantages and limitations of focused clustering compared to mixture models that do not distinguish variables. We apply the model to handle missing values in an analysis of the 2012 American National Election Study, estimating relationships among voting behavior, ideology, and political party affiliation.