Bayesian mixture modeling for multivariate conditional distributions

TL;DR

This paper introduces a Bayesian mixture model designed to estimate joint distributions of mixed data types conditioned on fixed variables, effectively capturing dependencies and improving missing data imputation.

Contribution

The paper proposes a novel Bayesian mixture model that incorporates a truncated local Dirichlet process to model dependencies between fixed and random variables in mixed data.

Findings

The model accurately estimates relationships and missing data distributions in simulated data fusion scenarios.

It outperforms joint mixture models in estimating distributions conditioned on fixed variables.

Application to real consumer data demonstrates practical utility in analyzing reading behaviors.

Abstract

We present a Bayesian mixture model for estimating the joint distribution of mixed ordinal, nominal, and continuous data conditional on a set of fixed variables. The model uses multivariate normal and categorical mixture kernels for the random variables. It induces dependence between the random and fixed variables through the means of the multivariate normal mixture kernels and via a truncated local Dirichlet process. The latter encourages observations with similar values of the fixed variables to share mixture components. Using a simulation of data fusion, we illustrate that the model can estimate underlying relationships in the data and the distributions of the missing values more accurately than a mixture model applied to the random and fixed variables jointly. We use the model to analyze consumers' reading behaviors using a quota sample, i.e., a sample where the empirical distribution of some variables is fixed by design and so should not be modeled as random, conducted by the book publisher HarperCollins.