Bayesian Gaussian Copula Factor Models for Mixed Data

TL;DR

This paper introduces Bayesian Gaussian copula factor models that separate dependence structure from marginal distributions, enabling scalable analysis of mixed data types with improved interpretability and computational efficiency.

Contribution

It proposes a novel Bayesian copula factor model with a semiparametric marginal specification and efficient inference methods, advancing analysis of mixed data types.

Findings

Effective in high-dimensional settings

Improves interpretability of dependence structures

Demonstrated through simulations and real data

Abstract

Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains, critical for scaling to high-dimensional applications. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The methods in this paper are implemented in the R package bfa.