  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.
