# Bayesian Variable Selection for Gaussian copula regression models

## TL;DR

This paper introduces a Bayesian variable selection method for Gaussian copula regression models that handle multiple response types and complex dependencies, improving model estimation efficiency and applicability.

## Contribution

The paper presents a novel Bayesian approach with a specialized MCMC algorithm for variable selection in multivariate regression with diverse response types.

## Key findings

- Effective in simulated data scenarios
- Successfully applied to real datasets with mixed response types
- Enhanced exploration of predictor model space

## Abstract

We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any combination of discrete and/or continuous responses and their association with a set of predictors. We utilize the parameter expansion for data augmentation strategy to construct a Markov chain Monte Carlo algorithm for the estimation of the parameters and the latent variables of the model. Based on a centered parametrization of the Gaussian latent variables, we design a fixed-dimensional proposal distribution to update jointly the latent binary vectors of important predictors and the corresponding non-zero regression coefficients. For Gaussian responses and for outcomes that can be modeled as a dependent version of a Gaussian response, this proposal leads to a Metropolis-Hastings step that allows an efficient exploration of the predictors' model space. The proposed strategy is tested on simulated data and applied to real data sets in which the responses consist of low-intensity counts, binary, ordinal and continuous variables.