Bayesian Variable Selection Regression with Quantitative and Qualitative Outcomes

Thomas M. Menino Convention & Exhibition Center 

In many scientific and public health studies, response data often comprise heterogeneous outcomes, such as continuous and binary variables, along with a set of predictors collected from experiments. It is important to account for the inherent association between these heterogeneous outcomes when simultaneously addressing parameter estimation and variable selection in scenarios where the goal is to jointly model both responses within a unified modeling framework. In this paper, we present a general strategy that employs a normal linear regression for the continuous outcome and a latent variable structure to approximate logistic regression for the binary outcome. A hybrid Gibbs sampling algorithm is developed, incorporating Metropolis–Hastings steps to efficiently update model parameters, particularly those with intractable conditional distributions. The proposed sampling strategy not only improves efficiency and reliability in statistical inference but is also well-suited for high-dimensional Bayesian models and complex datasets. Numerical simulations demonstrate the effectiveness of the proposed approach, and a real-world application is provided to illustrate its practical utility.

Bayesian Method

Joint Hierarchical Models

Mixed Responses

Variable Selection

MCMC Sampling 

Section on Bayesian Statistical Science