WITHDRAWN A Novel Bayesian Hierarchical Approach for the Joint Modeling of Binary and Continuous Outcomes

Music City Center 

In industrial and medical fields, it is common for experiments to generate data with both quantitative and qualitative (QQ) outcomes, along with a set of predictors that may influence these outcomes. Accurately modeling these outcomes while accounting for their inherent associations and identifying a subset of significant predictors is crucial for improving prediction and optimization. To address this, we propose an innovative Bayesian hierarchical model that employs a conditional approach for the continuous outcome based on the binary outcome. This model enables simultaneous parameter estimation and variable selection within the joint modeling framework for QQ outcomes. We develop an efficient Markov chain Monte Carlo (MCMC) sampling algorithm that integrates collapsed Gibbs sampling and the Metropolis-Hastings algorithm to compute posterior probabilities, facilitate feature selection, and optimize processes. Simulation studies are conducted to compare the performance of the proposed Bayesian method against several existing approaches in the literature. Finally, we illustrate the model's practical application with a real-data example.

Joint modeling

Bayesian hierarchical modeling

MCMC methods

Variable selection 

International Society for Bayesian Analysis (ISBA)