Bayesian Auxiliary Variable Model for Birth Records Data with Qualitative and Quantitative Responses

TL;DR

This paper introduces a Bayesian joint modeling approach for data with both qualitative and quantitative responses, improving prediction and understanding their dependency.

Contribution

A novel Bayesian method that jointly models qualitative and quantitative responses using a latent variable and efficient MCMC sampling.

Findings

Improved prediction accuracy for both response types.

Effective assessment of dependency between responses.

Application to birth records data reveals mutual dependence.

Abstract

Many applications involve data with qualitative and quantitative responses. When there is an association between the two responses, a joint model will provide improved results than modeling them separately. In this paper, we propose a Bayesian method to jointly model such data. The joint model links the qualitative and quantitative responses and can assess their dependency strength via a latent variable. The posterior distributions of parameters are obtained through an efficient MCMC sampling algorithm. The simulation shows that the proposed method can improve the prediction capacity for both responses. We apply the proposed joint model to the birth records data acquired by the Virginia Department of Health and study the mutual dependence between preterm birth of infants and their birth weights.