Many applications involve data with qualitative and quantitative responses. When there is an association between the two responses, a joint model will produce improved results than fitting them separately. In this paper, a Bayesian method is proposed 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 is conducted to show that the proposed method improves the prediction capacity for both responses. Further, the proposed joint model is applied to the birth records data acquired by the Virginia Department of Health for studying the mutual dependence between preterm birth of infants and their birth weights.
Keywords: Bayesian model; Latent variable; MCMC sampling; Quantitative and Qualitative Responses.