Bayesian quantile regression for joint modeling of longitudinal mixed ordinal and continuous data

Abstract

In this paper, we develop a joint model based on the random effects approach for bivariate longitudinal mixed ordinal and continuous responses using quantile regression for both responses. In order to model the continuous responses an asymmetric Laplace (AL) distribution is assigned to the error term in continuous model. For modeling the ordinal responses using quantile regression, the threshold concept and a latent variable model in which the error term has AL distribution, is applied. For estimating the parameters a Bayesian approach via Gibbs sampling method is used. Moreover, we use the Peabody Individual Achievement Test (PIAT) dataset to illustrate an application of the proposed model. According to the results, children with low levels of antisocial behavior have better reading ability than that of children with high levels of antisocial behavior.

Keywords:

• Asymmetric laplace distribution
• Gibbs sampler
• longitudinal data
• quantile regression
• random effect model