A Bayesian Semi-parametric Quantile Regression Approach for Joint Modeling of Longitudinal Ordinal and Continuous Responses

Abstract

Quantile regression (QR) models are one of the methods for longitudinal data analysis. When responses seemto be skew and asymmetric due to outliers and heavy-tails, QR models may work suitably. This paper developes the semi-parametric quantile regression model for analyzing longitudinal continuous and ordinal mixed responses. The latent variable model and some threshold parameters are used to perform the quantile regression model’s ordinal part. The error of the latent variable model has Asymmetric Laplace (AL) distribution. The error term’s distribution is assumed to be AL distribution to model the continuous responses. The correlations of longitudinal responses belong to the same individual and those of mixed continuous and ordinal responses are considered using a random-effects approach. The regression spline is used to approximate the non-parametric part of the model. The parameter estimation procedure is performed under aBayesian paradigm using the Gibbs sampling method. A simulation study is performed to demonstrate the proposed model’s performance where the relative biases, standard errors, and root of MSEs of estimated parameters are decreased in the semi- parametric QR joint model when the number of subjects is increased. In our application, it was found that the mother’s age and her child’s age have significant effects on reading ability, and antisocial behavior depends on the child’s gender.