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

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