Semi-parametric Quantile Regression for Analysing Continuous Longitudinal Responses

Recently, quantile regression (QR) models are often applied for longitudinal data analysis. When the distribution of responses seems to be skew and asymmetric due to outliers and heavy-tails, QR models may work suitably. In this paper, a semi-parametric quantile regression model is developed for analysing continuous longitudinal responses. The error term's distribution is assumed to be Asymmetric Laplace (AL) distribution for modeling the continuous responses. The correlation of longitudinal responses belong to the same individual is taken into account by using a random-effects approach. We use the local polynomial kernel to approximate the non-parametric part of the model. The parameter estimation procedure is performed under a Bayesian paradigm using the Gibbs sampling method. The performance of the model is evaluated in a simulation study. To show the proposed model's application, a Peabody Individual Achievement Test (PIAT) dataset is analyzed.