Zeinab Morshedi - Department of Statistics, University of Zanjan, Zanjan, Iran
Ali Aghamohammadi - Department of Statistics, University of Zanjan, Zanjan, Iran

The linear mixed model has become the most frequently used analytic tool for longitu- dinal data analysis with continuous repeated measures. A linear mixed model consistsof fixed effects and random effects and is characterized by the ability of accounting for both the between- and within- subject variabilities. Following Lin and Lee (2008), in this article we advocate the use of multivariate skew-elliptical distribution, so that the Bayesian quantile regression for skew-elliptical partially linear mixed model is developed. Using the connection between asymmet- ric Laplace distribution (ALD) and quantile regression discussed by Yu and Moyeed (2001), we develop a fully Bayesian hierarchical model to estimate the parameters of conditional quantile functions with random effects by adopting an ALD for random errors and a multivariate skew-elliptical distribution introduced by Sahu et al. (2003), for random effects.