Bayesian quantile regression for longitudinal data models

• Published in: Journal of statistical computation and simulation Vol. 82; no. 11; pp. 1635 - 1649
• Main Authors: Luo, Youxi, Lian, Heng, Tian, Maozai
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01.11.2012; Taylor & Francis Ltd
• Subjects: Arrays; asymmetric Laplace distribution; Bayesian analysis; Bayesian inference; Computation; Computer simulation; Gibbs sampler; Laplace transforms; longitudinal data; Markov analysis; Markov Chain Monte Carlo; Mathematical models; Metropolis-Hastings algorithm; Monte Carlo methods; Monte Carlo simulation; quantile regression; Quantiles; Regression; Sampling
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2011.590488

In this paper, we discuss a fully Bayesian quantile inference using Markov Chain Monte Carlo (MCMC) method for longitudinal data models with random effects. Under the assumption of error term subject to asymmetric Laplace distribution, we establish a hierarchical Bayesian model and obtain the posterior distribution of unknown parameters at τ-th level. We overcome the current computational limitations using two approaches. One is the general MCMC technique with Metropolis-Hastings algorithm and another is the Gibbs sampling from the full conditional distribution. These two methods outperform the traditional frequentist methods under a wide array of simulated data models and are flexible enough to easily accommodate changes in the number of random effects and in their assumed distribution. We apply the Gibbs sampling method to analyse a mouse growth data and some different conclusions from those in the literatures are obtained.