Bayesian quantile regression for longitudinal data models

Abstract

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.

Keywords:

• asymmetric Laplace distribution
• quantile regression
• Bayesian inference
• longitudinal data
• Markov Chain Monte Carlo
• Metropolis-Hastings algorithm
• Gibbs sampler

Acknowledgements

We would like to thank the reviewer, Associate Editor and Editor Richard G. Krutchkoff for their thoughtful and useful comments. The first author especially thanks Professor Haibin Wang for his valuable comments on MCMC method during his visit to Nanyang Technological University. The work was partially supported by National Natural Science Foundation of China (No.10871201), Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (No. 10XNL018), the Major Project of Humanities Social Science Foundation of Ministry of Education (No. 08JJD910247), Key Project of Chinese Ministry of Education (No.108120), and Beijing Natural Science Foundation (No. 1102021).