Bayesian quantile regression for hierarchical linear models

Abstract

The paper proposes a Bayesian quantile regression method for hierarchical linear models. Existing approaches of hierarchical linear quantile regression models are scarce and most of them were not from the perspective of Bayesian thoughts, which is important for hierarchical models. In this paper, based on Bayesian theories and Markov Chain Monte Carlo methods, we introduce Asymmetric Laplace distributed errors to simulate joint posterior distributions of population parameters and across-unit parameters and then derive their posterior quantile inferences. We run a simulation as the proposed method to examine the effects on parameters induced by units and quantile levels; the method is also applied to study the relationship between Chinese rural residents' family annual income and their cultivated areas. Both the simulation and real data analysis indicate that the method is effective and accurate.

Keywords:

• Bayesian quantile regression
• hierarchical linear models
• Metropolis–Gibbs algorithms
• asymmetric Laplace distribution

Subject Classification codes:

• 62F15

Acknowledgement

It is a great pleasure to appreciate my advisors, Prof. Chunyan Sun (School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, China) and Prof. Yaohui Chen (School of Economics, Nanjing University of Finance and Economics, Nanjing, China). They enlightened my inspiration to start the paper, gave me invaluable advices and insightful comments while refining the paper. I offer my sincerest appreciation and gratitude to their constant encouragement and warm help for me.