Flexible Bayesian quantile regression for nonlinear mixed effects models based on the generalized asymmetric Laplace distribution

Abstract

We propose flexible Bayesian quantile regression for a class of parametric nonlinear mixed effects models for longitudinal data based on the generalized asymmetric Laplace distribution, which exhibits more flexibility in skewness, mode and tail behaviour than the frequently used asymmetric Laplace distribution in quantile regression. An efficient Markov chain Monte Carlo procedure based on the adaptive random walk Metropolis-within-Gibbs sampling algorithm is derived for posterior inference. We demonstrate through simulation studies and empirical analysis that the proposed method could provide more accurate parameter estimation and better model fit than the existing methods.

Keywords:

• Bayesian quantile regression
• nonlinear mixed effects models
• generalized asymmetric Laplace distribution
• Markov chain Monte Carlo

Acknowledgments

The authors thank the editor, the associate editor and the reviewers for their insightful comments and constructive suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Hanjun is supported by Beijing Natural Science Foundation under Grant Number 1214020, Youth Academic Innovation Team Construction Project of Capital University of Economics and Business under Grant Number QNTD202207, and Science Challenge Project under Grant Number TZ2018001. Lichao is supported by the National Social Science Fund of China under Grant Number 18CTJ011 and National Statistical Science Research Project of China under Grant Number 2022LY087.