Hanfang Li, Youxi Luo, Maozai Tian

【Abstract】

We propose a nonparametric Bayesian quantile regression method for linear mixed effects models. By introducing a new hierarchical finite normal mixture distribution,we relax the modeling assumptions of error term only to quantile restraint. An extensive and flexible Stick-Breaking priori is assumed for mixture ratio parameters so that the model is made more powerful for capturing complex data distribution. By using the latent variables in the nonparametric Bayesian hierarchical quantile regression model,we reduce the computation burden from（2M）Nto N. Monte Carlo simulation studies show that nonparametric Bayesian quantile regression method has an advantage over parametric ones on estimation results when the error distribution becoming more and more complex.

【Keywords】

mixed effect models, finite normal mixture distribution, stick-breaking priori, latent variable, gibbs sampling algorithm