混合效应模型的非参数贝叶斯分位回归方法研究

Research on Nonparametric Bayesian Quantile Regression for Mixed Effect Models

本文对混合效应模型提出了一种非参数贝叶斯分位回归方法,通过引进一种新的分层有限正态混合分布,将分位回归建模时对随机误差项的假定放宽至仅有分位点约束之下。通过对混合比例参数假设广泛灵活的Stick-Breaking先验,使得模型捕捉复杂数据分布信息的能力更强。在建立的非参数贝叶斯分层分位回归模型中引入潜变量,使模型参数估计的Gibbs抽样算法中原来每次需要计算(2M)N项函数值变为每次只需计算N项即可。蒙特卡罗模拟显示,在误差分布函数变得较为复杂时,非参数贝叶斯分位回归方法比参数方法在估计效果上有更大的优势。

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.