基于融合Lasso惩罚变量的贝叶斯混合效应分位数回归方法研究

Bayesian quantile regression method based on fusion Lasso penalty variables

为了解决混合效应分位数回归模型中大量未知随机效应和固定效应的存在,给模型参数估计与变量选择带来的困难问题.提出一种带有融合Lasso惩罚的贝叶斯混合效应分位数回归方法来估计系数,给出了模型的后验分布,构造了参数估计的Gibbs抽样算法.模拟显示,该方法在不同的随机误差分布下都有较强的稳健性,且在稀疏数据类型下相比稠密数据类型具有更好的表现,在变量选择问题上,不仅能选择重要的变量,而且将无关变量推向0附近,提高了模型的乏化能力和解释性,为实际工作者研究稀疏纵向数据提供了一种有效的建模方法.

In order to solve the difficulty of parameter estimation and variable selection caused by the presence of a large number of unknown random and fixed effects in mixed effects quantile regression models,a Bayesian mixed effects quantile regression method with fused Lasso penalty is proposed to estimate coefficients,the posterior distribution of the model is given,and a Gibbs sampling algorithm for parameter estimation is constructed.Simulation results show that this method has strong robustness under different random error distributions,and performs better on sparse data types compared to dense data types.In variable selection problems,it can not only select important variables,but also push irrelevant variables towards zero,which improves the model′s fatigue and interpretability,and provides an effective modeling method for practical researchers studying sparse longitudinal data.