纵向数据下线性混合效应模型的贝叶斯变量选择  

Bayesian variable selection of linear mixed effect model under longitudinal data

作　　者：李纯净 陈雨 孙胜男 LI Chunjing;CHEN Yu;SUN Shengnan(School of Mathematics&Statistics,Changchun University of Technology,Changchun 130012,China)

机构地区：[1]长春工业大学数学与统计学院,吉林长春130012

出　　处：《长春工业大学学报》2024年第3期241-249,共9页Journal of Changchun University of Technology

基　　金：国家自然科学基金项目(12271060,12301332);吉林省哲学社会科学智库基金项目(2023JLSKZKZB021);吉林省教育厅科学研究项目(JJKH20230749KJ)。

摘　　要：在纵向数据下讨论了如何采用贝叶斯方法将线性混合效应模型分别进行固定效应和随机效应选择的问题。针对固定效应选择,首先给出线性混合模型的似然函数,然后对于固定效应引入Spike-and-Slab混合先验,对于随机效应中的协方差矩阵给定Inverse-Wishart分布先验,运用二元潜变量标记固定效应中的活跃协变量,给出满条件分布及相应的Gibbs抽样算法。针对随机效应选择,采用Cholesky分解对线性混合模型中的协方差矩阵进行重新参数化,从而将随机效应分布的协方差参数函数作为标准正态潜在变量的回归系数,通过为随机效应协方差分解后的参数选择Spike-and-Slab混合先验,利用分层贝叶斯模型识别零方差的随机效应,给出满条件分布以及相应的Gibbs抽样算法。使用模拟数据说明方法的有效性,最后将模型应用于2017年2月至2018年2月的26家上市银行的实际数据,验证了方法的优良性。Under the longitudinal data,the problem of how tOuse the Bayesian method tOselect the fixed effect and the random effect of the linear mixed effect model is discussed.For the selection of fixed effects,the likelihood function of the linear mixed model is first given,and then the Spike-and-Slab mixing prior is introduced for the fixed effects.For the covariance matrix in the random effects,the Inverse-Wishart distribution prior is given,and the active covariates in the fixed effects are marked by binary latent variables.The full conditional distribution and the corresponding Gibbs sampling algorithm are given.For the selection of random effects,Cholesky decomposition is used tOreparameterize the covariance matrix in the linear mixed model,sOthat the function of the covariance parameters of the random effect distribution is used as the regression coefficient of the standard normal latent variable.By selecting the Spike-and-Slab mixing prior for the decomposed parameters in the random effect covariance matrix,the hierarchical Bayesian model is used tOidentify the random effects of zerOvariance,and the full conditional distribution and the corresponding Gibbs sampling algorithm are given.The simulation data is used tOillustrate the effectiveness of the method.Finally,the model is applied tOthe actual data of 26 listed banks from February 2017 tOFebruary 2018 tOverify the superiority of the method.

关 键 词：纵向数据 线性混合效应模型 CHOLESKY分解 GIBBS抽样 贝叶斯变量选择 

分 类 号：O212[理学—概率论与数理统计]