半参数线性混合效应模型的联合变量选择

多数基于线性混合效应模型的变量选择方法分阶段对固定效应和随机效应进行选择,方法繁琐、易产生模型偏差,且大部分非参数和半参数的线性混合效应模型只涉及非参数部分的光滑度或者固定效应的选择,并未涉及非参变量或随机效应的选择。本文用B样条函数逼近非参数函数部分,从而把半参数线性混合效应模型转化为带逼近误差的线性混合效应模型。对随机效应的协方差矩阵采用改进的乔里斯基分解并重新参数化线性混合效应模型,接着对该模型的极大似然函数施加集群ALASSO惩罚和ALASSO惩罚两类惩罚,该法能实现非参数变量、固定效应和随机效应的联合变量选择,基于该法得出的估计量也满足相合性、稀疏性和Oracle性质。文章最后做了个数值模拟,模拟结果表明,本文提出的估计方法在变量选择的准确性、参数估计的精度两个方面均表现较好。

Joint Variable Selection of Semiparametric Linear Mixed-effects Models

Most of the researches based on linear mixed-effects models select the fixed effects and random effects separately,which are complicated,time-consuming and with models bias frequently.Traditional variable selection methods based on semiparametric and nonparametric linear mixed-effects models only study the selection of the degree of smoothness or fixed effects,regardless of the selection of nonparametric variables or random effects.This article uses B-splines to approximate the nonparametric function and transforms the semiparametric linear mixed-effects model into traditional linear mixed-effects model with approximation errors.Apply modified cholesky decomposition to covariance matrix and reparameterize linear mixed-effects model,then impose group ALASSO penalty and ALASSO penalties to maximum likelihood function of target model.This method can select nonparametric variables,fixed effects and random effects simultaneously and the estimators satisfy consistency,sparsity and Oracle property.In the end of this article,a simulation shows that the estimation method plays well in the accuracy of variable selection and the precision of parameter estimation.