High Dimensional Variable Selection In Finite Mixture Of Linear Mixed Effects Models

The linear mixed effects model can well reflect the correlation within each individual and overcome the assumption of independent variable in traditional models by introducing different levels of random effects.It is widely used in medicine,finance,biology and other fields.How-ever,there is some heterogeneity if individuals come from several sub-groups.Therefore,it is difficult to reflect this characteristic through a single linear mixed effect model.In this thesis,a finite mixture of linear mixed effects model is considered to solve this issue.That is to say,total population is divided into multiple sub-groups and different linear mixed effect model was established in each sub-group,which can not only reflect the correlation between individuals,but also reflect the heterogeneity between sub-groups.Variable selection has always been a hot research topic under high dimensional data.How-ever,there are few methods for variable selection in finite mixture of linear mixed effects models.In this model,the significance of each covariate varies with groups in which it is located,so it is necessary to determine the important effects in each sub-group.To solve this problem,a nested EM-ECM algorithm is proposed to select fixed effects and estimate unknown parameter in finite mixture of linear mixed effect model.Firstly,the external EM algorithm is used to determine the weight of each sub-group,and then internal multi-cycle ECM is used to select and estimate variables in each sub-model.The multi-cycle ECM algorithm is divided into two E steps and two CM steps:(1)random effects are updated in both E steps;(2)fixed effects are selected in the first CM step,the covariance matrix of random effects and the variance of error are estimated in the second CM step.Furthermore,the estimators obtained under l₁non-convex penalty function are proved to have consistent and oracle properties.Finally,the rationality of the algorithm are verified by establishing models of different dimensions through numerical simulation.