TITLE: Variable Selection in Linear Mixed Effects Models

SPEAKER: Professor Yingying Fan

ABSTRACT:

This paper is concerned with the selection and estimation of fixed and random effects in linear mixed effects models. We propose a class of nonconcave penalized profile likelihood methods for selecting and estimating significant fixed effects parameters simultaneously for the setting in which the number of predictors is allowed to grow exponentially with sample size.
To study the sampling properties of the proposed procedure, we establish a new theoretical framework which is distinguished from the existing ones (Fan and Li, 2001). We show that the proposed procedure enjoys the model selection consistency. We further propose a group variable selection strategy to simultaneously select and estimate the significant random effects. The resulting random effects estimator is compared with the oracle-assisted Bayes estimator. We prove that, with probability tending to one,  the proposed procedure identifies all true random effects, and furthermore, that the resulting estimates are close to the oracle-assisted Bayes estimates for the selected random effects. In the random effects selection and estimation, the dimensionality is also allowed to increase exponentially with sample size. Monte Carlo simulation studies are conducted to examine the finite sample performances of the proposed procedures. We further illustrate the proposed procedures via a real data example.