Open Access
August 2012 Variable selection in linear mixed effects models
Yingying Fan, Runze Li
Ann. Statist. 40(4): 2043-2068 (August 2012). DOI: 10.1214/12-AOS1028


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 important fixed effects. To overcome the difficulty of unknown covariance matrix of random effects, we propose to use a proxy matrix in the penalized profile likelihood. We establish conditions on the choice of the proxy matrix and show that the proposed procedure enjoys the model selection consistency where the number of fixed effects is allowed to grow exponentially with the sample size. We further propose a group variable selection strategy to simultaneously select and estimate important random effects, where the unknown covariance matrix of random effects is replaced with a proxy matrix. We prove that, with the proxy matrix appropriately chosen, the proposed procedure can identify all true random effects with asymptotic probability one, where the dimension of random effects vector is allowed to increase exponentially with the sample size. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed procedures. We further illustrate the proposed procedures via a real data example.


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Yingying Fan. Runze Li. "Variable selection in linear mixed effects models." Ann. Statist. 40 (4) 2043 - 2068, August 2012.


Published: August 2012
First available in Project Euclid: 30 October 2012

zbMATH: 1257.62077
MathSciNet: MR3059076
Digital Object Identifier: 10.1214/12-AOS1028

Primary: 62J05 , 62J07
Secondary: 62F10

Keywords: Adaptive LASSO , group variable selection , linear mixed effects models , oracle property , SCAD

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 4 • August 2012
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