The Annals of Statistics

Variable selection in linear mixed effects models

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 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.

Article information

Source
Ann. Statist., Volume 40, Number 4 (2012), 2043-2068.

Dates
First available in Project Euclid: 30 October 2012

https://projecteuclid.org/euclid.aos/1351602536

Digital Object Identifier
doi:10.1214/12-AOS1028

Mathematical Reviews number (MathSciNet)
MR3059076

Zentralblatt MATH identifier
1257.62077

Subjects
Primary: 62J05: Linear regression 62J07: Ridge regression; shrinkage estimators
Secondary: 62F10: Point estimation

Citation

Fan, Yingying; Li, Runze. Variable selection in linear mixed effects models. Ann. Statist. 40 (2012), no. 4, 2043--2068. doi:10.1214/12-AOS1028. https://projecteuclid.org/euclid.aos/1351602536

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Supplemental materials

• Supplementary material: Supplement to “Variable selection in linear mixed effects models”. We included additional simulation examples and technical proofs omitted from the main text: simulation Examples A.1–A.3, and technical proofs of Lemmas 1–3 and Proposition 1.