Variable selection in linear mixed effects models

Yingying Fan, Runze Li

Research output: Contribution to journalArticle

38 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)2043-2068
Number of pages26
JournalAnnals of Statistics
Volume40
Issue number4
DOIs
StatePublished - Aug 1 2012

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Linear Mixed Effects Model
Variable Selection
Random Effects
Fixed Effects
Profile Likelihood
Penalized Likelihood
Covariance matrix
Sample Size
Unknown
Likelihood Methods
Model Selection
Random effects
Variable selection
Monte Carlo Simulation
Simulation Study
Estimate
Fixed effects

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Fan, Yingying ; Li, Runze. / Variable selection in linear mixed effects models. In: Annals of Statistics. 2012 ; Vol. 40, No. 4. pp. 2043-2068.
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Variable selection in linear mixed effects models. / Fan, Yingying; Li, Runze.

In: Annals of Statistics, Vol. 40, No. 4, 01.08.2012, p. 2043-2068.

Research output: Contribution to journalArticle

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