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.

Published in at http://dx.doi.org/10.1214/12-AOS1028 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• Discussion of "Least angle regression" by Efron et al
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• Least Angle Regression
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• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
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• Nearly unbiased variable selection under minimax concave penalty
• Nonconcave penalized likelihood with a diverging number of parameters
• On the adaptive elastic-net with a diverging number of parameters
• One-step sparse estimates in nonconcave penalized likelihood models
• High-dimensional classification using features annealed independence rules
• A unified approach to model selection and sparse recovery using regularized least squares

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• Sparse Variable Selection on High Dimensional Heterogeneous Data with Tree Structured Responses
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• A scalable and efficient covariate selection criterion for mixed effects regression models with unknown random effects structure