Journal
STATISTICA SINICA
Volume 22, Issue 4, Pages 1539-1562Publisher
STATISTICA SINICA
DOI: 10.5705/ss.2011.054
Keywords
Hard thresholding; linear mixed model; shrinkage estimation; variance component selection
Categories
Funding
- National Science Foundation [DMS-0645293]
- National Institutes of Health [RO1 CA140632, P01 CA142538, R01 CA085848]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1347844] Funding Source: National Science Foundation
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The selection of random effects in linear mixed models is an important yet challenging problem in practice. We propose a robust and unified framework for automatically selecting random effects and estimating covariance components in linear mixed models. A moment-based loss function is first constructed for estimating the covariance matrix of random effects. Two types of shrinkage penalties, a hard thresholding operator and a new sandwich-type soft-thresholding penalty, are then imposed for sparse estimation and random effects selection. Compared with existing approaches, the new procedure does not require any distributional assumption on the random effects and error terms. We establish the asymptotic properties of the resulting estimator in terms of its consistency in both random effects selection and variance component estimation. Optimization strategies are suggested to tackle the computational challenges involved in estimating the sparse variance-covariance matrix. Furthermore, we extend the procedure to incorporate the selection of fixed effects as well. Numerical results show the promising performance of the new approach in selecting both random and fixed effects, and consequently, improving the efficiency of estimating model parameters. Finally, we apply the approach to a data set from the Amsterdam Growth and Health study.
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