Model Selection in Linear Mixed Models

Abstract

Linear mixed effects models are highly flexible in handling a broad range of data types and are therefore widely used in applications. A key part in the analysis of data is model selection, which often aims to choose a parsimonious model with other desirable properties from a possibly very large set of candidate statistical models. Over the last 5-10 years the literature on model selection in linear mixed models has grown extremely rapidly. The problem is much more complicated than in linear regression because selection on the covariance structure is not straightforward due to computational issues and boundary problems arising from positive semidefinite constraints on covariance matrices. To obtain a better understanding of the available methods, their properties and the relationships between them, we review a large body of literature on linear mixed model selection. We arrange, implement, discuss and compare model selection methods based on four major approaches: information criteria such as AIC or BIC, shrinkage methods based on penalized loss functions such as LASSO, the Fence procedure and Bayesian techniques.

Published in at http://dx.doi.org/10.1214/12-STS410 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (9)

• Pathwise coordinate optimization
• One-step sparse estimates in nonconcave penalized likelihood models
• Covariance Estimation: The GLM and Regularization Perspectives
• Estimation for High-Dimensional Linear Mixed-Effects Models Using ${\ell }_1$-Penalization
• Variable selection in linear mixed effects models
• Fence methods for mixed model selection
• Robust model selection in generalized linear models
• Iterative estimating equations: Linear convergence and asymptotic properties
• Bayesian model comparison and model averaging for small-area estimation

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