Statistical Science

Model Selection in Linear Mixed Models

Samuel Müller, J. L. Scealy, and A. H. Welsh

Full-text: Open access

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.

Article information

Source
Statist. Sci., Volume 28, Number 2 (2013), 135-167.

Dates
First available in Project Euclid: 21 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.ss/1369147909

Digital Object Identifier
doi:10.1214/12-STS410

Mathematical Reviews number (MathSciNet)
MR3112403

Zentralblatt MATH identifier
1331.62364

Keywords
AIC Bayes factor BIC Cholesky decomposition fence information criteria LASSO linear mixed model model selection shrinkage methods

Citation

Müller, Samuel; Scealy, J. L.; Welsh, A. H. Model Selection in Linear Mixed Models. Statist. Sci. 28 (2013), no. 2, 135--167. doi:10.1214/12-STS410. https://projecteuclid.org/euclid.ss/1369147909


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