Random Effects Selection in Linear Mixed Models

We address the important practical problem of how to select the random effects component in a linear mixed model. A hierarchical Bayesian model is used to identify any random effect with zero variance. The proposed approach reparameterizes the mixed model so that functions of the covariance paramete...

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Bibliographic Details
Published in:Biometrics 2003-12, Vol.59 (4), p.762-769
Main Authors: Chen, Zhen, Dunson, David B.
Format: Article
Language:English
Subjects:
Algorithms
Bayes factor
Biometrics
Biometry
Child
Child Development - physiology
Covariance
Covariance matrices
Epidemiology
Homogeneity test
Humans
Latent variables
Linear models
Longitudinal data
Markov Chains
MCMC
Model averaging
Modeling
Models, Statistical
Monte Carlo Method
Psychomotor development
Regression coefficients
Standard deviation
Statistical variance
Variable selection
Variance components
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Summary:We address the important practical problem of how to select the random effects component in a linear mixed model. A hierarchical Bayesian model is used to identify any random effect with zero variance. The proposed approach reparameterizes the mixed model so that functions of the covariance parameters of the random effects distribution are incorporated as regression coefficients on standard normal latent variables. We allow random effects to effectively drop out of the model by choosing mixture priors with point mass at zero for the random effects variances. Due to the reparameterization, the model enjoys a conditionally linear structure that facilitates the use of normal conjugate priors. We demonstrate that posterior computation can proceed via a simple and efficient Markov chain Monte Carlo algorithm. The methods are illustrated using simulated data and real data from a study relating prenatal exposure to polychlorinated biphenyls and psychomotor development of children.
ISSN:0006-341X
1541-0420
DOI:10.1111/j.0006-341X.2003.00089.x