Joint Variable Selection for Fixed and Random Effects in Linear Mixed-Effects Models

Summary It is of great practical interest to simultaneously identify the important predictors that correspond to both the fixed and random effects components in a linear mixed-effects (LME) model. Typical approaches perform selection separately on each of the fixed and random effect components. Howe...

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Bibliographic Details
Published in:Biometrics 2010-12, Vol.66 (4), p.1069-1077
Main Authors: Bondell, Howard D., Krishna, Arun, Ghosh, Sujit K.
Format: Article
Language:English
Subjects:
Adaptive LASSO
Algorithms
BIOMETRIC METHODOLOGY
Biometrics
Biometry - methods
Computer Simulation
Constrained EM algorithm
Covariance
Covariance matrices
Environmental agencies
Estimating techniques
Estimation methods
Estimators
Humans
Likelihood Functions
Linear mixed model
Linear Models
Linear regression
Maximum likelihood estimation
Modeling
Models, Statistical
Modified Cholesky decomposition
Oracles
Penalized likelihood
Statistical analysis
Variable selection
Variables
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Summary:Summary It is of great practical interest to simultaneously identify the important predictors that correspond to both the fixed and random effects components in a linear mixed-effects (LME) model. Typical approaches perform selection separately on each of the fixed and random effect components. However, changing the structure of one set of effects can lead to different choices of variables for the other set of effects. We propose simultaneous selection of the fixed and random factors in an LME model using a modified Cholesky decomposition. Our method is based on a penalized joint log likelihood with an adaptive penalty for the selection and estimation of both the fixed and random effects. It performs model selection by allowing fixed effects or standard deviations of random effects to be exactly zero. A constrained expectation-maximization algorithm is then used to obtain the final estimates. It is further shown that the proposed penalized estimator enjoys the Oracle property, in that, asymptotically it performs as well as if the true model was known beforehand. We demonstrate the performance of our method based on a simulation study and a real data example.
ISSN:0006-341X
1541-0420
DOI:10.1111/j.1541-0420.2010.01391.x