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Subset selection for linear mixed models

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  • Daniel R. Kowal

Abstract

Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates—while accounting for this structured dependence—remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy a cardinality constraint. Crucially, these estimates inherit shrinkage or regularization and uncertainty quantification from the underlying Bayesian model, and apply for any well‐specified Bayesian LMM. More broadly, our decision analysis strategy deemphasizes the role of a single “best” subset, which is often unstable and limited in its information content, and instead favors a collection of near‐optimal subsets. This collection is summarized by key member subsets and variable‐specific importance metrics. Customized subset search and out‐of‐sample approximation algorithms are provided for more scalable computing. These tools are applied to simulated data and a longitudinal physical activity dataset, and demonstrate excellent prediction, estimation, and selection ability.

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  • Daniel R. Kowal, 2023. "Subset selection for linear mixed models," Biometrics, The International Biometric Society, vol. 79(3), pages 1853-1867, September.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:3:p:1853-1867
    DOI: 10.1111/biom.13707
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    References listed on IDEAS

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    1. Satkartar K. Kinney & David B. Dunson, 2007. "Fixed and Random Effects Selection in Linear and Logistic Models," Biometrics, The International Biometric Society, vol. 63(3), pages 690-698, September.
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    3. Howard D. Bondell & Arun Krishna & Sujit K. Ghosh, 2010. "Joint Variable Selection for Fixed and Random Effects in Linear Mixed-Effects Models," Biometrics, The International Biometric Society, vol. 66(4), pages 1069-1077, December.
    4. Joseph G. Ibrahim & Hongtu Zhu & Ramon I. Garcia & Ruixin Guo, 2011. "Fixed and Random Effects Selection in Mixed Effects Models," Biometrics, The International Biometric Society, vol. 67(2), pages 495-503, June.
    5. Zhen Chen & David B. Dunson, 2003. "Random Effects Selection in Linear Mixed Models," Biometrics, The International Biometric Society, vol. 59(4), pages 762-769, December.
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