Subset selection for linear mixed models.

This article presents a Bayesian decision analysis framework for subset selection in linear mixed models (LMMs), which are regression models accommodating structured dependence such as longitudinal or clustered data. The approach employs a Mahalanobis loss function incorporating the LMM's covariance structure to derive optimal linear coefficients for any given subset of covariates and for all subsets constrained by cardinality, thereby inheriting regularization and uncertainty quantification from the Bayesian model. To address instability in selecting a single "best" subset, the method identifies an acceptable family of near-optimal subsets based on out-of-sample predictive performance, summarized by key subsets and variable importance metrics. The framework is computationally scalable via customized subset search algorithms and is demonstrated through simulations and an application to longitudinal physical activity data from the National Health and Nutrition Examination Survey (NHANES), showing improved prediction accuracy, estimation, and variable selection compared to existing methods.