The adaptive elastic net variable selection for linear mixed effects models based on the orthogonal projection

Yiping Yang, Jingjing Zou, Xu Zhao and Peixin Zhao

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 17, 5381-5405

Abstract: We propose a novel variable selection process for fixed effects in linear mixed effects models, incorporating QR decomposition and an adaptive elastic net penalty. The QR decomposition technique is utilized to eliminate the influence of random effects on the selection of fixed effect variables. Subsequently, an adaptive elastic net penalized least squares objective function is formulated, enabling the concurrent estimation and selection of fixed effects. Under a set of regularization conditions, we prove that the resulting estimators exhibit the oracle property. Our proposed variable selection method not only efficiently separates fixed and random effects, preventing mutual interference, but also exhibits the grouping effect and oracle property. The finite-sample performance of our approach is thoroughly examined through simulation studies and further substantiated by the analysis of real data.

Date: 2025
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DOI: 10.1080/03610926.2024.2437497

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