Fixed effects selection in the linear mixed-effects model using adaptive ridge procedure for L0 penalty performance

TL;DR

This paper introduces an adaptive ridge-based method for fixed effects selection in linear mixed-effects models, effectively handling high-dimensional data and outperforming LASSO in model selection and estimation consistency.

Contribution

It proposes a novel adaptive ridge procedure for fixed effects selection in linear mixed-effects models, addressing high-dimensional challenges with theoretical and empirical validation.

Findings

The method achieves model selection consistency.

It performs well in high-dimensional settings.

Outperforms LASSO in simulations.

Abstract

This paper is concerned with the selection of fixed effects along with the estimation of fixed effects, random effects and variance components in the linear mixed-effects model. We introduce a selection procedure based on an adaptive ridge (AR) penalty of the profiled likelihood, where the covariance matrix of the random effects is Cholesky factorized. This selection procedure is intended to both low and high-dimensional settings where the number of fixed effects is allowed to grow exponentially with the total sample size, yielding technical difficulties due to the non-convex optimization problem induced by L0 penalties. Through extensive simulation studies, the procedure is compared to the LASSO selection and appears to enjoy the model selection consistency as well as the estimation consistency.