Fixed effects Selection in high dimensional Linear Mixed Models

TL;DR

This paper introduces a fast, L1-penalized variable selection method for high-dimensional linear mixed models, capable of handling more parameters than observations, and demonstrating superior performance over existing methods.

Contribution

It proposes a novel multicycle ECM algorithm for fixed effects selection in high-dimensional linear mixed models, extending existing theoretical results and improving computational efficiency.

Findings

The method outperforms lmmLasso in both p<n and p>n scenarios.

The algorithm is faster due to avoiding matrix inversion.

It effectively estimates relevant fixed effects and variances.

Abstract

We consider linear mixed models in which the observations are grouped. A L1-penalization on the fixed effects coefficients of the log-likelihood obtained by considering the random effects as missing values is proposed. A multicycle ECM algorithm is used to solve the optimization problem; it can be combined with any variable selection method developed for linear models. The algorithm allows the number of parameters p to be larger than the total number of observations n; it is faster than the lmmLasso (Schelldorfer,2011) since no n*n matrix has to be inverted. We show that the theoretical results of Schelldorfer (2011) apply for our method when the variances of both the random effects and the residuals are known. The combination of the algorithm with a variable selection method (Rohart 2011) shows good results in estimating the set of relevant fixed effects coefficients as well as estimating the variances; it outperforms the lmmLasso both in the common case (p< n) and in the high-dimensional case (p > n).