Addressing cluster-constant covariates in mixed effects models via likelihood-based boosting techniques

TL;DR

This paper introduces an improved likelihood-based boosting algorithm for linear mixed models that correctly handles cluster-constant covariates, leading to better estimates and reduced computational effort.

Contribution

It proposes a novel boosting algorithm that properly weights random effects and corrects for correlations with cluster-constant covariates in mixed models.

Findings

Outperforms existing boosting methods in simulations.

Achieves more accurate variable selection.

Reduces computational complexity.

Abstract

Boosting techniques from the field of statistical learning have grown to be a popular tool for estimating and selecting predictor effects in various regression models and can roughly be separated in two general approaches, namely gradient boosting and likelihood-based boosting. An extensive framework has been proposed in order to fit generalised mixed models based on boosting, however for the case of cluster-constant covariates likelihood-based boosting approaches tend to mischoose variables in the selection step leading to wrong estimates. We propose an improved boosting algorithm for linear mixed models where the random effects are properly weighted, disentangled from the fixed effects updating scheme and corrected for correlations with cluster-constant covariates in order to improve quality of estimates and in addition reduce the computational effort. The method outperforms current state-of-the-art approaches from boosting and maximum likelihood inference which is shown via simulations and various data examples.