A scalable and efficient covariate selection criterion for mixed effects regression models with unknown random effects structure

TL;DR

This paper introduces a new covariate selection criterion for mixed effects regression models that is computationally efficient and applicable even when the random effects structure is unknown, aiding early-stage model building.

Contribution

It proposes a novel model selection criterion suitable for two-step fitted mixed effects models with unknown random effects structure, requiring only cluster-level likelihood evaluations.

Findings

The criterion performs well in simulations and real data analysis.

It simplifies covariate selection in mixed effects models.

The method is computationally efficient and broadly applicable.

Abstract

We propose a new model selection criterion for mixed effects regression models that is computable when the model is fitted with a two-step method, even when the structure and the distribution of the random effects are unknown. The criterion is especially useful in the early stage of the model building process when one needs to decide which covariates should be included in a mixed effects regression model but has no knowledge of the random effect structure. This is particularly relevant in substantive fields where variable selection is guided by information criteria rather than regularization. The calculation of the criterion requires only the evaluation of cluster-level log-likelihoods and does not rely on heavy numerical integration. We provide theoretical and numerical arguments to justify the method and we illustrate its usefulness by analyzing data on a socio-economic study of young American Indians.