An iterative algorithm for joint covariate and random effect selection in mixed effects models

TL;DR

This paper introduces an iterative stepwise algorithm for joint selection of fixed and random effects in mixed-effects models, improving interpretability and model accuracy in moderate-dimensional settings.

Contribution

It proposes a novel BIC-based stepwise selection method for simultaneous fixed and random effects selection in mixed-effects models.

Findings

Algorithm performs well in both linear and nonlinear models.

Simulation studies show competitive performance against existing methods.

Application to clinical data demonstrates practical utility.

Abstract

We consider joint selection of fixed and random effects in general mixed-effects models. The interpretation of estimated mixed-effects models is challenging since changing the structure of one set of effects can lead to different choices of important covariates in the model. We propose a stepwise selection algorithm to perform simultaneous selection of the fixed and random effects. It is based on BIC-type criteria whose penalties are adapted to mixed-effects models. The proposed procedure performs model selection in both linear and nonlinear models. It should be used in the low-dimension setting where the number of covariates and the number of random effects are moderate with respect to the total number of observations. The performance of the algorithm is assessed via a simulation study, that includes also a comparative study with alternatives when available in the literature. The use of the method is illustrated in the clinical study of an antibiotic agent kinetics.