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

摘要

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