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

We propose a new model selection criterion for mixed effects regression models that is computable even when the structure and the distribution of the random effects are unknown. The criterion is most 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. 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 the consumption of alcohol by young American Indians.

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