Post-selection inference for linear mixed models

Abstract

While the post-selection inference has received considerable attention in linear and generalized linear models, it seems to be a neglected topic in the field of mixed models and mixed effect predictions. Therefore we have developed a complete asymptotic theory for post-selection inference within the framework of linear mixed models once the conditional Akaike information criterion was employed as a model selection procedure. Our theory is then used to construct confidence intervals for regression parameters, linear statistics and mixed effects under different scenarios, nested and general model sets as well as sets composed only of misspecified models. The theoretical analysis is accompanied by a simulation study which confirms a good performance of our procedures. Moreover, our simulations reveal a startling robustness of the classical confidence intervals for a mixed parameter. This is in contrast to findings for the fixed parameters and may indicate that, under certain scenarios, random effects would automatically adjust for model selection. We illustrate the utility of our proposed methodology in a study of the body mass index across different subgroups of the US population.