Simple bootstrap for linear mixed effects under model misspecification

TL;DR

This paper introduces a simple semiparametric bootstrap method for linear mixed effects models that remains robust under model misspecification, providing reliable inference for cluster-level parameters.

Contribution

The paper develops a straightforward bootstrap approach for mixed effects models that is asymptotically consistent and robust to assumption violations, improving practical inference.

Findings

Bootstrap intervals maintain coverage under severe misspecification

Method outperforms competitors in simulation studies

Approach is simple and theoretically justified

Abstract

Linear mixed effects are considered excellent predictors of cluster-level parameters in various domains. However, previous work has shown that their performance can be seriously affected by departures from modelling assumptions. Since the latter are common in applied studies, there is a need for inferential methods which are to certain extent robust to misspecfications, but at the same time simple enough to be appealing for practitioners. We construct statistical tools for cluster-wise and simultaneous inference for mixed effects under model misspecification using straightforward semiparametric random effect bootstrap. In our theoretical analysis, we show that our methods are asymptotically consistent under general regularity conditions. In simulations our intervals were robust to severe departures from model assumptions and performed better than their competitors in terms of empirical coverage probability.