Bootstrapping robust estimates for clustered data

In mixed models, the use of robust estimates raises several interesting inferential challenges. One of these challenges arises from the realization that the effect of contamination is to increase the variability in the data, but robust estimates of variance components are usually smaller than their nonrobust counterparts. The robust estimates reflect the variability of the bulk of the data, which is not the same as the variability in the data-generating process. This means that the naive implementation of bootstrap procedures might not work. In this article we consider several bootstrap procedures, including random effect, transformation, and weighted bootstraps. We give conditions for the asymptotic validity of the bootstraps and assess their performance via a small simulation study. Both the transformation and generalized cluster bootstrap perform well and are asymptotically valid under reasonable conditions.