  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.
