  In spite of its high practical relevance, cluster specific multiple inference
for linear mixed model predictors has hardly been addressed so far. While
marginal inference for population parameters is well understood, conditional
inference for the cluster specific predictors is more intricate. This work
introduces a general framework for multiple inference in linear mixed models
for cluster specific predictors. Consistent confidence sets for multiple
inference are constructed under both, the marginal and the conditional law.
Furthermore, it is shown that, remarkably, corresponding multiple marginal
confidence sets are also asymptotically valid for conditional inference. Those
lend themselves for testing linear hypotheses using standard quantiles without
the need of re-sampling techniques. All findings are validated in simulations
and illustrated along a study on Covid-19 mortality in US state prisons.
