  Today, generalized linear mixed models are broadly used in many fields.
However, the development of tools for performing simultaneous inference has
been largely neglected in this domain. A framework for joint inference is
indispensable to carry out statistically valid multiple comparisons of
parameters of interest between all or several clusters. We therefore develop
simultaneous confidence intervals and multiple testing procedures for empirical
best predictors under generalized linear mixed models. In addition, we
implement our methodology to study widely employed examples of mixed models,
that is, the unit-level binomial, the area-level Poisson-gamma and the
area-level Poisson-lognormal mixed models. The asymptotic results are
accompanied by extensive simulations. A case study on predicting poverty rates
illustrates applicability and advantages of our simultaneous inference tools.
