  Generalized linear mixed models (GLMM) are used for inference and prediction
in a wide range of different applications providing a powerful scientific tool.
An increasing number of sources of data are becoming available, introducing a
variety of candidate explanatory variables for these models. Selection of an
optimal combination of variables is thus becoming crucial. In a Bayesian
setting, the posterior distribution of the models, based on the observed data,
can be viewed as a relevant measure for the model evidence. The number of
possible models increases exponentially in the number of candidate variables.
Moreover, the space of models has numerous local extrema in terms of posterior
model probabilities. To resolve these issues a novel MCMC algorithm for the
search through the model space via efficient mode jumping for GLMMs is
introduced. The algorithm is based on that marginal likelihoods can be
efficiently calculated within each model. It is recommended that either exact
expressions or precise approximations of marginal likelihoods are applied. The
suggested algorithm is applied to simulated data, the famous U.S. crime data,
protein activity data and epigenetic data and is compared to several existing
approaches.
