  In this paper, we propose a Bayesian approach to obtain a sparse
representation of the effect of a categorical predictor in regression type
models. As the effect of a categorical predictor is captured by a group of
level effects, sparsity cannot only be achieved by excluding single irrelevant
level effects but also by excluding the whole group of effects associated to a
predictor or by fusing levels which have essentially the same effect on the
response. To achieve this goal, we propose a prior which allows for almost
perfect as well as almost zero dependence between level effects a priori. We
show how this prior can be obtained by specifying spike and slab prior
distributions on all effect differences associated to one categorical predictor
and how restricted fusion can be implemented. An efficient MCMC method for
posterior computation is developed. The performance of the proposed method is
investigated on simulated data. Finally, we illustrate its application on real
data from EU-SILC.
