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.
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