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Title: Bayesian effect fusion with spike and slab prior Authors:  Daniela Pauger - Johannes Kepler University Linz (Austria) [presenting]
Helga Wagner - Johannes Kepler University (Austria)
Abstract: In many applications, especially in social or economic studies, potential covariates for a regression analysis are categorical, measured either on an ordinal or on a nominal scale. Including categorical variables in regression models can easily lead to a high-dimensional vector of effects. We present a method for sparse modelling of the effects of categorical covariates, where sparsity is achieved by excluding irrelevant predictors and/or by fusing levels which have essentially the same effect on the response. To encourage effect fusion, we construct a prior that is based on the specification of spike and slab priors on differences of level effects and hence allows for selective shrinkage of these level effects to each other. The proposed prior is designed mainly for fusion of effects but automatically excludes irrelevant predictors as well. Furthermore, the prior allows to take into account any available information on the ordering of categories and to incorporate prior information which levels should not be fused. We demonstrate the performance of the developed method in simulation studies and in a real data example.