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A0777
Title: Sparse Bayesian modelling for categorical predictors Authors:  Daniela Pauger - Johannes Kepler University Linz (Austria) [presenting]
Helga Wagner - Johannes Kepler University (Austria)
Gertraud Malsiner-Walli - Johannes Kepler University Linz (Austria)
Abstract: The usual strategy to include a categorical covariate in a regression type model is to define one of the levels as baseline and to introduce dummy variables for all other levels. As this can result in a high-dimensional vector of regression effects, methods which allow sparser representation of the effect of categorical covariates are required. We achieve a sparse representation of the effect of a nominal predictor by defining informative prior distributions. The specification of a spike and slab prior on level effect differences allows classification of these differences as (practically) zero or non-zero. Thus, we can decide whether (1) a categorical predictor has no effect at all, (2) some (all) level effects are non-zero and/or (3) some (all) categories can be fused as they have essentially the same effect on the response. Additionally we consider a modification of the standard spike-and slab prior where the spike at zero is combined with a slab distribution which is a location mixture distribution. Model-based clustering of the effects during MCMC allows to detect levels which have essentially the same effect size. We demonstrate the performance of the developed methods in simulation studies and for real data.