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Title: Bayesian effect fusion for categorical predictors in logistic regression Authors:  Magdalena Leitner - Johannes Kepler University Linz (Austria) [presenting]
Helga Wagner - Johannes Kepler University (Austria)
Abstract: For regression type models sparsity is an important goal as usually a large number of covariates is available in applications. Many methods have been developed for variable selection and for the selection of level effects of categorical covariates. However, for a categorical covariate, which is captured by a group of level effects, a sparse representation of its effect can also be achieved by fusing predictor levels that have essentially the same effect on the response. In a Bayesian framework, this can be accomplished by specifying appropriate prior distributions. In order to encourage fusion of level effects in logistic regression models, we extend methods developed for Bayesian effect fusion in linear regression. In the first method a joint multivariate Normal prior is specified on all level effects associated with one covariate. Equivalently, spike and slab priors can be specified on the effect differences of a covariate, considering the linear restrictions between them. The second method relies on a sparse finite mixture prior of spiky components constructed to encourage clustering of level effects that are almost identical. For both prior distributions, MCMC sampling is feasible using data augmentation with latent Polya-Gamma variables. We compare the performance of both approaches for simulated data and illustrate the methods by analyzing a real data set.