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June 2019 Bayesian Effect Fusion for Categorical Predictors
Daniela Pauger, Helga Wagner
Bayesian Anal. 14(2): 341-369 (June 2019). DOI: 10.1214/18-BA1096

Abstract

We propose a Bayesian approach to obtain a sparse representation of the effect of a categorical predictor in regression type models. As this effect is captured by a group of level effects, sparsity cannot only be achieved by excluding single irrelevant level effects or the whole group of effects associated to this predictor but also 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. This prior can alternatively be obtained by specifying spike and slab prior distributions on all effect differences associated to this categorical predictor. We show how restricted fusion can be implemented and develop an efficient MCMC (Markov chain Monte Carlo) method for posterior computation. The performance of the proposed method is investigated on simulated data and we illustrate its application on real data from EU-SILC (European Union Statistics on Income and Living Conditions).

Citation

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Daniela Pauger. Helga Wagner. "Bayesian Effect Fusion for Categorical Predictors." Bayesian Anal. 14 (2) 341 - 369, June 2019. https://doi.org/10.1214/18-BA1096

Information

Published: June 2019
First available in Project Euclid: 25 May 2018

zbMATH: 07045434
MathSciNet: MR3934089
Digital Object Identifier: 10.1214/18-BA1096

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Vol.14 • No. 2 • June 2019
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