Title: Effect fusion using sparse finite mixtures
Authors: Gertraud Malsiner-Walli - Johannes Kepler University Linz (Austria) [presenting]
Helga Wagner - Johannes Kepler University (Austria)
Daniela Pauger - Johannes Kepler University Linz (Austria)
Bettina Gruen - Wirtschaftsuniversität Wien (Austria)
Abstract: In social studies, variables are often measured on a nominal scale with many categories. However, different classification scales using either a finer or a coarser grid are possible. If such a variable is included in a regression model, the inclusion of too many categories can lead to imprecise estimates of the effects. In contrast, if the categorization is too coarse, important effects could be missed. Therefore, it would be appealing to have a method available which achieves classification automatically. For clustering categories, we propose the specification of a modified standard spike and slab prior on the effects. The spike component at zero allows to capture categories with no effect. The slab distribution is a spiky location mixture distribution and allows to identify categories with similar effect size. Model-based clustering of the effects during MCMC allows to both detect categories which have the same effect size and identify variables with no effect at all.