Statistical Modelling 18 (2) (2018), 175–196

Effect fusion using model-based clustering

Gertraud Malsiner-Walli
Institute for Statistics and Mathematics,
Vienna University for Economics and Business,
Austria
e-mail: gmalsine@wu.ac.at

Daniela Pauger
Department of Applied Statistics,
Johannes Kepler University Linz,
Austria


Helga Wagner
Department of Applied Statistics,
Johannes Kepler University Linz,
Austria


Abstract:

In social and economic studies many of the collected variables are measured on a nominal scale, often with a large number of categories. The definition of categories can be ambiguous and different classification schemes using either a finer or a coarser grid are possible. Categorization has an impact when such a variable is included as covariate in a regression model: a too fine grid will result in imprecise estimates of the corresponding effects, whereas with a too coarse grid important effects will be missed, resulting in biased effect estimates and poor predictive performance.

To achieve an automatic grouping of the levels of a categorical covariate with essentially the same effect, we adopt a Bayesian approach and specify the prior on the level effects as a location mixture of spiky Normal components. Model-based clustering of the effects during MCMC sampling allows to simultaneously detect categories which have essentially the same effect size and identify variables with no effect at all. Fusion of level effects is induced by a prior on the mixture weights which encourages empty components. The properties of this approach are investigated in simulation studies. Finally, the method is applied to analyse effects of high-dimensional categorical predictors on income in Austria.


Keywords:

categorical covariate; Sparse finite mixture prior; sparsity; MCMC sampling.

Downloads:

Related code and simulated data are available in the R package "effectFusion" available from CRAN at here. The article's appendix can be found here.
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