Bayesian variable selection in a class of mixture models for ordinal data: a comparative study

Abstract

In this paper, we consider a special finite mixture model named Combination of Uniform and shifted Binomial (CUB), recently introduced in the statistical literature to analyse ordinal data expressing the preferences of raters with regards to items or services. Our aim is to develop a variable selection procedure for this model using a Bayesian approach. Bayesian methods for variable selection and model choice have become increasingly popular in recent years, due to advances in Markov chain Monte Carlo computational algorithms. Several methods have been proposed in the case of linear and generalized linear models (GLM). In this paper, we adapt to the CUB model some of these algorithms: the Kuo–Mallick method together with its ‘metropolized’ version and the Stochastic Search Variable Selection method. Several simulated examples are used to illustrate the algorithms and to compare their performance. Finally, an application to real data is introduced.

Keywords:

• CUB models
• Markov chain Monte Carlo
• Kuo–Mallick method
• metropolized-Kuo–Mallick method
• SSVS method

Acknowledgements

We are grateful to the referee whose careful reading and detailed comments improved the paper. This work has been supported by a MIUR grant [code 2008WKHJPK-PRIN2008] for the project: ‘Modelli per variabili latenti basati su dati ordinali: metodi statistici ed evidenze empiriche’, CUP number E61J10000020001, Research Unit at University of Naples Federico II.