Abstract
We consider a special finite mixture model for ordinal data expressing the preferences of raters with regards to items or services, named CUB (Covariate Uniform Binomial), recently introduced in statistical literature. The mixture is made up of two components that belong to different families of distributions: a shifted Binomial and a discrete Uniform. Bayesian analysis of the CUB model naturally comes from the elicitation of some priors on its parameters. In this case the parameters estimation must be performed through the analysis of the posterior distribution. In the theory of finite mixture models complex posterior distributions are usually evaluated through computational methods of simulation such as the Markov Chain Monte Carlo (MCMC) algorithms. Since the mixture type of the CUB model is non-standard, a suitable MCMC algorithm has been developed and its performance has been evaluated via a simulation study and an application on real data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bini, M., Monari, P., Piccolo, D., & Salmaso, L. (Eds.). (2009). Statistical methods for the evaluation of educational services and quality of products (Contribution to statistics). Berlin: Springer.
Corduas, M., Iannario, M., & Piccolo, D. (2009). A class of statistical models for evaluating services and performances. In M. Bini, et al. (Eds.), Statistical methods for the evaluation of educational services and quality of products (Contribution to statistics). Berlin: Springer.
D’Elia, A. (2003). Finite sample performance of the E-M algorithm for ranks data modelling. Statistica, LXIII, 41–51.
D’Elia, A., & Piccolo, D. (2005). A mixture model for preferences data analysis. Computational Statistics & Data Analysis, 49, 917–934.
Früwirth-Schnatter, S. (2006). Finite mixture and markov switching models (Springer series in statistics). New York: Springer.
Iannario, M. (2010). On the identifiability of a mixture model for ordinal data. Metron, LXVIII, 87.
MacLachlan, G., & Peel, D. (2000). Finite mixture models (Wiley series in probability and statistics). New York: Wiley
Piccolo, D. (2006). Observed information matrix for MUB models. Quaderni di Statistica, 8, 33–78.
Acknowledgements
The paper has been prepared within a MIUR grant (code 2008WKHJP-KPRIN2008-PUC number E61J10000020001) for the project: “Modelli per variabili latenti basati su dati ordinali: metodi statistici ed evidenze empiriche” (research Unit University of Naples Federico II).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Deldossi, L., Paroli, R. (2013). Inference on the CUB Model: An MCMC Approach. In: Giusti, A., Ritter, G., Vichi, M. (eds) Classification and Data Mining. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28894-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-28894-4_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28893-7
Online ISBN: 978-3-642-28894-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)