Inference on the CUB Model: An MCMC Approach

Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


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.


Mixture Model Markov Chain Monte Carlo Ordinal Data Markov Chain Monte Carlo Method Markov Chain Monte Carlo Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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).


  1. 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.Google Scholar
  2. 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.Google Scholar
  3. D’Elia, A. (2003). Finite sample performance of the E-M algorithm for ranks data modelling. Statistica, LXIII, 41–51.Google Scholar
  4. D’Elia, A., & Piccolo, D. (2005). A mixture model for preferences data analysis. Computational Statistics & Data Analysis, 49, 917–934.MathSciNetMATHCrossRefGoogle Scholar
  5. Früwirth-Schnatter, S. (2006). Finite mixture and markov switching models (Springer series in statistics). New York: Springer.Google Scholar
  6. Iannario, M. (2010). On the identifiability of a mixture model for ordinal data. Metron, LXVIII, 87.Google Scholar
  7. MacLachlan, G., & Peel, D. (2000). Finite mixture models (Wiley series in probability and statistics). New York: WileyGoogle Scholar
  8. Piccolo, D. (2006). Observed information matrix for MUB models. Quaderni di Statistica, 8, 33–78.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Dipartimento di Scienze StatisticheUniversità Cattolica del Sacro CuoreMilanoItaly

Personalised recommendations