Inference on the CUB Model: An MCMC Approach
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.
KeywordsMixture Model Markov Chain Monte Carlo Ordinal Data Markov Chain Monte Carlo Method Markov Chain Monte Carlo Algorithm
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).
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