A proposal for the multidimensional extension of CUB models

Particular emphasis has been put, lately, on the analysis of categorical data and many proposals have appeared, ranging from pure methodological contributions to more applicative ones. Among such proposals, the CUB class of distributions, a mixture model for the analysis of ordinal data that has been successfully employed in various fields, seems of particular interest. CUB are univariate models that do not possess, at present, a multivariate version: aim of the present work is to investigate the feasibility of building a higher-dimensional version of such models and its possible applications. In order to achieve such results, we propose to employ techniques typical of the framework of copula models, that have proven to be valid tools for multivariate models construction and data analysis