Statistical Modelling 16 (4) (2016), 322–340
A class of mixture models for multidimensional ordinal data
Roberto Colombi
Department of Management,
Information and Production Engineering,
University of Bergamo,
Italy
Sabrina Giordano
Department of Economics,
Statistics and Finance,
University of Calabria,
Italy
e-mail: sabrina.giordano@unical.it
Abstract:
In rating surveys, people are requested to express preferences on several aspects related to a topic by selecting a category in an ordered scale. For such data, we propose a model defined by a mixture of a uniform distribution and a Sarmanov distribution with CUB (combination of uniform and shifted binomial) marginal distributions (D'Elia and Piccolo, 2005). This mixture generalizes the CUB model to the multivariate case by taking into account the association among answers of the same individual to the items of a questionnaire. It also allows us to distinguish two kinds of uncertainty: specific uncertainty, related to the indecision for single items, and global uncertainty referred to the respondent's hesitancy in completing the whole questionnaire. A simulation and a real case study highlight the usefulness of the new methodology.
Keywords:
CUB models; Rating survey; Sarmanov distributions; uncertainty.
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