A class of mixture models for multidimensional ordinal data. (August 2016)

• Record Type: Journal Article
• Authors: Colombi, Roberto; Giordano, Sabrina
• Is Part Of: Statistical modelling. Volume 16:Number 4(2016)
• Page Start: 322
• Page End: 340
• Publication Date: 2016-08
• Subjects: CUB models -- Rating survey -- Sarmanov distributions -- uncertainty; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X16649730
• Languages: English
• ISSNs: 1471-082X

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.