The class of cub models: statistical foundations, inferential issues and empirical evidence

• Published in: Statistical methods & applications Vol. 28; no. 3; pp. 389 - 435
• Main Authors: Piccolo, Domenico, Simone, Rosaria
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2019; Springer Nature B.V
• Subjects: Chemistry and Earth Sciences; Computer Science; Economics; Empirical analysis; Finance; Health Sciences; Humanities; Insurance; Law; Management; Mathematics and Statistics; Medicine; Original Paper; Parameterization; Performance prediction; Physics; Random variables; Statistical models; Statistical Theory and Methods; Statistics; Statistics for Business; Statistics for Engineering; Statistics for Life Sciences; Statistics for Social Sciences; Uncertainty; models; Explicative power; Predictability; Data generating process; Ordinal data; Ratings
• ISSN: 1618-2510; 1613-981X
• DOI: 10.1007/s10260-019-00461-1

This paper discusses a general framework for the analysis of rating and preference data that is rooted on a class of mixtures of discrete random variables. These models have been extensively studied and applied in the last 15 years thanks to a flexible and parsimonious parametrization of data generating process and to prompt interpretation of results. The approach considers the final response as the combination of feeling and uncertainty, by allowing for finer model specifications to include refuge options, response styles and possible overdispersion, also in relation to subjects’ and objects’ covariates. The article establishes the state of art of the research inherent to this paradigm, in terms of methodology, inferential procedures and fitting measures, by emphasizing capabilities and limitations yet establishing new findings. In particular, explicative power and predictive performances of cub statistical models for ordinal data are examined and new topics that could boost and support the modelling of uncertainty in this framework are provided. Possible developments are outlined throughout the whole presentation and final comments conclude the paper.