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

  • Domenico Piccolo
  • Rosaria SimoneEmail author
Original Paper


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.


Ordinal data Ratings Data generating process cub models Explicative power Predictability 



Authors thank all the Discussants for their constructive comments. The research has been funded by the ‘cubRegression Model Trees project’ (Project No. 000025_ALTRI_DR_1043_2017-C-CAPPELLI) of the University of Naples Federico II, Italy.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Political SciencesUniversity of Naples Federico IINaplesItaly

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