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

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  • Domenico Piccolo

    (University of Naples Federico II)

  • Rosaria Simone

    (University of Naples Federico II)

Abstract

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.

Suggested Citation

  • Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    • Handle: RePEc:spr:stmapp:v:28:y:2019:i:3:d:10.1007_s10260-019-00461-1
    DOI: 10.1007/s10260-019-00461-1
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    4. Gerhard Tutz, 2020. "Modelling heterogeneity: on the problem of group comparisons with logistic regression and the potential of the heterogeneous choice model," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(3), pages 517-542, September.
    5. Ribecco, Nunziata & D'Uggento, Angela Maria & Labarile, Angela, 2022. "What influences the perception of immigration in Italian adolescents? An analysis with CUB models for rating data," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    6. Rosaria Simone, 2023. "Uncertainty Diagnostics of Binomial Regression Trees for Ordered Rating Data," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 79-105, April.
    7. Roberto Colombi & Sabrina Giordano & Gerhard Tutz, 2021. "A Rating Scale Mixture Model to Account for the Tendency to Middle and Extreme Categories," Journal of Educational and Behavioral Statistics, , vol. 46(6), pages 682-716, December.
    8. Mazzi Gian Luigi & Mitchell James & Carausu Florabela, 2021. "Measuring and Communicating the Uncertainty in Official Economic Statistics," Journal of Official Statistics, Sciendo, vol. 37(2), pages 289-316, June.
    9. Heng Xu & Nan Zhang, 2022. "From Contextualizing to Context Theorizing: Assessing Context Effects in Privacy Research," Management Science, INFORMS, vol. 68(10), pages 7383-7401, October.
    10. Roberto Colombi & Sabrina Giordano & Anna Gottard, 2019. "Discussion of “The class of CUB models: statistical foundations, inferential issues and empirical evidence”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 441-444, September.
    11. Cantone, Giulio Giacomo & Tomaselli, Venera, 2023. "Quasi-experimental network-based design for semantic analysis of small clusters of bi-polar online reviews," SocArXiv v7u3h, Center for Open Science.
    12. Capecchi, Stefania & Amato, Mario & Sodano, Valeria & Verneau, Fabio, 2019. "Understanding beliefs and concerns towards palm oil: Empirical evidence and policy implications," Food Policy, Elsevier, vol. 89(C).
    13. Rosaria Simone, 2022. "On finite mixtures of Discretized Beta model for ordered responses," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 828-855, September.
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    15. Corduas, Marcella, 2022. "Gender differences in the perception of inflation," Journal of Economic Psychology, Elsevier, vol. 90(C).
    16. Domenico Piccolo & Rosaria Simone, 2019. "Rejoinder to the discussion of “The class of cub models: statistical foundations, inferential issues and empirical evidence”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 477-493, September.

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