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Cumulative and CUB Models for Rating Data: A Comparative Analysis

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  • Domenico Piccolo
  • Rosaria Simone
  • Maria Iannario

Abstract

Ordinal measurements as ratings, preference and evaluation data are very common in applied disciplines, and their analysis requires a proper modelling approach for interpretation, classification and prediction of response patterns. This work proposes a comparative discussion between two statistical frameworks that serve these goals: the established class of cumulative models and a class of mixtures of discrete random variables, denoted as CUB models, whose peculiar feature is the specification of an uncertainty component to deal with indecision and heterogeneity. After surveying their definition and main features, we compare the performances of the selected paradigms by means of simulation experiments and selected case studies. The paper is tailored to enrich the understanding of the two approaches by running an extensive and comparative analysis of results, relative advantages and limitations, also at graphical level. In conclusion, a summarising review of the key issues of the alternative strategies and some final remarks are given, aimed to support a unifying setting.

Suggested Citation

  • Domenico Piccolo & Rosaria Simone & Maria Iannario, 2019. "Cumulative and CUB Models for Rating Data: A Comparative Analysis," International Statistical Review, International Statistical Institute, vol. 87(2), pages 207-236, August.
    • Handle: RePEc:bla:istatr:v:87:y:2019:i:2:p:207-236
    DOI: 10.1111/insr.12282
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    Cited by:

    1. 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).
    2. Rosaria Simone, 2021. "An accelerated EM algorithm for mixture models with uncertainty for rating data," Computational Statistics, Springer, vol. 36(1), pages 691-714, March.
    3. Francesca Iorio & Riccardo Lucchetti & Rosaria Simone, 2024. "Testing distributional assumptions in CUB models for the analysis of rating data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(3), pages 669-701, September.
    4. Antonio Calcagnì & Luigi Lombardi, 2022. "Modeling random and non-random decision uncertainty in ratings data: a fuzzy beta model," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(1), pages 145-173, March.
    5. 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).

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