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Modeling rating data with Nonlinear CUB models

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  • Manisera, Marica
  • Zuccolotto, Paola

Abstract

A general statistical model for ordinal or rating data, which includes some existing approaches as special cases, is proposed. The focus is on the CUB models and a new class of models, called Nonlinear CUB, which generalize CUB. In the framework of the Nonlinear CUB models, it is possible to express a transition probability, i.e. the probability of increasing one rating point at a given step of the decision process. Transition probabilities and the related transition plots are able to describe the state of mind of the respondents about the response scale used to express judgments. Unlike classical CUB, the Nonlinear CUB models are able to model decision processes with non-constant transition probabilities.

Suggested Citation

  • Manisera, Marica & Zuccolotto, Paola, 2014. "Modeling rating data with Nonlinear CUB models," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 100-118.
  • Handle: RePEc:eee:csdana:v:78:y:2014:i:c:p:100-118 DOI: 10.1016/j.csda.2014.04.001
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    References listed on IDEAS

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    1. Maria Iannario & Marica Manisera & Domenico Piccolo & Paola Zuccolotto, 2012. "Sensory analysis in the food industry as a tool for marketing decisions," 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. 6(4), pages 303-321, December.
    2. Maria Iannario, 2010. "On the identifiability of a mixture model for ordinal data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 87-94.
    3. Bohning, Dankmar & Seidel, Wilfried & Alfo, Macro & Garel, Bernard & Patilea, Valentin & Walther, Gunther, 2007. "Advances in Mixture Models," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5205-5210, July.
    4. D'Elia, Angela & Piccolo, Domenico, 2005. "A mixture model for preferences data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 917-934, June.
    5. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
    6. Maria Iannario, 2012. "Modelling shelter choices in a class of mixture models for ordinal responses," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(1), pages 1-22, March.
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    Cited by:

    1. Manisera, Marica & Zuccolotto, Paola, 2015. "Identifiability of a model for discrete frequency distributions with a multidimensional parameter space," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 302-316.
    2. repec:spr:advdac:v:11:y:2017:i:2:d:10.1007_s11634-016-0247-9 is not listed on IDEAS

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