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Robustness issues for cub models

Author

Listed:
  • Maria Iannario

    (University of Naples Federico II)

  • Anna Clara Monti

    (University of Sannio)

  • Domenico Piccolo

    (University of Naples Federico II)

Abstract

The present paper deals with a parametric class of models implemented for ordered categorical data, denoted as cub model, which is defined as a discrete mixture of a shifted binomial and a uniform random variable. For these models, robustness issues are considered. In particular, the influence function is introduced and subsequently used to define the robustness measures for categorical data. By exploiting the peculiar parametrization of the cub models, diagnostic plots are proposed which allow to display the effect of a contamination in the data, simultaneously for all categories. The breakdown point is also considered and a computational procedure is suggested to determine an upper bound. The paper provides evidence that, despite the limited range of the support, contaminations in the data can heavily affect the inferential procedures and hence robustness topics are indeed relevant for ordinal data.

Suggested Citation

  • Maria Iannario & Anna Clara Monti & Domenico Piccolo, 2016. "Robustness issues for cub models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 731-750, December.
    • Handle: RePEc:spr:testjl:v:25:y:2016:i:4:d:10.1007_s11749-016-0493-3
    DOI: 10.1007/s11749-016-0493-3
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    References listed on IDEAS

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    1. Croux, Christophe, 1998. "Limit behavior of the empirical influence function of the median," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 331-340, March.
    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. Romina Gambacorta & Maria Iannario, 2013. "Measuring Job Satisfaction with CUB Models," LABOUR, CEIS, vol. 27(2), pages 198-224, June.
    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. 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. 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.
    2. Roberto Colombi & Sabrina Giordano, 2019. "Likelihood-based tests for a class of misspecified finite mixture models for ordinal categorical data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1175-1202, December.
    3. Maria Iannario & Anna Clara Monti, 2023. "Generalized residuals and outlier detection for ordinal data with challenging data structures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1197-1216, October.

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