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Varying uncertainty in CUB models

Author

Listed:
  • Anna Gottard

    (University of Florence)

  • Maria Iannario

    (University of Naples Federico II)

  • Domenico Piccolo

    (University of Naples Federico II)

Abstract

This paper presents a generalization of a mixture model used for the analysis of ratings and preferences by introducing a varying uncertainty component. According to the standard mixture model, called CUB model, the response probabilities are defined as a convex combination of shifted Binomial and discrete Uniform random variables. Our proposal introduces uncertainty distributions with different shapes, which could capture response style and indecision of respondents with greater effectiveness. Since we consider several alternative specifications that are nonnested, we suggest the implementation of a Vuong test for choosing among them. In this regard, some simulation experiments and real case studies confirm the usefulness of the approach.

Suggested Citation

  • Anna Gottard & Maria Iannario & Domenico Piccolo, 2016. "Varying uncertainty in CUB models," 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. 10(2), pages 225-244, June.
    • Handle: RePEc:spr:advdac:v:10:y:2016:i:2:d:10.1007_s11634-016-0235-0
    DOI: 10.1007/s11634-016-0235-0
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    References listed on IDEAS

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    1. Maria Iannario, 2015. "Detecting latent components in ordinal data with overdispersion by means of a mixture distribution," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 977-987, May.
    2. Kokonendji, Célestin C. & Zocchi, Silvio S., 2010. "Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1655-1662, November.
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    4. Leonardo Grilli & Maria Iannario & Domenico Piccolo & Carla Rampichini, 2014. "Latent class CUB models," 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. 8(1), pages 105-119, March.
    5. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    6. Guy Moors, 2008. "Exploring the effect of a middle response category on response style in attitude measurement," Quality & Quantity: International Journal of Methodology, Springer, vol. 42(6), pages 779-794, December.
    7. D. R. Cox, 2013. "A return to an old paper: ‘Tests of separate families of hypotheses’," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 207-215, March.
    8. 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. Rosaria Simone & Gerhard Tutz, 2018. "Modelling uncertainty and response styles in ordinal data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 224-245, August.
    3. Simone, Rosaria & Tutz, Gerhard & Iannario, Maria, 2020. "Subjective heterogeneity in response attitude for multivariate ordinal outcomes," Econometrics and Statistics, Elsevier, vol. 14(C), pages 145-158.
    4. Ryan H. L. Ip & K. Y. K. Wu, 2024. "A mixture distribution for modelling bivariate ordinal data," Statistical Papers, Springer, vol. 65(7), pages 4453-4488, September.
    5. Stefania Capecchi & Maria Iannario & Rosaria Simone, 2018. "Well-Being and Relational Goods: A Model-Based Approach to Detect Significant Relationships," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 135(2), pages 729-750, January.
    6. E. Nardo & R. Simone, 2019. "A model-based fuzzy analysis of questionnaires," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 187-215, June.
    7. 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.
    8. Maria Iannario & Domenico Piccolo, 2016. "A comprehensive framework of regression models for ordinal data," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 233-252, August.
    9. 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.
    10. 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.
    11. 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.
    12. Manisera, Marica & Zuccolotto, Paola, 2022. "A mixture model for ordinal variables measured on semantic differential scales," Econometrics and Statistics, Elsevier, vol. 22(C), pages 98-123.

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