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Latent class CUB models

Author

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  • Leonardo Grilli
  • Maria Iannario
  • Domenico Piccolo
  • Carla Rampichini

Abstract

The paper proposes a latent class version of Combination of Uniform and (shifted) Binomial random variables ( CUB ) models for ordinal data to account for unobserved heterogeneity. The extension, called LC-CUB , is useful when the heterogeneity is originated by clusters of respondents not identified by covariates: this may generate a multimodal response distribution, which cannot be adequately described by a standard CUB model. The LC-CUB model is a finite mixture of CUB models yielding a multimodal theoretical distribution. Model identification is achieved by constraining the uncertainty parameters to be constant across latent classes. A simulation experiment shows the performance of the maximum likelihood estimator, whereas the usefulness of the approach is illustrated by means of a case study on political self-placement measured on an ordinal scale. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:advdac:v:8:y:2014:i:1:p:105-119
    DOI: 10.1007/s11634-013-0143-5
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    References listed on IDEAS

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    1. 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.
    2. Romina Gambacorta & Maria Iannario, 2013. "Measuring Job Satisfaction with CUB Models," LABOUR, CEIS, vol. 27(2), pages 198-224, June.
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    8. Grn, Bettina & Leisch, Friedrich, 2009. "Dealing with label switching in mixture models under genuine multimodality," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 851-861, May.
    9. Salvatore Ingrassia & Simona Minotti & Giorgio Vittadini, 2012. "Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions," Journal of Classification, Springer;The Classification Society, vol. 29(3), pages 363-401, October.
    10. Salvatore Ingrassia & Simona Minotti & Giorgio Vittadini, 2012. "Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions," Journal of Classification, Springer;The Classification Society, vol. 29(3), pages 363-401, October.
    11. 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. 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.
    3. Gerhard Tutz & Micha Schneider & Maria Iannario & Domenico Piccolo, 2017. "Mixture models for ordinal responses to account for uncertainty of choice," 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. 11(2), pages 281-305, June.
    4. Manisera, Marica & Zuccolotto, Paola, 2014. "Modeling rating data with Nonlinear CUB models," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 100-118.
    5. Maria Iannario & Marica Manisera & Domenico Piccolo & Paola Zuccolotto, 2020. "Ordinal Data Models for No-Opinion Responses in Attitude Survey," Sociological Methods & Research, , vol. 49(1), pages 250-276, February.
    6. 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.
    7. Maurizio Carpita & Enrico Ciavolino & Mariangela Nitti, 2019. "The MIMIC–CUB Model for the Prediction of the Economic Public Opinions in Europe," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(1), pages 287-305, November.
    8. 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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