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Latent class CUB models

Author

Listed:
  • 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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    File URL: http://hdl.handle.net/10.1007/s11634-013-0143-5
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    References listed on IDEAS

    as
    1. Romina Gambacorta & Maria Iannario, 2013. "Measuring Job Satisfaction with CUB Models," LABOUR, CEIS, vol. 27(2), pages 198-224, June.
    2. Roderick McDonald, 1982. "A note on the investigation of local and global identifiability," Psychometrika, Springer;The Psychometric Society, vol. 47(1), pages 101-103, March.
    3. 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.
    4. Michel Wedel & Wayne DeSarbo, 1995. "A mixture likelihood approach for generalized linear models," Journal of Classification, Springer;The Classification Society, vol. 12(1), pages 21-55, March.
    5. Schofield, Normal & Martin, Andrew D. & Quinn, Kevin M. & Whitford, Andrew B., 1998. "Multiparty Electoral Competition in the Netherlands and Germany: A Model Based on Multinomial Probit," Public Choice, Springer, vol. 97(3), pages 257-293, December.
    6. 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.
    7. 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.
    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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    Citations

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    Cited by:

    1. 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.
    2. Marica Manisera & Paola Zuccolotto, 2016. "Treatment of ‘don’t know’ responses in a mixture model for rating data," METRON, Springer;Sapienza Università di Roma, vol. 74(1), pages 99-115, April.
    3. 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.

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