IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v8y2014i1p105-119.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11634-013-0143-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11634-013-0143-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. 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.
    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. 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.
    6. 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.
    7. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. Manisera, Marica & Zuccolotto, Paola, 2014. "Modeling rating data with Nonlinear CUB models," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 100-118.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gennaro Punzo & Rosalia Castellano & Mirko Buonocore, 2018. "Job Satisfaction in the “Big Four” of Europe: Reasoning Between Feeling and Uncertainty Through CUB Models," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 139(1), pages 205-236, August.
    2. 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.
    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, 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.
    5. 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.
    6. 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.
    7. 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.
    8. Manisera, Marica & Zuccolotto, Paola, 2014. "Modeling rating data with Nonlinear CUB models," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 100-118.
    9. Maria Iannario, 2012. "Preliminary estimators for a mixture model of ordinal data," 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(3), pages 163-184, October.
    10. Xiaoqiong Fang & Andy W. Chen & Derek S. Young, 2023. "Predictors with measurement error in mixtures of polynomial regressions," Computational Statistics, Springer, vol. 38(1), pages 373-401, March.
    11. 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.
    12. Salvatore Ingrassia & Antonio Punzo & Giorgio Vittadini & Simona Minotti, 2015. "The Generalized Linear Mixed Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 32(1), pages 85-113, April.
    13. 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.
    14. Aßmann, Christian & Boysen-Hogrefe, Jens & Pape, Markus, 2014. "Bayesian analysis of dynamic factor models: An ex-post approach towards the rotation problem," Kiel Working Papers 1902, Kiel Institute for the World Economy (IfW Kiel).
    15. Salvatore Ingrassia & Antonio Punzo, 2020. "Cluster Validation for Mixtures of Regressions via the Total Sum of Squares Decomposition," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 526-547, July.
    16. Stefania Capecchi & Romina Gambacorta & Rosaria Simone & Domenico Piccolo, 2024. "Modelling cognitive response patterns to survey questions using the class of CUB models," Questioni di Economia e Finanza (Occasional Papers) 885, Bank of Italy, Economic Research and International Relations Area.
    17. Aßmann, Christian & Boysen-Hogrefe, Jens & Pape, Markus, 2016. "Bayesian analysis of static and dynamic factor models: An ex-post approach towards the rotation problem," Journal of Econometrics, Elsevier, vol. 192(1), pages 190-206.
    18. 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.
    19. Gore, Madison & Joshi, Omkar & Chapagain, Binod & Poudyal, Neelam C. & Fairbanks, Sue, 2023. "Visitor satisfaction with WMAs: A case study from Oklahoma," Forest Policy and Economics, Elsevier, vol. 147(C).
    20. Ingrassia, Salvatore & Minotti, Simona C. & Punzo, Antonio, 2014. "Model-based clustering via linear cluster-weighted models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 159-182.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:advdac:v:8:y:2014:i:1:p:105-119. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.