IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v140y2015icp302-316.html
   My bibliography  Save this article

Identifiability of a model for discrete frequency distributions with a multidimensional parameter space

Author

Listed:
  • Manisera, Marica
  • Zuccolotto, Paola

Abstract

This paper is concerned with the identifiability of models depending on a multidimensional parameter vector, aimed at fitting a probability distribution to discrete observed data, with a special focus on a recently proposed mixture model. Starting from the necessary and sufficient condition derived by the definition of identifiability, we describe a general method to verify whether a specific model is identifiable or not. This procedure is then applied to investigate the identifiability of a recently proposed mixture model for rating data, Nonlinear CUB, which is an extension of a class of mixture models called CUB (Combination of Uniform and Binomial). Formal proofs and a numerical study show that some sufficient conditions for identifiability of Nonlinear CUB are always satisfied, provided that in the estimation procedure one quantity is fixed at a relatively small value.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:302-316
    DOI: 10.1016/j.jmva.2015.05.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X15001268
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2015.05.011?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. 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.
    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. Manisera, Marica & Zuccolotto, Paola, 2014. "Modeling rating data with Nonlinear CUB models," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 100-118.
    5. 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.
    6. 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.
    7. N. Atienza & J. Garcia-Heras & J. Muñoz-Pichardo, 2006. "A new condition for identifiability of finite mixture distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(2), pages 215-221, April.
    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.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Manisera, Marica & Zuccolotto, Paola, 2014. "Modeling rating data with Nonlinear CUB models," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 100-118.
    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. 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.
    5. 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.
    6. 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.
    7. 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.
    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.
    9. 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.
    10. 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.
    11. 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.
    12. Shaoting Li & Jiahua Chen, 2023. "Mixture of shifted binomial distributions for rating data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 833-853, October.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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).
    18. 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.
    19. 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.
    20. Stefania Capecchi & Maria Iannario & Domenico Piccolo, 2012. "Modelling Job Satisfaction in AlmaLaurea Surveys," Working Papers 56, AlmaLaurea Inter-University Consortium.

    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:eee:jmvana:v:140:y:2015:i:c:p:302-316. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.