IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v108y2024i3d10.1007_s10182-024-00498-y.html
   My bibliography  Save this article

Testing distributional assumptions in CUB models for the analysis of rating data

Author

Listed:
  • Francesca Iorio

    (Università degli Studi di Napoli Federico II)

  • Riccardo Lucchetti

    (Università Politecnica delle Marche)

  • Rosaria Simone

    (Università degli Studi di Napoli Federico II)

Abstract

In this paper, we propose a portmanteau test for misspecification in combination of uniform and binomial (CUB) models for the analysis of ordered rating data. Specifically, the test we build belongs to the class of information matrix (IM) tests that are based on the information matrix equality. Monte Carlo evidence indicates that the test has excellent properties in finite samples in terms of actual size and power versus several alternatives. Differently from other tests of the IM family, finite-sample adjustments based on the bootstrap seem to be unnecessary. An empirical application is also provided to illustrate how the IM test can be used to supplement model validation and selection.

Suggested Citation

  • Francesca Iorio & Riccardo Lucchetti & Rosaria Simone, 2024. "Testing distributional assumptions in CUB models for the analysis of rating data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(3), pages 669-701, September.
    • Handle: RePEc:spr:alstar:v:108:y:2024:i:3:d:10.1007_s10182-024-00498-y
    DOI: 10.1007/s10182-024-00498-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-024-00498-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10182-024-00498-y?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. Lucchetti, Riccardo & Pigini, Claudia, 2014. "A simple and effective misspecification test for the double-hurdle model," Economics Letters, Elsevier, vol. 123(1), pages 75-78.
    2. Rosaria Simone, 2022. "On finite mixtures of Discretized Beta model for ordered responses," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 828-855, September.
    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. Orme, Chris, 1990. "The small-sample performance of the information-matrix test," Journal of Econometrics, Elsevier, vol. 46(3), pages 309-331, December.
    5. Jinchi Lv & Jun S. Liu, 2014. "Model selection principles in misspecified models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 141-167, January.
    6. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-1053, July.
    7. Stefania Capecchi & Rosaria Simone, 2019. "A Proposal for a Model-Based Composite Indicator: Experience on Perceived Discrimination in Europe," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 141(1), pages 95-110, January.
    8. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
    9. Chesher, Andrew, 1983. "The information matrix test : Simplified calculation via a score test interpretation," Economics Letters, Elsevier, vol. 13(1), pages 45-48.
    10. 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.
    11. Corduas, Marcella, 2022. "Gender differences in the perception of inflation," Journal of Economic Psychology, Elsevier, vol. 90(C).
    12. Ribecco, Nunziata & D'Uggento, Angela Maria & Labarile, Angela, 2022. "What influences the perception of immigration in Italian adolescents? An analysis with CUB models for rating data," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    13. 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.
    14. 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.
    15. Domenico Piccolo & Rosaria Simone & Maria Iannario, 2019. "Cumulative and CUB Models for Rating Data: A Comparative Analysis," International Statistical Review, International Statistical Institute, vol. 87(2), pages 207-236, August.
    16. Riccardo Lucchetti & Claudia Pigini, 2013. "A test for bivariate normality with applications in microeconometric models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 535-572, November.
    17. 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.
    18. Stefania Capecchi & Maurizio Curtarelli, 2020. "A mixture model to assess perception of discrimination on grounds of sexual orientation for policy considerations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(3), pages 554-567, February.
    19. Richard M. Golden & Steven S. Henley & Halbert White & T. Michael Kashner, 2016. "Generalized Information Matrix Tests for Detecting Model Misspecification," Econometrics, MDPI, vol. 4(4), pages 1-24, November.
    20. 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.
    21. Alan Agresti & Sabrina Giordano & Anna Gottard, 2022. "A Review of Score-Test-Based Inference for Categorical Data," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 31-48, September.
    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. repec:ebl:ecbull:v:3:y:2008:i:5:p:1-7 is not listed on IDEAS
    2. 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.
    3. Daisuke Nagakura, 2008. "A note on the relationship between the information matrx test and a score test for parameter constancy," Economics Bulletin, AccessEcon, vol. 3(5), pages 1-7.
    4. Riccardo Lucchetti & Claudia Pigini, 2013. "A test for bivariate normality with applications in microeconometric models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 535-572, November.
    5. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2024. "The information matrix test for Gaussian mixtures," Working Papers wp2024_2401, CEMFI.
    6. Stomberg, Christopher & White, Halbert, 2000. "Bootstrapping the Information Matrix Test," University of California at San Diego, Economics Working Paper Series qt158451cr, Department of Economics, UC San Diego.
    7. King, Maxwell L. & Zhang, Xibin & Akram, Muhammad, 2020. "Hypothesis testing based on a vector of statistics," Journal of Econometrics, Elsevier, vol. 219(2), pages 425-455.
    8. Dirk Hoorelbeke, 2004. "Bootstrap correcting the score test," Econometric Society 2004 North American Summer Meetings 228, Econometric Society.
    9. Dhaene, Geert & Hoorelbeke, Dirk, 2004. "The information matrix test with bootstrap-based covariance matrix estimation," Economics Letters, Elsevier, vol. 82(3), pages 341-347, March.
    10. Wanling Huang & Artem Prokhorov, 2014. "A Goodness-of-fit Test for Copulas," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 751-771, October.
    11. 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.
    12. Mai, Tien & Frejinger, Emma & Bastin, Fabian, 2015. "A misspecification test for logit based route choice models," Economics of Transportation, Elsevier, vol. 4(4), pages 215-226.
    13. Wasel Shadat, 2011. "On the Nonparametric Tests of Univariate GARCH Regression Models," Economics Discussion Paper Series 1115, Economics, The University of Manchester.
    14. Teresa Aparicio & Inmaculada Villanua, 2001. "The asymptotically efficient version of the information matrix test in binary choice models. A study of size and power," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(2), pages 167-182.
    15. Boldea, Otilia & Magnus, Jan R., 2009. "Maximum Likelihood Estimation of the Multivariate Normal Mixture Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1539-1549.
    16. 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.
    17. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
    18. Dante Amengual & Gariele Fiorentini & Enrique Sentan, 2024. "Information matrix tests for multinomial logit models," Working Papers wp2024_2406, CEMFI.
    19. Esmeralda A. Ramalho & Joaquim J.S. Ramalho & José M.R. Murteira, 2011. "Alternative Estimating And Testing Empirical Strategies For Fractional Regression Models," Journal of Economic Surveys, Wiley Blackwell, vol. 25(1), pages 19-68, February.
    20. 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.
    21. 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.

    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:alstar:v:108:y:2024:i:3:d:10.1007_s10182-024-00498-y. 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.