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Likelihood-based tests for a class of misspecified finite mixture models for ordinal categorical data

Author

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  • Roberto Colombi

    (University of Bergamo)

  • Sabrina Giordano

    (University of Calabria)

Abstract

The main purpose of this paper is to apply likelihood-based hypothesis testing procedures to a class of latent variable models for ordinal responses that allow for uncertain answers (Colombi et al. in Scand J Stat, 2018. https://doi.org/10.1111/sjos.12366). As these models are based on some assumptions, needed to describe different respondent behaviors, it is essential to discuss inferential issues without assuming that the tested model is correctly specified. By adapting the works of White (Econometrica 50(1):1–25, 1982) and Vuong (Econometrica 57(2):307–333, 1989), we are able to compare nested models under misspecification and then contrast the limiting distributions of Wald, Lagrange multiplier/score and likelihood ratio statistics with the classical asymptotic Chi-square to show the consequences of ignoring misspecification.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:4:d:10.1007_s11749-019-00626-w
    DOI: 10.1007/s11749-019-00626-w
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Colombi, Roberto, 2020. "Selection tests for possibly misspecified hierarchical multinomial marginal models," Econometrics and Statistics, Elsevier, vol. 16(C), pages 136-147.
    2. 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.
    3. Roberto Colombi & Sabrina Giordano & Gerhard Tutz, 2021. "A Rating Scale Mixture Model to Account for the Tendency to Middle and Extreme Categories," Journal of Educational and Behavioral Statistics, , vol. 46(6), pages 682-716, December.
    4. Roberto Colombi & Sabrina Giordano & Anna Gottard, 2019. "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 441-444, September.

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