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Goodness-of-fit tests for discrete response models with covariates

Author

Listed:
  • Simos G. Meintanis

    (National and Kapodistrian University of Athens
    North-West University)

  • Joseph Ngatchou-Wandji

    (Université de Lorraine
    Université de Rennes)

  • Leonard Santana

    (North-West University)

  • Marius Smuts

    (North-West University)

Abstract

We propose goodness-of-fit tests for models of count responses with covariates. Our main focus is on the null hypothesis that the observed data come from a Poisson, a negative binomial, or a binomial regression model, but the method is fairly general allowing for the responses to follow, conditionally on covariates, any given discrete distribution. The test criteria are formulated by using the probability generating function and they are convenient from a computational point of view. Asymptotic as well as Monte Carlo results are presented. Applications on real data are also reported.

Suggested Citation

  • Simos G. Meintanis & Joseph Ngatchou-Wandji & Leonard Santana & Marius Smuts, 2025. "Goodness-of-fit tests for discrete response models with covariates," Statistical Papers, Springer, vol. 66(3), pages 1-36, April.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:3:d:10.1007_s00362-024-01654-x
    DOI: 10.1007/s00362-024-01654-x
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    References listed on IDEAS

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    1. Dimitris Karlis, 2003. "An EM algorithm for multivariate Poisson distribution and related models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(1), pages 63-77.
    2. Zdeněk Hlávka & Marie Hušková & Claudia Kirch & Simos G. Meintanis, 2017. "Fourier--type tests involving martingale difference processes," Econometric Reviews, Taylor & Francis Journals, vol. 36(4), pages 468-492, April.
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    4. Giacomini, Raffaella & Politis, Dimitris N. & White, Halbert, 2013. "A Warp-Speed Method For Conducting Monte Carlo Experiments Involving Bootstrap Estimators," Econometric Theory, Cambridge University Press, vol. 29(3), pages 567-589, June.
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    6. Nikola Surjanovic & Richard A. Lockhart & Thomas M. Loughin, 2024. "A generalized Hosmer–Lemeshow goodness-of-fit test for a family of generalized linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(2), pages 589-608, June.
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