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Goodness of fit for the logistic regression model using relative belief

Author

Listed:
  • Luai Al-Labadi

    (University of Toronto)

  • Zeynep Baskurt

    (Genetics and Genome Biology, Hospital for Sick Children)

  • Michael Evans

    (University of Toronto)

Abstract

A logistic regression model is a specialized model for product-binomial data. When a proper, noninformative prior is placed on the unrestricted model for the product-binomial model, the hypothesis H 0 of a logistic regression model holding can then be assessed by comparing the concentration of the posterior distribution about H 0 with the concentration of the prior about H 0. This comparison is effected via a relative belief ratio, a measure of the evidence that H 0 is true, together with a measure of the strength of the evidence that H 0 is either true or false. This gives an effective goodness of fit test for logistic regression.

Suggested Citation

  • Luai Al-Labadi & Zeynep Baskurt & Michael Evans, 2017. "Goodness of fit for the logistic regression model using relative belief," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-12, December.
    • Handle: RePEc:spr:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0070-7
    DOI: 10.1186/s40488-017-0070-7
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    References listed on IDEAS

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    1. Evans, Michael & Jang, Gun Ho, 2011. "A limit result for the prior predictive applied to checking for prior-data conflict," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1034-1038, August.
    2. A. Racine & A. P. Grieve & H. Flühler & A. F. M. Smith, 1986. "Bayesian Methods in Practice: Experiences in the Pharmaceutical Industry," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 35(2), pages 93-120, June.
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    Cited by:

    1. Luai Al-Labadi, 2021. "The two-sample problem via relative belief ratio," Computational Statistics, Springer, vol. 36(3), pages 1791-1808, September.
    2. Luai Al-Labadi & Forough Fazeli Asl & Zahra Saberi, 2022. "A Bayesian nonparametric multi-sample test in any dimension," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 217-242, June.

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