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Testing equivalence to binary generalized linear models with application to logistic regression

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  • Ostrovski, Vladimir

Abstract

We introduce a new equivalence test to show sufficiently good agreement of observed data with a binary generalized linear model (GLM). The test statistic is constructed via the minimum distance method. The test is developed for the important special case where all covariates are categorical. The critical values can be calculated using an asymptotic approximation or by means of bootstrapping. The application of the test to logistic regression is illustrated on two real data sets. The finite sample performance of the proposed test is studied by simulations which are based on these two data sets.

Suggested Citation

  • Ostrovski, Vladimir, 2022. "Testing equivalence to binary generalized linear models with application to logistic regression," Statistics & Probability Letters, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:stapro:v:191:y:2022:i:c:s0167715222001778
    DOI: 10.1016/j.spl.2022.109658
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    References listed on IDEAS

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    1. Hosmer, D.W. & Taber, S. & Lemeshow, S., 1991. "The importance of assessing the fit of logistic regression models: A case study," American Journal of Public Health, American Public Health Association, vol. 81(12), pages 1630-1635.
    2. Howard D. Bondell, 2005. "Minimum distance estimation for the logistic regression model," Biometrika, Biometrika Trust, vol. 92(3), pages 724-731, September.
    3. Ostrovski, Vladimir, 2018. "Testing equivalence to families of multinomial distributions with application to the independence model," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 61-66.
    4. Ostrovski, Vladimir, 2017. "Testing equivalence of multinomial distributions," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 77-82.
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