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Assessing the goodness of fit of logistic regression models in large samples: a modification of the Hosmer-Lemeshow test

Nattino, Giovanni, Pennell, Michael L., Lemeshow, Stanley·2020·Biometrics

DOI 10.1111/biom.13249

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Abstract

Evaluating the goodness of fit of logistic regression models is crucial to ensure the accuracy of the estimated probabilities. Unfortunately, such evaluation is problematic in large samples. Because the power of traditional goodness of fit tests increases with the sample size, practically irrelevant discrepancies between estimated and true probabilities are increasingly likely to cause the rejection of the hypothesis of perfect fit in larger and larger samples. This phenomenon has been widely documented for popular goodness of fit tests, such as the Hosmer-Lemeshow test. To address this limitation, we propose a modification of the Hosmer-Lemeshow approach. By standardizing the noncentrality parameter that characterizes the alternative distribution of the Hosmer-Lemeshow statistic, we introduce a parameter that measures the goodness of fit of a model but does not depend on the sample size. We provide the methodology to estimate this parameter and construct confidence intervals for it. Finally, we propose a formal statistical test to rigorously assess whether the fit of a model, albeit not perfect, is acceptable for practical purposes. The proposed method is compared in a simulation study with a competing modification of the Hosmer-Lemeshow test, based on repeated subsampling. We provide a step-by-step illustration of our method using a model for postneonatal mortality developed in a large cohort of more than 300 000 observations.

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Authors: Nattino, G., Pennell, M. L., & Lemeshow, S.
Affiliations: The Ohio State University (US)
Corresponding author: Nattino, Giovanni
ORCID: Nattino, Giovanni
Pennell, Michael L.
Venue: Biometrics
Publisher: Oxford University Press (OUP)
Published: 2020-04-06
Volume: 76
Issue: 2
Pages: 549-560
ISSN: 0006-341X (ISSN-L)
1541-0420
DOI: 10.1111/biom.13249
OpenAlex: W3009925463
Cited by: 229
References: 27
Citations by year: 2026: 29 · 2025: 48 · 2024: 67 · 2023: 27 · 2022: 35 · 2021: 21 · 2020: 2
FWCI: 14.98
Type: journal article
Language: en
Open access: closed
Licence: onlinelibrary.wiley.com/termsAndConditions#vor (vor)
Locations: Biometrics (publishedVersion)
PubMed (publishedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
Keywords: goodness of fit, logistic regression, Hosmer-Lemeshow test, large samples, noncentrality parameter, confidence intervals, model fit assessment, postneonatal mortality
MeSH terms: Biometry, Computer Simulation, Female, Humans, Infant, Infant Mortality, Male, Monte Carlo Method, Ohio, Probability, Models, Statistical, Confidence Intervals, Chi-Square Distribution, Linear Models, Logistic Models, Sample Size

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Assessing the goodness of fit of logistic regression models in large samples: a modification of the Hosmer-Lemeshow test

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