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

Biometrics
Giovanni NattinoS Lemeshow

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 Hosm...Continue Reading

References

Jun 15, 2007·Critical Care Medicine·Andrew A Kramer, Jack E Zimmerman
Jul 27, 2012·Statistics in Medicine·Prabasaj PaulStanley Lemeshow
May 23, 2014·Medical Care·Patricia KipnisGabriel J Escobar
Oct 7, 2015·Statistics in Medicine·Giovanni NattinoGuido Bertolini
Apr 1, 1990·Multivariate Behavioral Research·J H Steiger

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Citations

Mar 10, 2021·Journal of Interpersonal Violence·Muluken Dessalegn MulunehVirginia Stulz
Jul 31, 2021·Anesthesiology·Steven J Staffa, David Zurakowski
Aug 17, 2021·Journal of American College Health : J of ACH·Dalia El KhouryMargo Mountjoy

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