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Goodness‐of‐Fit Testing for the Logistic Regression Model when the Estimated Probabilities are Small
Author(s) -
Hosmer D. W.,
Lemeshow S.,
Klar J.
Publication year - 1988
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710300805
Subject(s) - goodness of fit , statistics , statistic , logistic regression , mathematics , mahalanobis distance , test statistic , chi square test , decile , press statistic , ancillary statistic , econometrics , statistical hypothesis testing
The distribution of the Hosmer‐Lemeshow chi‐square type goodness‐of‐fit tests ( Č g , Ȟ g ) for the logistic regression model are examined via simulations designed to examine their behavior when most of the estimated probabilities are small or are expected to fall in a few deciles. The results of the simulations show statistic Č g should be used when the two outcome groups ( y = 0, 1) are not well separated, Δ≤2, where Δ 2 is the Mahalanobis distance. Statistic Ȟ g should be used when Δ ≥ 8. Either statistic may be used when 2 ≦ Δ ≦ 8. All tests should be used with caution when the proportion in the sample with y = 1 is less than 0.1.