Goodness‐of‐Fit Testing for the Logistic Regression Model when the Estimated Probabilities are Small
- 1 January 1988
- journal article
- research article
- Published by Wiley in Biometrical Journal
- Vol. 30 (8) , 911-924
- https://doi.org/10.1002/bimj.4710300805
Abstract
The distribution of the Hosmer‐Lemeshow chi‐square type goodness‐of‐fit tests (Čg, Ȟg) 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 Čg should be used when the two outcome groups (y = 0, 1) are not well separated, Δ≤2, where Δ2 is the Mahalanobis distance. Statistic Ȟg 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.Keywords
This publication has 7 references indexed in Scilit:
- Assessing the Fit of the Logistic Model: A Case Study of Children with the Haemolytic Uraemic SyndromeJournal of the Royal Statistical Society Series C: Applied Statistics, 1986
- Graphical Methods for Assessing Logistic Regression ModelsJournal of the American Statistical Association, 1984
- A REVIEW OF GOODNESS OF FIT STATISTICS FOR USE IN THE DEVELOPMENT OF LOGISTIC REGRESSION MODELS1American Journal of Epidemiology, 1982
- On a goodness of fit test for the logistic model based on score statisticsCommunications in Statistics - Theory and Methods, 1982
- Goodness of fit tests for the multiple logistic regression modelCommunications in Statistics - Theory and Methods, 1980
- How Many Classes in the Pearson Chi-Square Test?Journal of the American Statistical Association, 1973
- The Advanced Theory of StatisticsRevista Mexicana de Sociologia, 1961