Supporting information may be found in the online version of this article.
A goodness-of-fit test for the proportional odds regression model†
Article first published online: 4 OCT 2012
Copyright © 2012 John Wiley & Sons, Ltd.
Statistics in Medicine
Volume 32, Issue 13, pages 2235–2249, 15 June 2013
How to Cite
Fagerland, M. W. and Hosmer, D. W. (2013), A goodness-of-fit test for the proportional odds regression model. Statist. Med., 32: 2235–2249. doi: 10.1002/sim.5645
- Issue published online: 8 MAY 2013
- Article first published online: 4 OCT 2012
- Manuscript Accepted: 11 SEP 2012
- Manuscript Received: 30 MAR 2012
- ordinal logistic regression;
- ordinal response;
- ordinal models;
- proportional odds;
- goodness of fit;
- Hosmer–Lemeshow test
We examine goodness-of-fit tests for the proportional odds logistic regression model—the most commonly used regression model for an ordinal response variable. We derive a test statistic based on the Hosmer–Lemeshow test for binary logistic regression. Using a simulation study, we investigate the distribution and power properties of this test and compare these with those of three other goodness-of-fit tests. The new test has lower power than the existing tests; however, it was able to detect a greater number of the different types of lack of fit considered in this study. Moreover, the test allows for the results to be summarized in a contingency table of observed and estimated frequencies, which is a useful supplementary tool to assess model fit. We illustrate the ability of the tests to detect lack of fit using a study of aftercare decisions for psychiatrically hospitalized adolescents. The test proposed in this paper is similar to a recently developed goodness-of-fit test for multinomial logistic regression. A unified approach for testing goodness of fit is now available for binary, multinomial, and ordinal logistic regression models. Copyright © 2012 John Wiley & Sons, Ltd.