A goodness‐of‐fit test for the proportional odds regression model
- 4 October 2012
- journal article
- research article
- Published by Wiley in Statistics in Medicine
- Vol. 32 (13), 2235-2249
- https://doi.org/10.1002/sim.5645
Abstract
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.Keywords
This publication has 12 references indexed in Scilit:
- Applied Logistic RegressionWiley Series in Probability and Statistics, 2013
- Analysis of Ordinal Categorical DataWiley Series in Probability and Statistics, 2010
- Graphical diagnostics to check model misspecification for the proportional odds regression modelStatistics in Medicine, 2009
- Need or availability? Modeling aftercare decisions for psychiatrically hospitalized adolescentsChildren and Youth Services Review, 2008
- Assessing Ordinal Logistic Regression Models via Nonparametric SmoothingCommunications in Statistics - Theory and Methods, 2008
- Multinomial goodness‐of‐fit tests for logistic regression modelsStatistics in Medicine, 2008
- Goodness‐of‐fit tests for ordinal response regression modelsStatistics in Medicine, 2004
- Applied Logistic RegressionPublished by Wiley ,2000
- Goodness-of-Fit Tests for Ordinal Response Regression ModelsJournal of the Royal Statistical Society Series C: Applied Statistics, 1996
- Goodness of fit tests for the multiple logistic regression modelCommunications in Statistics - Theory and Methods, 1980