A goodness-of-fit test for the proportional odds regression model

Stat Med. 2013 Jun 15;32(13):2235-49. doi: 10.1002/sim.5645. Epub 2012 Oct 4.

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.

Publication types

  • Comparative Study

MeSH terms

  • Adolescent
  • Computer Simulation
  • Data Interpretation, Statistical*
  • Female
  • Humans
  • Logistic Models*
  • Male
  • Mental Disorders / therapy
  • Odds Ratio