title: A goodness-of-fit test for the proportional odds regression model.
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.
authors.affiliation: Unit of Biostatistics and Epidemiology, Oslo University Hospital, Oslo, Norway. morten.fagerland@medisin.uio.no
authors.forename: Morten W
authors.initials: MW
authors.lastname: Fagerland
authors.forename: David W
authors.initials: DW
authors.lastname: Hosmer
mesh_terms: D000293:Adolescent; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D016015:Logistic Models; D008297:Male; D001523:Mental Disorders / Q000628:therapy; D016017:Odds Ratio