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Graphical diagnostics to check model misspecification for the proportional odds regression model
Author(s) -
Liu Ivy,
Mukherjee Bhramar,
Suesse Thomas,
Sparrow David,
Park Sung Kyun
Publication year - 2009
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.3386
Subject(s) - covariate , ordinal regression , logistic regression , ordered logit , statistics , goodness of fit , logit , odds , ordinal data , econometrics , mathematics , regression analysis , computer science
The cumulative logit or the proportional odds regression model is commonly used to study covariate effects on ordinal responses. This paper provides some graphical and numerical methods for checking the adequacy of the proportional odds regression model. The methods focus on evaluating functional misspecification for specific covariate effects, but misspecification of the link function can also be dealt with under the same framework. For the logistic regression model with binary responses, Arbogast and Lin ( Statist. Med. 2005; 24 :229–247) developed similar graphical and numerical methods for assessing the adequacy of the model using the cumulative sums of residuals. The paper generalizes their methods to ordinal responses and illustrates them using an example from the VA Normative Aging Study. Simulation studies comparing the performance of the different diagnostic methods indicate that some of the graphical methods are more powerful in detecting model misspecification than the Hosmer–Lemeshow‐type goodness‐of‐fit statistics for the class of models studied. Copyright © 2008 John Wiley & Sons, Ltd.