Graphical diagnostics to check model misspecification for the proportional odds regression model.
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.
Liu
Ivy
I
School of Mathematics, Statistics, and Computer Science, Victoria University of Wellington, Wellington, New Zealand. i-ming.liu@mcs.vuw.ac.nz
Mukherjee
Bhramar
B
Suesse
Thomas
T
Sparrow
David
D
Park
Sung Kyun
SK
D000368:Aged; D000369:Aged, 80 and over; D000375:Aging; D001786:Blood Glucose / Q000032:analysis; D003955:Diagnostic Tests, Routine / Q000706:statistics & numerical data*; D006801:Humans; D008137:Longitudinal Studies; D008297:Male; D008875:Middle Aged; D016011:Normal Distribution; D016016:Proportional Hazards Models; D014481:United States; D014493:United States Department of Veterans Affairs
D001786:Blood Glucose