Supporting information may be found in the online version of this article.
The trend odds model for ordinal data†
Article first published online: 6 DEC 2012
Copyright © 2012 John Wiley & Sons, Ltd.
Statistics in Medicine
Volume 32, Issue 13, pages 2250–2261, 15 June 2013
How to Cite
Capuano, A. W. and Dawson, J. D. (2013), The trend odds model for ordinal data. Statist. Med., 32: 2250–2261. doi: 10.1002/sim.5689
- Issue published online: 8 MAY 2013
- Article first published online: 6 DEC 2012
- Manuscript Accepted: 2 NOV 2012
- Manuscript Received: 5 OCT 2011
- non-proportional odds;
- constrained cumulative odds;
- latent distributions;
- logistic distribution
Ordinal data appear in a wide variety of scientific fields. These data are often analyzed using ordinal logistic regression models that assume proportional odds. When this assumption is not met, it may be possible to capture the lack of proportionality using a constrained structural relationship between the odds and the cut-points of the ordinal values. We consider a trend odds version of this constrained model, wherein the odds parameter increases or decreases in a monotonic manner across the cut-points. We demonstrate algebraically and graphically how this model is related to latent logistic, normal, and exponential distributions. In particular, we find that scale changes in these potential latent distributions are consistent with the trend odds assumption, with the logistic and exponential distributions having odds that increase in a linear or nearly linear fashion. We show how to fit this model using SAS Proc NLMIXED and perform simulations under proportional odds and trend odds processes. We find that the added complexity of the trend odds model gives improved power over the proportional odds model when there are moderate to severe departures from proportionality. A hypothetical data set is used to illustrate the interpretation of the trend odds model, and we apply this model to a swine influenza example wherein the proportional odds assumption appears to be violated. Copyright © 2012 John Wiley & Sons, Ltd.