On testing proportional odds assumptions for proportional odds models

Abstract

Proportional odds models are commonly used to model ordinal responses, but the proportional odds assumption may not hold in practice, leading to biased inference. Tests such as score, Wald and likelihood ratio (LR) have been proposed to evaluate the proportional odds assumption based on models without the assumption. Brant has proposed an independent binary model-based Wald-type test, and Wolfe and Gould have extended the idea to propose an LR-type test. This paper provides a brief review of the Brant and Wolfe-Gould tests for evaluating the proportional odds assumption and evaluates their performance through simulation studies and a real data example. Sample programs are provided in SAS, SPSS and Stata to facilitate the implementation of these tests using standard statistical software packages. This study highlights the importance of evaluating the proportional odds assumption when using proportional odds models for ordinal responses. The sample programs provided in this paper make it easy for researchers to apply these tests in their own analyses using standard statistical software packages.