Conditional risk models for ordinal response data: Simultaneous logistic regression analysis and generalized score tests

A general class of conditional risk models is introduced for ordinal regression. Special cases include the cumulative logit models, continuation ratio models and adjacent category odds models. A simultaneous logistic regression (SLR) approach is introduced for fitting the models in a unified fashion. Inferences are obtained by adapting the theory of generalized estimating equations. SLR is fully efficient for the continuation ratio model and has high efficiency in other cases. The general approach applies to other link functions such as ordinal probit analysis as well. Rao-type generalized score tests are developed for model assessment within this framework. These tests are useful in testing for parallelism within the general class of models. Real data examples illustrate the unified modeling made possible by this approach.