Tutz, Gerhard and Scholz, T.
Ordinal regression modelling between proportional odds and non-proportional odds.
Collaborative Research Center 386, Discussion Paper 304
The proportional odds model has become the most widely used model in ordinal regression. Despite favourable properties in applications it is often an inappropriate simplification yielding bad data fit. The more flexible non-proportional odds model or partial proportional odds model have the disadvantage that common estimation procedures as Fisher scoring often fail to converge. Then neither estimates nor test statistics for the validity of partial proportional odds models are available. In the present paper estimates are proposed which are based on penalization of parameters across response categories. For appropriate smoothing penalized estimates exist almost always and are used to derive test statistics for the assumption of partial proportional odds. In addition, models are considered where the variation of parameters across response categories is constrained. Instead of using prespecified scalars (Peterson&Harrell 1990) penalized estimates are used in the identification of these constrained models. The methods are illustrated by various applications. The application to the retinopathy status in chronic diabetes shows how the proposed test statistics may be used in the diagnosis of partial proportional odds models in order to prevent artefacts.