Ordinal regression: A review and a taxonomy of models

Ordinal models can be seen as being composed from simpler, in particular binary models. This view on ordinal models allows to derive a taxonomy of models that includes basic ordinal regression models, models with more complex parameterizations, the class of hierarchically structured models, and the more recently developed finite mixture models. The structured overview that is given covers existing models and shows how models can be extended to account for further effects of explanatory variables. Particular attention is given to the modeling of additional heterogeneity as, for example, dispersion effects. The modeling is embedded into the framework of response styles and the exact meaning of heterogeneity terms in ordinal models is investigated. It is shown that the meaning of terms is crucially determined by the type of model that is used. Moreover, it is demonstrated how models with a complex category-specific effect structure can be simplified to obtain simpler models that fit sufficiently well. The fitting of models is illustrated by use of a real data set, and a short overview of existing software is given. This article is categorized under: Statistical Models > Fitting Models Data: Types and Structure > Categorical Data Statistical Models > Generalized Linear Models