A comprehensive framework of regression models for ordinal data

Literature on the models for ordinal variables grew very fast in the last decades and several proposals have been advanced when ordered data are expression of ratings, preferences, judgments, opinions, etc. A dichotomy has been emphasized between methods based on a latent variable which is behind the ordered selection and methods anchored to a probability distribution with a well defined pattern. In this paper, a comprehensive framework to regression models is proposed in case ordinal data come out from a discrete choice. The added value of this unifying perspective is the possibility to introduce further generalizations and also to deepen similarities and differences among the proposed models. A case study confirms the usefulness of this general framework. Some concluding remarks end the paper.