ABSTRACT
Editor Introduction: This chapter elaborates the development of the most general polytomous IRT model covered in this book. It is the only model in this book that does not assume ordered polytomous response data and can therefore be used to measure traits and abilities with items that have unordered response categories. It can be used to identify the empirical ordering of response categories where that ordering is unknown a priori but of interest, or it can be used to check whether the expected ordering of response categories is supported in data. The authors present a new parameterization of this model that may serve to expand the model and to facilitate a more widespread use of the model. Also discussed are various derivations of the model and its relationship to other models. The chapter concludes with a special section by Bock, where he elaborates on the background of the nominal model.
