In this chapter, the discrete mixture distribution framework is developed for Rasch models for items with a polytomous ordered response format. Four of these models will be considered, based on different restrictions regarding the so-called threshold distances (Section 20.2). Since the concept of thresholds is basic for understanding this family of Rasch models, Section 20.1 elaborates the threshold concept in some detail. Section 20.3 focusses on parameter estimation, particularly describing some results on the computation of the γ-functions which correspond to the symmetric functions of the dichotomous Rasch model. Section 20.4 gives some references to applications of these models.
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