Derivation of the Threshold Form of the Polytomous Rasch Model

Ordered categories are taken as analogous to physical measurement with a continuum partitioned by successive thresholds. However, unlike physical measurements, the thresholds which form the categories are not assumed to be equidistant. Thresholds are defined by minimum proficiencies required to succeed at the thresholds. The threshold form of the polytomous Rasch model involves the hypothesis that the thresholds are ordered. Threshold estimates from data may be disordered, in which case they reflect a problem with the empirical ordering of the categories.