The relationship between the Rating Scale and Partial Credit Models and the implication of disordered thresholds of the Rasch models for polytomous responses.

There is a perception in the literature that the Rating Scale Model (RSM) and Partial Credit Model (PCM) are two different types of Rasch models. This paper clarifies the relationship between the RSM and PCM from the perspectives of literature history and mathematical logic. It is shown that not only are the RSM and the PCM identical, but the two approaches used to introduce them are statistically equivalent. Then the implication of disordered thresholds is discussed. In addition, the difference between the structural thresholds and the Thurstone thresholds are clarified.