The "Partial Credit" Rasch model was devised for multiple-choice questions in which credit is given for almost-correct distractors. But there is no reason to believe that the almost-correctness of distractors to different questions is the same. Consequently, each item is modeled to have its own response structure.

 

This model was extended to any questionnaire using ordered polytomies in which the response structure is modeled to be unique to each item.

 

Winsteps estimates response structures by item groupings, using ISGROUPS=. From this perspective, the Andrich Rating Scale Model includes all items in one grouping. The Masters Partial Credit Model allocates each item to its own grouping.

 

The conventional representation of the Partial Credit model is

 

log ( Pnij / Pni(j-1) ) = Bn - Dij

 

Winsteps parameterizes Dij as Di + Fij where sum(Fij) = 0. And Di is the average (Dij).

 

log ( Pnij / Pni(j-1) ) = Bn - Di -Fij

 

Algebraically these two representations are identical.

 

Thus every item has a mean difficulty, Di. This simplifies communication, because the results of a Partial Credit analysis now have the same form as any other polytomous analysis supported by Winsteps.