Partial Credit model

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 = theta - delta

 

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.

 

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Evaluating a PCM analysis

 

In Winsteps, most of this is in Table 3.2

 

1.Do the average measures increase with the categories?

2.Do the observations fit the categories?

3.Do the Andrich thresholds advance with the categories?
 
The alternative could be the Rating Scale Model, if so:

4.Are the item ICC/IRFs different enough to require the added burden on your audience to understand the PCM structures, and also the loss of generalization across current and future items?

5.Is the PCM person "test" reliability noticeably higher than the RSM reliability?