# [Rasch] Partial Credit Model vs Dichotomous Model

Yoke Mooi Ong ongyokemooi at gmail.com
Sat Oct 18 20:33:53 EST 2008

```Dear all,

Can we model sums of dichotomous responses by the Partial Credit Model?

I am working on a dataset, a mathematics test that consists of 100 items and
a sample size of 2892.
14 out of 100 items, partial credit is awarded for partial response. Two
marks are awarded for these 14 items.
In the dataset, these items are score as dichotomous items (2 items i.e.
(1i) and (1ii). ) These base items seems to violate the Rasch model
assumption of local independence.

So I sum the dichotomous scoring in the dataset (i.e 0 (0,0), 1(1,0),
2(1,1)) to form a polytomous score item).

I analysed with the Partial Credit model.

7 out of 14 items indicating misfit (i.e. Infit MNSQ > 1.30).

When I analysed with the dichotomous model, all the items fitted well within
the accepted range of fit statistics.

Here are 2 examples of the analysis:

Item 1
PCM
delta1 = 1.38
delta2 = 1.54
Infit MNSQ = 1.40

Item 1(i) -base item for Item 1
Dichotomous
delta = 1.38
Infit MNSQ = 1.06

Item 1(ii)
Dichotomous
delta = 1.65
Infit MNSQ = 1.01

Item 2
PCM
delta 1 = -0.69
delta2 = -0.08
Infit MNSQ = 1.40

Item 2(i)
Dichotomous
delta = -1.43
Infit MNSQ =0.99

Item 2(ii)
Dichotomous
delta = -0.43
Infit MNSQ = 1.16

>From the results of  the dichotomous and the PCM analyses, it seems to
indicate that the dataset fitted the dichotomous model better than PCM.

My questions:

(1) How can I explain this? Why?
(2) Is PCM an adequate model to describe the distribution of sums of
dichotomous item scores? If yes, to what extent? if no, why?

Thank you.

Regards,

Yoke Mooi
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