# [Rasch] Partial Credit Model vs Dichotomous Model

Mike Linacre (RMT) rmt at rasch.org
Wed Oct 22 17:57:51 EST 2008

```Thank you for your questions, Yoke Mooi.

Here is my assessment of your analysis ....

Transforming your data from dichotomies to partial-credit-scales has
re-arranged the randomness in the data.

So the first step is to discover whether the rearrangement has increased or
decreased the predictability of the data.

Please look at the standard deviation of your person measures. Is the
person S.D. larger for the dichotomous or larger for the PCM analysis? If
the person S.D. increases, then the PCM data are more predictable then the
dichotomous data, and vice-versa. You have noticed that there is dependence
between the pairs of dichotomous items. Dependence implies that the
dichotomous data are too predictable, so your intention in using the PCM
model is to reduce the predictability of the data, and so to reduce the
person measure S.D.

Look at your item difficulties. Item 1 has two dichotomies. If these two
dichotomous items are independent, we would predict that the partial credit
deltas would differ by at least 1.39 logits www.rasch.org/rmt/rmt201d.htm .
This suggests that the dichotomous items for Item 1 are highly dependent.
You are correct to combine them.

Mean-square fit statistics indicate relative (not absolute) fit. So, by
reducing the dependency in the data, you have changed the relative fit
pattern across the items. In your reduced data, the responses to the PCM
items are now more different, on average, than were the responses to the
dichotomous items, so that the pattern of relative misfit across the items
is also more diverse.

The fit statistics for the dichotomous items were misleading. Those fit
statistics were too good, because of the dependence in the data. Your PCM
fit statistics are more accurate.

Cordially,
Mike L.

At 10/18/2008, you wrote:
>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

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  22:1 Summer 2008
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