[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 . 
Your item 1 deltas advance by 0.16 logits, a surprisingly small advance. 
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.

Mike L.

At 10/18/2008, you wrote:
>Item 1
>delta1 = 1.38
>delta2 = 1.54
>Infit MNSQ = 1.40
>Item 1(i) -base item for Item 1
>delta = 1.38
>Infit MNSQ = 1.06
>Item 1(ii)
>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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