Computer programs are routinely used to estimate Rasch measures. But is your program functioning correctly? Are the estimates based on the intended data? Are they based on the model you think you specified? A quick manual check of the computer's results can reassure you, or point you to a discrepancy.
Estimates for partial credit items, i.e., items specified to have unique rating scales, can be awkward to verify. Here is one approach. Imagine a sample of students who respond to both a dichotomous item and a polytomous "partial credit" items. We take the reported difficulty of the dichotomy, item i, as the benchmark difficulty. From this we estimate the difficulty of the dichotomy, Djk, between each pair of two adjacent categories, k-1 and k, of the partial credit item, j.
From their respective Rasch models,
So that
We can use this equivalence to estimate the difficulty of all the {Djk}. The mean item difficulty is
So that, within the item, the adjacent category dichotomies, Fjk, are located at
Here is an example from Items 12 and 14 of the "Liking for Science" data (Wright and Masters, 1982), specified as "partial credit".
Paired Frequencies for "Liking for Science" items 12 and 14. (Item 12 recoded 0,1) | |||||
N00 | N01 | N02 | N10 | N11 | N12 |
5 | 6 | 2 | 9 | 28 | 25 |
According to an analysis, the difficulty of the dichotomous item i=12, is -1.14. So that for item j=14,
In this example, the reported estimates are -.71 and 1.30, somewhat more central than the values, - 1.55 and 1.50, given by our approximation.
Andrew Stephanou, Australian Council for Educational Research
Manual estimation of partil credit item difficulties. Stephanou A. 16:1 p.867
Manual estimation of partil credit item difficulties. Stephanou A. Rasch Measurement Transactions, 2002, 16:1 p.867
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