"Suppose a dichotomous data set produced by 100 persons responding to 40 items fit the Rasch model, with no noticeably misfitting persons or items.
Is it possible that when only a subset of these items (say, 20 items) are analyzed, some misfitting persons or items will appear?"
Fukushima National College of Technology
Examine the fit statistics for your 40 items. Construct a subset
of the 19 items with the lowest mean-squares (say in the range 0.8
- 1.0) and the 1 item with the highest mean-square (say 1.2).
Reanalyze this subset. Fit is relative, so your 19 items now have
mean-squares 0.9-1.1 and your high mean-square item is reported at
1.3 or even 1.4. In the context of this new, better fitting
subset, you now have a misfitting item! This paradox is often
encountered by those who use arbitrary rules to drop misfitting
items. Dropping badly fitting items changes the fit context for
the remaining items, so that a new crop of badly fitting items
appears. Followed mechanically, fit-based exclusion rules can
result in every item being dropped!
Benjamin D. Wright
Subset fit.Wright B.D. Rasch Measurement Transactions, 1998, 12:2 p. 635.
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