Subset Fit

"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?"

Tetushito Shizuka
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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Rasch Measurement Transactions (free, online)	Rasch Measurement research papers (free, online)	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Applying the Rasch Model 3rd. Ed., Bond & Fox	Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters	Introduction to Rasch Measurement, E. Smith & R. Smith	Introduction to Many-Facet Rasch Measurement, Thomas Eckes	Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr.	Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Journal of Applied Measurement	Rasch models for measurement, David Andrich	Constructing Measures, Mark Wilson	Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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