Seeking the real item difficulty: bias-corrected item difficulty and some consequences in Rasch and IRT modeling
In: Behaviormetrika, Band 50, Heft 1, S. 121-154
Abstract
AbstractWhen the response pattern in a test item deviates from the deterministic pattern, the percentage of correct answers (p) is shown to be a biased estimator for the latent item difficulty (π). This is specifically true with the items of medium item difficulty. Four elements of impurities in p are formalized in the binary settings and four new estimators of π are proposed and studied. Algebraic reasons and a simulation suggest that, except the case of deterministic item discrimination, the real item difficulty is almost always more extreme than what p indicates. This characteristic of p to be biased toward a medium-leveled item difficulty has a strict consequence to item response theory (IRT) and Rasch modeling. Because the classical estimator of item difficulty p is a biased estimator of the latent difficulty level, the item parameters A and B and the person parameter θ within IRT modeling are, consequently, biased estimators of item discrimination and item difficulty as well as ability levels of the test takers.
Sprachen
Englisch
Verlag
Springer Science and Business Media LLC
ISSN: 1349-6964
DOI
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