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On the Finiteness of the Weighted Likelihood Estimator of Ability
David Magis1, Norman Verhelst2
1Research Unit on Childhood, University of Liège, Building B32, Quartier Agora, Place des Orateurs 2, 4000 , Liege, Belgium. david.magis@ulg.ac.be.
Abstract:
The purpose of this note is to focus on the finiteness of the weighted likelihood estimator (WLE) of ability in the context of dichotomous and polytomous item response theory (IRT) models. It is established that the WLE always returns finite ability estimates. This general result is valid for dichotomous (one-, two-, three- and four-parameter logistic) IRT models, the class of polytomous difference models and divide-by-total models, independently of the number of items, the item parameters and the response patterns. Further implications of this result are outlined.
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