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On the Finiteness of the Weighted Likelihood Estimator of Ability

Published online by Cambridge University Press:  01 January 2025

David Magis  and
Norman Verhelst
David Magis*
Affiliation:
University of Liège
Norman Verhelst
Affiliation:
Eurometrics
*
Correspondence should be made to David Magis, Research Unit on Childhood, University of Liège, Building B32,Quartier Agora, Place des Orateurs 2, 4000 Liege, Belgium. Email: david.magis@ulg.ac.be
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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.

Keywords

item response theorydichotomous modelspolytomous modelsweighted likelihood estimationBayesian estimationfiniteness
Type
Original paper
Information
Psychometrika , Volume 82 , Issue 3 , September 2017 , pp. 637 - 647
Copyright
Copyright © 2016 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (doi:10.1007/s11336-016-9518-9) contains supplementary material, which is available to authorized users.

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