title: On the Finiteness of the Weighted Likelihood Estimator of Ability.
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.
authors.affiliation: Research Unit on Childhood, University of Liège, Building B32, Quartier Agora, Place des Orateurs 2, 4000 , Liege, Belgium. david.magis@ulg.ac.be.
authors.forename: David
authors.initials: D
authors.lastname: Magis
authors.affiliation: Eurometrics, Tiel, The Netherlands.
authors.forename: Norman
authors.initials: N
authors.lastname: Verhelst
keywords: Bayesian estimation; dichotomous models; finiteness; item response theory; polytomous models; weighted likelihood estimation