Magis David, Verhelst Norman
Research Unit on Childhood, University of Liège, Building B32, Quartier Agora, Place des Orateurs 2, 4000 , Liege, Belgium.
Eurometrics, Tiel, The Netherlands.
Psychometrika. 2017 Sep;82(3):637-647. doi: 10.1007/s11336-016-9518-9. Epub 2016 Oct 3.
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.
本笔记的目的是在二分和多分项目反应理论（IRT）模型的背景下，聚焦于能力的加权似然估计量（WLE）的有限性。已证明WLE总是返回有限的能力估计值。这一普遍结果对于二分（一参数、二参数、三参数和四参数逻辑斯蒂）IRT模型、多分差异模型和总分相除模型均有效，且与项目数量、项目参数和反应模式无关。文中概述了这一结果的进一步影响。
