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On the finiteness and uniqueness of the weighted likelihood estimator of ability in polytomous IRT models
Magis, David; Verhelst, Norman
2014RCEC workshop on Item Response Theory and Educational Measurement
 

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Keywords :
Item response theory; polytomous models; weighted likelihood estimation; finiteness; uniqueness
Abstract :
[en] In item response theory (IRT), the weighted likelihood (WL) estimator has become a central method to estimate ability levels of respondents. Primarily introduced with dichotomous IRT models (Warm, 1989), it was later extended to polytomous IRT models (Samejima, 1998). However, very few information is available about the behavior of the WL estimator, and especially about the uniqueness of the ability estimates as well as their finiteness. The purpose of this talk is to establish that with polytomous item response models, the WL estimator of ability always returns finite values. This result is valid for the class of difference models and divide-by-total models, independently of the number of items and the response patterns. However, such estimates may not necessarily be unique, as the WL solving equation may provide several optimal values. Some examples are considered to illustrate both findings.
Disciplines :
Education & instruction
Author, co-author :
Magis, David ;  Université de Liège - ULiège > Département Education et formation > Psychométrie et édumétrie
Verhelst, Norman
Language :
English
Title :
On the finiteness and uniqueness of the weighted likelihood estimator of ability in polytomous IRT models
Publication date :
21 November 2014
Event name :
RCEC workshop on Item Response Theory and Educational Measurement
Event organizer :
Research Center for Examinations and Certification
Event place :
Twente, Netherlands
Event date :
19-21 novembre 2014
Audience :
International
Available on ORBi :
since 21 October 2014

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