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ERIC Number: EJ1079889
Record Type: Journal
Publication Date: 2015-Oct
Pages: 18
Abstractor: As Provided
ISSN: ISSN-1076-9986
The Asymptotic Distribution of Ability Estimates: Beyond Dichotomous Items and Unidimensional IRT Models
Sinharay, Sandip
Journal of Educational and Behavioral Statistics, v40 n5 p511-528 Oct 2015
The maximum likelihood estimate (MLE) of the ability parameter of an item response theory model with known item parameters was proved to be asymptotically normally distributed under a set of regularity conditions for tests involving dichotomous items and a unidimensional ability parameter (Klauer, 1990; Lord, 1983). This article first considers the more general case of tests that include a mix of dichotomous and polytomous items. A proof is given of the asymptotic normality of the MLE of the ability parameter for such tests under a set of regularity conditions. Then, it is proved that a similar result holds for the weighted likelihood estimate and the posterior mode of the ability parameter. Multidimensional ability parameters are considered next. Numerical illustrations are provided to demonstrate the asymptotic results.
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Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A