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The Asymptotic Posterior Normality of the Latent Trait for Polytomous IRT Models

Published online by Cambridge University Press:  01 January 2025

Hua-Hua Chang
Hua-Hua Chang*
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Hua-Hua Chang, Educational Testing Service, Rosedale Road, Princeton, NJ 08541.
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Abstract

Chang and Stout (1993) presented a derivation of the asymptotic posterior normality of the latent trait given examinee responses under nonrestrictive nonparametric assumptions for dichotomous IRT models. This paper presents an extention of their results to polytomous IRT models in a fairly straightforward manner. In addition, a global information function is defined, and the relationship between the global information function and the currently used information functions is discussed. An information index that combines both the global and local information is proposed for adaptive testing applications.

Keywords

consistencyefficiencyitem response theorypolytomous itemFisher informationKullback-Leibler informationordered categoriesitem category response function
Type
Original Paper
Information
Psychometrika , Volume 61 , Issue 3 , September 1996 , pp. 445 - 463
Copyright
Copyright © 1996 The Psychometric Society

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Footnotes

This research was partially supported by Educational Testing Service Allocation Project No. 79424. The author wishes to thank Charles Davis, Xuming He, Frank Jenkins, Spence Swinton, William Stout, Ming-Mai Wang, and Zhiliang Ying for their helpful comments and discussions. The author particularly wishes to thank the Editor, Shizuhiko Nishisato, the Associate Editor, and three anonymous reviewers for their thoroughness and thoughtful suggestions.

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