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June 2009 Nonlinear sequential designs for logistic item response theory models with applications to computerized adaptive tests
Hua-Hua Chang, Zhiliang Ying
Ann. Statist. 37(3): 1466-1488 (June 2009). DOI: 10.1214/08-AOS614

Abstract

Computerized adaptive testing is becoming increasingly popular due to advancement of modern computer technology. It differs from the conventional standardized testing in that the selection of test items is tailored to individual examinee’s ability level. Arising from this selection strategy is a nonlinear sequential design problem. We study, in this paper, the sequential design problem in the context of the logistic item response theory models. We show that the adaptive design obtained by maximizing the item information leads to a consistent and asymptotically normal ability estimator in the case of the Rasch model. Modifications to the maximum information approach are proposed for the two- and three-parameter logistic models. Similar asymptotic properties are established for the modified designs and the resulting estimator. Examples are also given in the case of the two-parameter logistic model to show that without such modifications, the maximum likelihood estimator of the ability parameter may not be consistent.

Citation

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Hua-Hua Chang. Zhiliang Ying. "Nonlinear sequential designs for logistic item response theory models with applications to computerized adaptive tests." Ann. Statist. 37 (3) 1466 - 1488, June 2009. https://doi.org/10.1214/08-AOS614

Information

Published: June 2009
First available in Project Euclid: 10 April 2009

zbMATH: 1160.62073
MathSciNet: MR2509080
Digital Object Identifier: 10.1214/08-AOS614

Subjects:
Primary: 62L05
Secondary: 62P15

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 3 • June 2009
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