Open Access
March 2013 Bayesian analysis of dynamic item response models in educational testing
Xiaojing Wang, James O. Berger, Donald S. Burdick
Ann. Appl. Stat. 7(1): 126-153 (March 2013). DOI: 10.1214/12-AOAS608


Item response theory (IRT) models have been widely used in educational measurement testing. When there are repeated observations available for individuals through time, a dynamic structure for the latent trait of ability needs to be incorporated into the model, to accommodate changes in ability. Other complications that often arise in such settings include a violation of the common assumption that test results are conditionally independent, given ability and item difficulty, and that test item difficulties may be partially specified, but subject to uncertainty. Focusing on time series dichotomous response data, a new class of state space models, called Dynamic Item Response (DIR) models, is proposed. The models can be applied either retrospectively to the full data or on-line, in cases where real-time prediction is needed. The models are studied through simulated examples and applied to a large collection of reading test data obtained from MetaMetrics, Inc.


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Xiaojing Wang. James O. Berger. Donald S. Burdick. "Bayesian analysis of dynamic item response models in educational testing." Ann. Appl. Stat. 7 (1) 126 - 153, March 2013.


Published: March 2013
First available in Project Euclid: 9 April 2013

zbMATH: 06171266
MathSciNet: MR3086413
Digital Object Identifier: 10.1214/12-AOAS608

Keywords: dynamic linear models , forward filtering and backward sampling , Gibbs sampling , IRT models , local dependence , random effects

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.7 • No. 1 • March 2013
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