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Asymptotic expansions for the ability estimator in item response theory

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Abstract

Asymptotic approximations to the distributions of the ability estimator and its transformations in item response theory are derived beyond the usual normal one when associated item parameters are given as in tailored testing. For the approximations, the asymptotic cumulants of the estimators up to the fourth order with the higher-order asymptotic variances are obtained under possible model misspecification. For testing and interval estimation of abilities, the asymptotic cumulants of the pivots studentized in four ways are derived. Numerical examples with simulations including those for confidence intervals for abilities are given using the three-parameter logistic model.

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Authors and Affiliations

  1. Department of Information and Management Science, Otaru University of Commerce, 3-5-21, Midori, Otaru, 047-8501, Japan

    Haruhiko Ogasawara

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  1. Haruhiko Ogasawara
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Correspondence to Haruhiko Ogasawara.

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This work was partially supported by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Culture, Sports, Science and Technology No.20500341.

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Ogasawara, H. Asymptotic expansions for the ability estimator in item response theory. Comput Stat 27, 661–683 (2012). https://doi.org/10.1007/s00180-011-0282-0

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