Asymptotic expansions for the ability estimator in item response theory

Computational Statistics - Tập 27 - Trang 661-683 - 2011
Haruhiko Ogasawara1
1Department of Information and Management Science, Otaru University of Commerce, Otaru, Japan

Tóm tắt

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.

Tài liệu tham khảo

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