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Asymptotic properties of the Bayes modal estimators of item parameters in item response theory

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  • Haruhiko Ogasawara

Abstract

Asymptotic cumulants of the Bayes modal estimators of item parameters using marginal likelihood in item response theory are derived up to the fourth order with added higher-order asymptotic variances under possible model misspecification. Among them, only the first asymptotic cumulant and the higher-order asymptotic variance for an estimator are different from those by maximum likelihood. Corresponding results for studentized Bayes estimators and asymptotically bias-corrected ones are also obtained. It was found that all the asymptotic cumulants of the bias-corrected Bayes estimator up to the fourth order and the higher-order asymptotic variance are identical to those by maximum likelihood with bias correction. Numerical illustrations are given with simulations in the case when the 2-parameter logistic model holds. In the numerical illustrations, the maximum likelihood and Bayes estimators are used, where the same independent log-normal priors are employed for discriminant parameters and the hierarchical model is adopted for the prior of difficulty parameters. Copyright Springer-Verlag Berlin Heidelberg 2013

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  • Haruhiko Ogasawara, 2013. "Asymptotic properties of the Bayes modal estimators of item parameters in item response theory," Computational Statistics, Springer, vol. 28(6), pages 2559-2583, December.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:6:p:2559-2583
    DOI: 10.1007/s00180-013-0418-5
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    9. Ogasawara, Haruhiko, 2014. "Supplement to the paper“Asymptotic properties of the Bayes modal estimators of item parameters in item response theory”," 商学討究 (Shogaku Tokyu), Otaru University of Commerce, vol. 65(1), pages 1-10.
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    1. Ogasawara, Haruhiko, 2013. "Asymptotic cumulants of ability estimators using fallible item parameters," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 144-162.

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