Asymptotic expansions for the ability estimator in item response theory
Asymptotic expansions for the ability estimator in item response theory
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DOI：
10.1007/s00180-011-0282-0
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发表时间：
2012-12
影响因子：
1.3
通讯作者：
H. Ogasawara
中科院分区：
文献类型：
--
作者：
H. Ogasawara
在项目反应理论中，当给定相关项目参数时，如在定制测验中，能力估计及其变换的分布的渐近近似被导出。对于这种近似，在可能的模型错误指定下，得到了具有高阶渐近方差的四阶估计量的渐近累积量。对于能力的测试和区间估计，推导了四种方法学习的枢轴的渐近累积量。利用三参数Logistic模型给出了模拟的数值算例，包括能力可信区间的数值算例。
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.