Asymptotic cumulants of ability estimators using fallible item parameters.
Asymptotic cumulants of ability estimators using fallible item parameters.
复制标题
使用易错项目参数的能力估计器的渐近累积量。
DOI：
10.1016/j.jmva.2013.04.008
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发表时间：
2013
影响因子：
1.6
通讯作者：
H.
中科院分区：
文献类型：
--
作者：
Ogasawara;H.
在基于项目反应理论的能力测试中，给出了可错项目参数和估计项目参数的能力估计量的渐近累积量，其渐近累积量可达四阶，且具有高阶渐近方差。能力估计量包括最大似然估计、贝叶斯估计和伪贝叶斯模态估计。对于项目参数的估计，采用了边际极大似然和贝叶斯方法。给出了具有高阶渐近方差的渐近累积量在模型不规范和模型不规范的情况下，以及学生化前后的情况。提出了能力估计题数与试题参数校正题数相对大小的三个条件；其中两个给出了忽略估计项目参数抽样变化的一些理由。采用双参数逻辑模型进行了数值模拟。
The asymptotic cumulants of ability estimators using fallible or estimated item parameters in an ability test based on item response theory are given up to the fourth order with higher-order asymptotic variance. The ability estimators cover those obtained by maximum likelihood, Bayes, and pseudo Bayes modal estimation. For estimation of item parameters, the marginal maximum likelihood and Bayes methods are used. Asymptotic cumulants with higher-order asymptotic variance are given with and without model misspecification, and before and after studentization. Three conditions for the relative size of the number of items for ability estimation to that of examinees for item parameter calibration are presented; two of them give some justification for neglecting sampling variation of estimated item parameters. Numerical illustration with simulations is shown using the two-parameter logistic model.