Asymptotic properties of the Bayes modal estimators of item parameters in item response theory.
Asymptotic properties of the Bayes modal estimators of item parameters in item response theory.
复制标题
项目响应理论中项目参数的贝叶斯模态估计量的渐近性质。
DOI：
10.1007/s00180-013-0418-5
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发表时间：
2013
影响因子：
1.3
通讯作者：
H.
中科院分区：
文献类型：
--
作者：
Ogasawara;H.
渐近累积量的贝叶斯模式估计的项目参数使用边际似然项目响应理论推导出四阶下可能的模型误指定的高阶渐近方差。其中，估计量的第一阶渐近累积量和高阶渐近方差与极大似然估计的结果不同。相应的结果，学生化贝叶斯估计和渐近偏差校正的。结果表明，该估计量的四阶渐近累积量和高阶渐近方差与最大似然估计量的四阶渐近累积量和高阶渐近方差完全相同。数值例子与模拟的情况下，两参数逻辑模型举行。在数值例子中，最大似然估计和贝叶斯估计被使用，其中相同的独立对数正态先验被用于判别参数和层次模型被采用的难度参数的先验。
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.