Approximations of Normal IRT Models for Change
Approximations of Normal IRT Models for Change
复制标题
变化的正常 IRT 模型的近似值
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
T. Imbos
中科院分区：
文献类型：
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作者：
Elaine Tan;A. W. Ambergen;Ronald J. M. M. Does;T. Imbos
本文研究了纵向背景下具有正态项目特征曲线的单参数项目反应理论模型。这些能力是根据一般的混合效应线性回归模型构建的。这些项目应该是从一个大型项目库中抽取的样本，平均难度恒定。如果重复测量的数量是大的，那么常用的同时估计程序往往会导致实际问题的多维数值积分。在这篇文章中，一个近似的正常ICC的介绍，导致简单的能力和困难的估计与良好的渐近性质。研究了能力估计量的相对有效性和偏差。用真实的数据进行的说明表明，在ICC域的可接受范围内，具有较高的相对效率。此外，偏差非常小。模拟研究显示了非正态项参数对回归估计的影响。结果表明，所提出的程序是相当强大的偏离正态分布。然而，回归参数之间的相关性的估计可以严重偏差。
In this paper the one parameter Item Response Theory (IRT) model with normal Item Characteristic Curves (ICC) in longitudinal context has been studied. The abilities are structured according to a general mixed effects linear regression model. The items are supposed to be a sample from a large bank of items with constant mean difficulty. If the number of repeated measures is large, then commonly used simultaneous estimation procedures often lead to practical problems with respect to multidimensional numerical integrations. In this article, an approximation of the normal ICC is introduced that leads to simple ability and difficulty estimators with nice asymptotic properties. The relative efficiency and bias of the ability estimator are studied. An illustration with real data shows high relative efficiency within an acceptable range of the domain of the ICC. Moreover, the bias is very small. A simulation study shows the effect of non-normal item parameters on the regression estimates. The results suggest that the proposed procedure is rather robust against departures from normality. However, the estimation of the correlations between regression parameters can be seriously biased.