Fitting an item response theory model with random item effects across groups by a variational approximation method
Fitting an item response theory model with random item effects across groups by a variational approximation method
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通过变分近似法拟合具有跨组随机项目效应的项目响应理论模型
DOI：
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发表时间：
2013
影响因子：
4.8
通讯作者：
M. Jeon
中科院分区：
文献类型：
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作者：
F. Rijmen;M. Jeon
目的。在许多国家进行的国际教育评估的数据大多使用项目反应理论进行分析。认为所有物品在所有国家的表现都一样的假设往往是站不住脚的。可以通过假设项目参数是随机效应来考虑各国项目参数的可变性（De Jong等人，J. Consum. 34：260-278，2007; De Jong和Steenkamp in Psychometrika 75：3-32，2010）。然而，这样一个模型的复杂的潜在结构，在项目和人的水平上的潜在变量，使最大似然估计计算上具有挑战性。我们描述了一种变分估计技术，包括近似的似然函数的计算上听话的下限。
方法.使用了隐变量后验分布的平均场近似。针对离散随机效应的特定情况推导更新方程，并在最大化最大化算法中实施（Neal和欣顿，M. I. Jordan（Ed.）学习图形模型，Kluwer Academic，多尔德雷赫特，pp. 355-368，1998）。在模拟研究中研究了参数恢复。2006年国际阅读研究进展也采用了这种方法。
结果在模拟研究的所有条件下，模型参数恢复良好。在应用中，由于缺乏跨组的项目不变性，随机项目效应的方差估计值与传统测量值呈现高度正相关。
结论.平均场近似和变分方法在一般情况下提供了一个计算上易于处理的替代精确的最大似然估计。
AbstractPurpose. Data from international educational assessments conducted in many countries are mostly analyzed using item response theory. The assumption that all items behave the same in all countries is often not tenable. The variability of item parameters across countries can be taken into account by assuming that the item parameters are random effects (De Jong et al. in J. Consum. Res. 34:260–278, 2007; De Jong and Steenkamp in Psychometrika 75:3–32, 2010). However, the complex latent structure of such a model, with latent variables both at the item and the person level, renders maximum likelihood estimation computationally challenging. We describe a variational estimation technique that consists of approximating the likelihood function by a computationally tractable lower bound.
Methods. A mean field approximation to the posterior distribution of the latent variables was used. The update equations were derived for the specific case of discrete random effects and implemented in a Maximization Maximization algorithm (Neal and Hinton in M.I. Jordan (Ed.) Learning in Graphical Models, Kluwer Academic, Dordrecht, pp. 355–368, 1998). Parameter recovery was investigated in a simulation study. The method was also applied to the Progress in International Reading Study of 2006.
Results. The model parameters were recovered well under all conditions of the simulation study. In the application, the estimated variances of the random item effects showed a high positive correlation with traditional measures for the lack of item invariance across groups.
Conclusions. The mean field approximation and variational methods in general offer a computationally tractable alternative to exact maximum likelihood estimation.