University of Twente, Enschede, The Netherlands.
Br J Math Stat Psychol. 2010 Nov;63(Pt 3):603-26. doi: 10.1348/000711009X481360. Epub 2010 Jan 28.
Marginal maximum-likelihood procedures for parameter estimation and testing the fit of a hierarchical model for speed and accuracy on test items are presented. The model is a composition of two first-level models for dichotomous responses and response times along with multivariate normal models for their item and person parameters. It is shown how the item parameters can easily be estimated using Fisher's identity. To test the fit of the model, Lagrange multiplier tests of the assumptions of subpopulation invariance of the item parameters (i.e., no differential item functioning), the shape of the response functions, and three different types of conditional independence were derived. Simulation studies were used to show the feasibility of the estimation and testing procedures and to estimate the power and Type I error rate of the latter. In addition, the procedures were applied to an empirical data set from a computerized adaptive test of language comprehension.
Marginal maximum-likelihood procedures for parameter estimation and testing the fit of a hierarchical model for speed and accuracy on test items are presented. 提出了用于参数估计和检验测试项目速度和准确性的层次模型拟合的边缘最大似然程序。
The model is a composition of two first-level models for dichotomous responses and response times along with multivariate normal models for their item and person parameters. 该模型是二项反应和反应时间的两个一级模型以及它们的项目和人员参数的多元正态模型的组合。
It is shown how the item parameters can easily be estimated using Fisher's identity. 展示了如何使用费希尔恒等式轻松估计项目参数。
To test the fit of the model, Lagrange multiplier tests of the assumptions of subpopulation invariance of the item parameters (i.e., no differential item functioning), the shape of the response functions, and three different types of conditional independence were derived. 为了检验模型的拟合度，推导出了对项目参数（即无差异项目功能）、响应函数形状和三种不同类型的条件独立性的亚群不变性假设的拉格朗日乘数检验。
Simulation studies were used to show the feasibility of the estimation and testing procedures and to estimate the power and Type I error rate of the latter. 模拟研究用于展示估计和检验程序的可行性，并估计后者的功效和第一类错误率。
In addition, the procedures were applied to an empirical data set from a computerized adaptive test of language comprehension. 此外，这些程序还应用于语言理解计算机自适应测试的经验数据集。
