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l_z Person-Fit Index to Identify Misfit Students With Achievement Test Data

机译：l_z人员适应指数，用于通过成绩测试数据识别不合适的学生

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摘要

The usefulness of the l_z person-fit index was investigated with achievement test data from 20 exams given to more than 3,200 college students. Results for three methods of estimating θ showed that the distributions of l_z were not consistent with its theoretical distribution, resulting in general overfit to the item response theory model and underidentification of potentially nonfitting response vectors. The distributions of l_z were not improved for the Bayesian estimation method. A follow-up Monte Carlo simulation study using item parameters estimated from real data resulted in mean l_z approximating the theoretical value of 0.0 for one of three θ estimation methods, but all standard deviations were substantially below the theoretical value of 1.0. Use of the l_z distributions from these simulations resulted in levels of identification of significant misfit consistent with the nominal error rates. The reasons for the nonstandardized distributions of l_z observed in both these data sets were investigated in additional Monte Carlo simulations. Previous studies showed that the distribution of item difficulties was primarily responsible for the nonstandardized distributions, with smaller effects for item discrimination and guessing. It is recommended that with real tests, identification of significantly nonfitting examinees be based on empirical distributions of l_z generated from Monte Carlo simulations using item parameters estimated from real data.
机译：l_z人格指数的有用性是通过对20 200项考试进行的成就测试数据进行的，调查对象是3200多名大学生。三种估计θ的方法的结果表明，l_z的分布与其理论分布不一致，从而导致对项目响应理论模型的总体过度拟合以及对潜在不合适的响应向量的识别不足。对于贝叶斯估计方法，l_z的分布没有改善。使用从真实数据中估计的项目参数进行的后续蒙特卡洛模拟研究，得出三种θ估计方法之一的均值l_z近似于理论值0.0，但所有标准偏差均大大低于理论值1.0。从这些模拟中使用lzz分布，可以确定与额定误差率一致的重大失配水平。在另外的蒙特卡洛模拟中研究了在这两个数据集中观察到的l_z非标准化分布的原因。以前的研究表明，项目难度的分布主要是造成非标准化分布的原因，而对项目区分和猜测的影响较小。建议在实际测试中，使用从真实数据中估算出的项目参数，根据蒙特卡罗模拟生成的l_z的经验分布，对明显不合格的考生进行识别。

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