2PL模型的EM缺失数据处理方法研究
Extension of EM Algorithm for Finite Mixture in IRT for Missing Response Data
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摘要: 项目反应理论(IRT)模型是教育统计与测量中一种十分重要的模型, 它包含项目参数和能力参数. 目前一种常用的估计IRT模型项目参数的方法是由Woodruff和Hanson\,(1997)应用EM算法给出的, 它用于完全反应数据, 而把能力参数看作缺失数据. 本文将Woodruff的方法推广到处理缺失反应的情况, 基本思想是把能力参数和缺失反应均看作缺失数据, 再运用EM算法估计参数. 通过模拟研究, 在不同被试人数和不同缺失比例的情况下, 本文比较了我们给出的方法和BILOG-MG软件的缺失数据处理方法的参数估计效果. 结果表明, 在大多数情况下, 本文提出的方法能得到更好的估计.Abstract: Item Response Theory (IRT) model is a dramatically important model in educational and psychological measurement. There are two kinds of parameters in the model --- item parameters and ability parameters. Nowadays, a commonly used method for estimating item parameters of IRT model is given by Woodruff and Hanson (1997). They treated the ability parameter \theta as missing and applied EM Algorithm for finite mixture to estimate item parameters under the condition that the examinees' responses are complete. Here, we extend the Woodruff's method to deal with incomplete response data. That is, we keep the incomplete response cases and regard missing response data as ``missing'' like \theta and then apply EM Algorithm. In our simulation study, we compare the relative performance of the missing data treatment method of us with that of the software BILOG-MG under different sample size and missing ratio. The simulation results show that our new method can obtain better estimation than BILOG-MG in most cases.