关于补充期望最大化算法应用于项目反应模型的计算说明
A Computational Note on the Application of the Supplemented EM Algorithm to Item Response Models
摘要：
期望最大化算法是一种在存在缺失数据的情况下求模型的最大似然估计的方法。不幸的是，EM不产生标准误的参数协方差阵。补充EM（SEM; Meng & Rubin，1991）是用于获得参数协方差阵的一种方法。SEM在开源（例如，Chalmers，2012; Pritikin，Hunter，& Boker，2015）和商业（例如，Cai，Thissen，& du Toit，2011）项目响应模型估计软件。然而，SEM的原始公式没有充分考虑IEEE 754浮点的限制。Agile-SEM是SEM的一种新改进，并在各种项目反应模型模拟研究中与原始算法和最近的改进（Tian，Cai，Thissen，& Xin，2013）进行了比较。通过在每个参数的基础上控制数值噪声强度，Agile-SEM表现出最佳的收敛特性，精度和效率，同时，需要更少的调整参数。完整的源代码是免费提供的。Agile-SEM的其他EM应用程序，除了项目反应模型的潜在推广是留给未来的工作。
英文摘要：
The EM algorithm is a method for finding the maximum likelihood estimate of a model in the presence of missing data. Unfortunately, EM does not produce a parameter covariance matrix for standard errors. Supplemented EM (SEM; Meng & Rubin, 1991) is one method for obtaining the parameter covariance matrix. SEM is implemented in both open-source (e.g., Chalmers, 2012; Pritikin, Hunter, & Boker, 2015) and commercial (e.g., Cai, Thissen, & du Toit, 2011) item response model estimation software. However, the original formulation of SEM did not adequately account for the limitations of IEEE 754 floating-point. Agile-SEM, a novel refinement of SEM, is proposed and compared against the original algorithm and a recent refinement (Tian, Cai, Thissen, & Xin, 2013) in a variety of item response model simulation studies. By controlling for the numerical noise intensity on a per-parameter basis, Agile-SEM demonstrated the best convergence properties, accuracy, and efficiency while, at the same time, requiring fewer tuning parameters. Complete source code is made freely available. The potential generalization of Agile-SEM to other EM application besides item response models is left as future work.
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