An efficient and accurate numerical approximation methodology useful for obtaining the observed information matrix and subsequent asymptotic covariance matrix when fitting models with the EM algorithm is presented. The numerical approximation approach is compared to existing algorithms intended for the same purpose, and the computational benefits and accuracy of this new approach are highlighted. Instructive and real‐world examples are included to demonstrate the methodology concretely, properties of the estimator are discussed in detail, and a Monte Carlo simulation study is included to investigate the behaviour of a multi‐parameter item response theory model using three competing finite‐difference algorithms.

中文翻译：

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观测信息矩阵与Oakes身份的数值近似。

提出了一种有效且准确的数值近似方法，可用于在使用EM算法拟合模型时获得观测信息矩阵和随后的渐近协方差矩阵。将数值逼近方法与旨在达到相同目的的现有算法进行了比较，并突出了此新方法的计算优势和准确性。包含指导性和实际示例，以具体说明该方法，详细讨论了估计量的属性，并包括了蒙特卡洛模拟研究，以使用三个竞争性有限差分法研究多参数项目响应理论模型的行为。算法。