This study revisits the parameter estimation issues in multidimensional item response theory more thoroughly and investigates some computation details that have seldom been addressed previously when implementing the expectation-maximization (EM) algorithm for finite mixtures (EM–FM). Two research questions are: Should we rescale after each EM cycle or after the final EM cycle? How to adapt the supplemented EM algorithm to the EM–FM framework to estimate standard errors (SEs) of all unknown parameters? Analytic details of the methods are provided, and a comprehensive simulation study is conducted to provide supporting evidence. Results reveal that rescaling after each EM cycle accelerates convergence without affecting the calibration accuracy. Moreover, the SEs of all model parameters, including item parameters and population mixing proportions, recover well when the sample size is relatively large (e.g., 2000).

本研究更彻底地重新审视了多维项目响应理论中的参数估计问题，并研究了以前在为有限混合 (EM-FM) 实施期望最大化 (EM) 算法时很少涉及的一些计算细节。两个研究问题是：我们应该在每个 EM 周期之后还是在最后一个 EM 周期之后重新调整规模？如何使补充的 EM 算法适应 EM-FM 框架以估计所有未知参数的标准误差 (SE)？提供了方法的分析细节，并进行了全面的模拟研究以提供支持证据。结果表明，在每个 EM 周期后重新缩放会加速收敛，而不会影响校准精度。此外，所有模型参数的SEs，包括项目参数和人口混合比例，