Department of Statistics, University of Michigan, 456 West Hall, 1085 South University, Ann Arbor, MI, 48109, USA.
College of Education, University of Washington, 312 E Miller Hall, 2012 Skagit Lane, Seattle, WA, 98105, USA.
Psychometrika. 2024 Mar;89(1):172-204. doi: 10.1007/s11336-023-09939-0. Epub 2023 Nov 18.
Survey instruments and assessments are frequently used in many domains of social science. When the constructs that these assessments try to measure become multifaceted, multidimensional item response theory (MIRT) provides a unified framework and convenient statistical tool for item analysis, calibration, and scoring. However, the computational challenge of estimating MIRT models prohibits its wide use because many of the extant methods can hardly provide results in a realistic time frame when the number of dimensions, sample size, and test length are large. Instead, variational estimation methods, such as Gaussian variational expectation-maximization (GVEM) algorithm, have been recently proposed to solve the estimation challenge by providing a fast and accurate solution. However, results have shown that variational estimation methods may produce some bias on discrimination parameters during confirmatory model estimation, and this note proposes an importance-weighted version of GVEM (i.e., IW-GVEM) to correct for such bias under MIRT models. We also use the adaptive moment estimation method to update the learning rate for gradient descent automatically. Our simulations show that IW-GVEM can effectively correct bias with modest increase of computation time, compared with GVEM. The proposed method may also shed light on improving the variational estimation for other psychometrics models.
在社会科学的许多领域中，经常使用调查工具和评估。当这些评估试图测量的结构变得多方面和多维时，多维项目反应理论 (MIRT) 为项目分析、校准和评分提供了一个统一的框架和方便的统计工具。然而，由于许多现有的方法在维度数量、样本大小和测试长度较大时几乎无法在现实时间范围内提供结果，因此估计 MIRT 模型的计算挑战阻碍了其广泛使用。相反，最近提出了变分估计方法，例如高斯变分期望最大化 (GVEM) 算法，通过提供快速准确的解决方案来解决估计挑战。然而，结果表明，变分估计方法在验证模型估计时可能会对判别参数产生一些偏差，本注释提出了一种用于 MIRT 模型的 GVEM 的重要性加权版本（即 IW-GVEM）来纠正这种偏差。我们还使用自适应矩估计方法自动更新梯度下降的学习率。我们的模拟表明，与 GVEM 相比，IW-GVEM 可以有效地纠正偏差，同时适度增加计算时间。该方法还可能为改进其他心理计量模型的变分估计提供启示。
