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.

翻译：调查工具与评估在社会科学的诸多领域中被广泛使用。当这些评估试图测量的构念呈现多面性时，多维项目反应理论（MIRT）为项目分析、校准和评分提供了统一框架与便捷的统计工具。然而，MIRT模型的估计计算挑战制约了其广泛应用，因为当维度数量、样本量和测验长度较大时，现有方法大多难以在现实时间内提供结果。为此，近年来提出的变分估计方法（如高斯变分期望最大化算法，GVEM）通过提供快速准确的解决方案来应对这一估计挑战。但结果表明，在验证性模型估计过程中，变分估计方法可能会对区分度参数产生偏差。本文提出一种重要性加权版本的GVEM（即IW-GVEM），用于校正MIRT模型中的此类偏差。同时，我们采用自适应矩估计方法自动更新梯度下降的学习率。仿真实验表明，与GVEM相比，IW-GVEM能够在适度增加计算时间的情况下有效校正偏差。所提出的方法也可能为改进其他心理测量学模型的变分估计提供启示。