Liu Tianci, Wang Chun, Xu Gongjun
Department of Statistics, University of Michigan, Ann Arbor, MI, United States.
College of Education, University of Washington, Seattle, WA, United States.
Front Psychol. 2022 Aug 15;13:935419. doi: 10.3389/fpsyg.2022.935419. eCollection 2022.
Multidimensional Item Response Theory (MIRT) is widely used in educational and psychological assessment and evaluation. With the increasing size of modern assessment data, many existing estimation methods become computationally demanding and hence they are not scalable to big data, especially for the multidimensional three-parameter and four-parameter logistic models (i.e., M3PL and M4PL). To address this issue, we propose an importance-weighted sampling enhanced Variational Autoencoder (VAE) approach for the estimation of M3PL and M4PL. The key idea is to adopt a variational inference procedure in machine learning literature to approximate the intractable marginal likelihood, and further use importance-weighted samples to boost the trained VAE with a better log-likelihood approximation. Simulation studies are conducted to demonstrate the computational efficiency and scalability of the new algorithm in comparison to the popular alternative algorithms, i.e., Monte Carlo EM and Metropolis-Hastings Robbins-Monro methods. The good performance of the proposed method is also illustrated by a NAEP multistage testing data set.
多维项目反应理论（MIRT）在教育和心理评估与评价中被广泛应用。随着现代评估数据规模的不断增大，许多现有的估计方法在计算上要求很高，因此它们无法扩展到大数据，特别是对于多维三参数和四参数逻辑模型（即M3PL和M4PL）。为了解决这个问题，我们提出了一种重要性加权采样增强变分自编码器（VAE）方法来估计M3PL和M4PL。关键思想是采用机器学习文献中的变分推理过程来近似难以处理的边际似然，进而使用重要性加权样本以更好的对数似然近似来提升训练后的VAE。进行了模拟研究，以证明新算法与流行的替代算法（即蒙特卡罗期望最大化和Metropolis-Hastings Robbins-Monro方法）相比的计算效率和可扩展性。一个NAEP多阶段测试数据集也说明了所提出方法的良好性能。
