da Silva Marcelo A, Liu Ren, Huggins-Manley Anne C, Bazán Jorge L
University of São Paulo, São Paulo, Brazil.
Federal University of São Carlos, São Carlos, Brazil.
Educ Psychol Meas. 2019 Aug;79(4):665-687. doi: 10.1177/0013164418814898. Epub 2018 Nov 30.
Multidimensional item response theory (MIRT) models use data from individual item responses to estimate multiple latent traits of interest, making them useful in educational and psychological measurement, among other areas. When MIRT models are applied in practice, it is not uncommon to see that some items are designed to measure all latent traits while other items may only measure one or two traits. In order to facilitate a clear expression of which items measure which traits and formulate such relationships as a math function in MIRT models, we applied the concept of the Q-matrix commonly used in diagnostic classification models to MIRT models. In this study, we introduced how to incorporate a Q-matrix into an existing MIRT model, and demonstrated benefits of the proposed hybrid model through two simulation studies and an applied study. In addition, we showed the relative ease in modeling educational and psychological data through a Bayesian approach via the NUTS algorithm.
多维项目反应理论（MIRT）模型利用个体项目反应的数据来估计多个感兴趣的潜在特质，这使得它们在教育和心理测量等领域很有用。当MIRT模型在实践中应用时，经常会看到一些项目被设计用来测量所有潜在特质，而其他项目可能只测量一两个特质。为了便于清晰表达哪些项目测量哪些特质，并将这种关系在MIRT模型中表述为数学函数，我们将诊断分类模型中常用的Q矩阵概念应用于MIRT模型。在本研究中，我们介绍了如何将Q矩阵纳入现有的MIRT模型，并通过两项模拟研究和一项应用研究展示了所提出的混合模型的优势。此外，我们展示了通过NUTS算法采用贝叶斯方法对教育和心理数据进行建模相对容易。
