Department of Statistics, University of Michigan, 456 West Hall, 1085 South University, Ann Arbor, MI, 48109, USA.
College of Education, University of Washington, 312E Miller Hall, 2012 Skagit Ln, Seattle, WA, 98105, USA.
Psychometrika. 2024 Mar;89(1):347-375. doi: 10.1007/s11336-022-09874-6. Epub 2022 Jul 13.
Item factor analysis (IFA), also known as Multidimensional Item Response Theory (MIRT), is a general framework for specifying the functional relationship between respondents' multiple latent traits and their responses to assessment items. The key element in MIRT is the relationship between the items and the latent traits, so-called item factor loading structure. The correct specification of this loading structure is crucial for accurate calibration of item parameters and recovery of individual latent traits. This paper proposes a regularized Gaussian Variational Expectation Maximization (GVEM) algorithm to efficiently infer item factor loading structure directly from data. The main idea is to impose an adaptive -type penalty to the variational lower bound of the likelihood to shrink certain loadings to 0. This new algorithm takes advantage of the computational efficiency of GVEM algorithm and is suitable for high-dimensional MIRT applications. Simulation studies show that the proposed method accurately recovers the loading structure and is computationally efficient. The new method is also illustrated using the National Education Longitudinal Study of 1988 (NELS:88) mathematics and science assessment data.
项目因子分析（IFA），也称为多维项目反应理论（MIRT），是一种用于指定受访者的多个潜在特征与其对评估项目的反应之间的功能关系的通用框架。MIRT 的关键要素是项目与潜在特征之间的关系，即所谓的项目因子负载结构。正确指定此加载结构对于准确校准项目参数和恢复个体潜在特征至关重要。本文提出了一种正则化高斯变分期望最大化（GVEM）算法，可直接从数据中有效推断项目因子负载结构。主要思想是对似然函数的变分下界施加自适应 - 范数惩罚，以使某些负载收缩到 0。这种新算法利用了 GVEM 算法的计算效率，适用于高维 MIRT 应用。模拟研究表明，所提出的方法可以准确地恢复加载结构，并且计算效率高。还使用 1988 年国家教育纵向研究（NELS：88）数学和科学评估数据说明了新方法。
