Xu Xin, Guo Jinxin, Xin Tao
College of Science, Minzu University of China, Beijing, China.
Collaborative Innovation Center of Assessment Toward Basic Education Quality, Beijing Normal University, Beijing, China.
Appl Psychol Meas. 2024 Dec 26:01466216241310598. doi: 10.1177/01466216241310598.
In psychological and educational measurement, a testlet-based test is a common and popular format, especially in some large-scale assessments. In modeling testlet effects, a standard bifactor model, as a common strategy, assumes different testlet effects and the main effect to be fully independently distributed. However, it is difficult to establish perfectly independent clusters as this assumption. To address this issue, correlations among testlets could be taken into account in fitting data. Moreover, one may desire to maintain a good practical interpretation of the sparse loading matrix. In this paper, we propose data-driven learning of significant correlations in the covariance matrix through a latent variable selection method. Under the proposed method, a regularization is performed on the weak correlations for the extended bifactor model. Further, a stochastic expectation maximization algorithm is employed for efficient computation. Results from simulation studies show the consistency of the proposed method in selecting significant correlations. Empirical data from the 2015 Program for International Student Assessment is analyzed using the proposed method as an example.
在心理和教育测量中，基于测验题组的测试是一种常见且流行的形式，尤其是在一些大规模评估中。在对测验题组效应进行建模时，作为一种常见策略，标准双因素模型假设不同的测验题组效应和主效应是完全独立分布的。然而，按照这个假设很难建立完全独立的聚类。为了解决这个问题，在拟合数据时可以考虑测验题组之间的相关性。此外，人们可能希望对稀疏载荷矩阵保持良好的实际解释。在本文中，我们提出通过一种潜在变量选择方法对协方差矩阵中的显著相关性进行数据驱动学习。在所提出的方法下，对扩展双因素模型的弱相关性进行正则化。此外，采用随机期望最大化算法进行高效计算。模拟研究结果表明了所提出方法在选择显著相关性方面的一致性。以2015年国际学生评估项目的实证数据为例，使用所提出的方法进行了分析。
