School of Psychology, Jiangxi Nomal University, Nanchang, China.
School of Computer and Information Engineering, Jiangxi Normal University, Nanchang, China.
Behav Res Methods. 2024 Oct;56(7):7647-7673. doi: 10.3758/s13428-024-02442-z. Epub 2024 Jul 26.
Cognitive diagnostic assessment (CDA) is widely used because it can provide refined diagnostic information. The Q-matrix is the basis of CDA, and can be specified by domain experts or by data-driven estimation methods based on observed response data. The data-driven Q-matrix estimation methods have become a research hotspot because of their objectivity, accuracy, and low calibration cost. However, most of the existing data-driven methods require known prior knowledge, such as initial Q-matrix, partial q-vector, or the number of attributes. Under the G-DINA model, we propose to estimate the number of attributes and Q-matrix elements simultaneously without any prior knowledge by the sparse non-negative matrix factorization (SNMF) method, which has the advantage of high scalability and universality. Simulation studies are carried out to investigate the performance of the SNMF. The results under a wide variety of simulation conditions indicate that the SNMF has good performance in the accuracy of attribute number and Q-matrix elements estimation. In addition, a set of real data is taken as an example to illustrate its application. Finally, we discuss the limitations of the current study and directions for future research.
认知诊断评估（CDA）被广泛应用，因为它可以提供更精细的诊断信息。Q 矩阵是 CDA 的基础，可以由领域专家指定，也可以通过基于观察到的反应数据的数据驱动估计方法指定。由于其客观性、准确性和低校准成本，数据驱动的 Q 矩阵估计方法已成为研究热点。然而，大多数现有的数据驱动方法需要先验知识，例如初始 Q 矩阵、部分 q-向量或属性数量。在 G-DINA 模型下，我们提出通过稀疏非负矩阵分解（SNMF）方法同时估计属性数量和 Q 矩阵元素，而无需任何先验知识，该方法具有可扩展性和通用性的优势。通过仿真研究来研究 SNMF 的性能。在广泛的仿真条件下的结果表明，SNMF 在属性数量和 Q 矩阵元素估计的准确性方面具有良好的性能。此外，还以一组真实数据为例说明了它的应用。最后，我们讨论了当前研究的局限性和未来研究的方向。
