Data‐driven Q‐matrix learning based on Boolean matrix factorization in cognitive diagnostic assessment

• Published in: British journal of mathematical & statistical psychology Vol. 75; no. 3; pp. 638 - 667
• Main Authors: Xiong, Jianhua, Luo, Zhaosheng, Luo, Guanzhong, Yu, Xiaofeng
• Format: Journal Article
• Language: English
• Published: England British Psychological Society 01.11.2022
• Subjects: Algorithms; attribute mastery pattern; Boolean algebra; Boolean matrix factorization; cognitive diagnostic assessment; Diagnostic systems; DINA model; Factorization; Heuristic methods; Learning; Q‐matrix; Q-matrix; cognitive diagnostic assessment; attribute mastery pattern; Boolean matrix factorization; DINA model
• ISSN: 0007-1102; 2044-8317; 2044-8317
• DOI: 10.1111/bmsp.12271

Attributes and the Q‐matrix are the central components for cognitive diagnostic assessment, and are usually defined by domain experts. However, it is challenging and time consuming for experts to specify the attributes and Q‐matrix manually. Thus, there is an urgent need for an automatic and intelligent means to address this concern. This paper presents a new data‐driven approach for learning the Q‐matrix from response data. By constructing a statistical index and a heuristic algorithm based on Boolean matrix factorization, the response matrix is decomposed into the Boolean product of the Q‐matrix and the attribute mastery patterns. The feasibility of the proposed approach is evaluated using simulated data generated under various conditions. A real data example is also presented to demonstrate the usefulness of the proposed approach.