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

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.