An exploratory Q-matrix estimation method based on sparse non-negative matrix factorization

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.