Q-matrix Extraction from Real Response Data Using Nonnegative Matrix Factorizations

In this paper we illustrate the use of Nonnegative Matrix Factorization (NMF) to analyze real data derived from an e-learning context. NMF is a matrix decomposition method which extracts latent information from data in such a way that it can be easily interpreted by humans. Particularly, the NMF of a score matrix can automatically generate the so called Q-matrix. In an e-learning scenario, the Q-matrix describes the abilities to be acquired by students to correctly answer evaluation exams. An example on real response data illustrates the effectiveness of this factorization method as a tool for EDM.