Sparse probit factor analysis for learning analytics

We develop a new model and algorithm for machine learning-based learning analytics, which estimate a learner´s knowledge of the concepts underlying a domain. Our model represents the probability that a learner provides the correct response to a question in terms of three factors: their understanding of a set of underlying concepts, the concepts involved in each question, and each question´s intrinsic difficulty. We estimate these factors given the graded responses to a set of questions. We develop a bi-convex algorithm to solve the resulting SPARse Factor Analysis (SPARFA) problem. We also incorporate user-defined tags on questions to facilitate the interpretability of the estimated factors. Experiments with synthetic and real-world data demonstrate the efficacy of our approach.