Linear models of student skills for static data.
Michel C. Desmarais, Rhouma Naceur, Behzad Beheshti · PolyPublie (École Polytechnique de Montréal) · 2012
Abstract. Current student skills models rely on non linear models such as Bayesian Networks and Bayesian Knowledge Tracing, and on general linear models, such as IRT which can be considered a logistic regression. Only a handful of recent studies have looked at linear models based on matrix factorization techniques. These studies obtained good success over data from dynamic student knowledge states when compared with widely used techniques such as Bayesian Knowledge Tracing. However, there are no reports of linear models applied to static knowledge states data. We introduce different linear models of student skill for small, static student test data that does not contain missing values. We compare their predictive performance the traditional psychometric Item Response Theory approach, and the k-nearest-neighbours approach that is widely used in recommender systems. The results show that that the IRT model is far better than all others. These results are somewhat unexpected given the recent relative success of factorization models for dynamic student test data. They raise the question of whether there is still a large amount of potential performance gain from other non-linear models for dynamic data. 1