Bayesian Student Models Based on Item to Item Knowledge Structures

Bayesian networks are commonly used in cognitive student modeling and assessment. They typically represent the item-concepts relationships, where items are observable responses to questions or exercises and concepts represent latent traits and skills. Bayesian networks can also represent concepts-concepts and concepts-misconceptions relationships. We explore their use for modeling item-item relationships, in accordance with the theory of knowledge spaces. We compare two Bayesian frameworks for that purpose, a standard Bayesian network approach and a more constrained framework that relies on a local independence assumption. Their performance is compared over their respective ability to predict item outcome and through simulations over two data sets. The simulation results show that both approaches can effectively perform accurate predictions, but the constrained approach shows higher predictive power than a Bayesian Network. We discuss the applications of item to item structure for cognitive modeling within different contexts.