Student Modeling from Conventional Test Data: A Bayesian Approach without Priors

Abstract

Although conventional tests are often used for determining a student’s overall competence, they are seldom used for determining a fine-grained model. However, this problem does arise occasionally, such as when a conventional test is used to initialize the student model of an ITS. Existing psychometric techniques for solving this problem are intractable. Straight-forward Bayesian techniques are also inapplicable because they depend too strongly on the priors, which are often not available. Our solution is to base the assessment on the difference between the prior and posterior probabilities. If the test data raise the posterior probability of mastery of a piece of knowledge even slightly above its prior probability, then that is interpreted as evidence that the student has mastered that piece of knowledge. Evaluation of this technique with artificial students indicates that it can deliver highly accurate assessments.