Optimally Discriminative Choice Sets in Discrete Choice Models: Application to Data-Driven Test Design

Difficult test questions can be made easy by providing a set of possible answer options of which most are obviously wrong. In the education literature, a plethora of instructional guides exist for crafting a suitable set of wrong choices (distractors) in order to probe the students' understanding of the tested concept. The art of multiple-choice question design thus hinges on the question-maker's experience and knowledge of the potential misconceptions. In contrast, we advocate a data-driven approach, where correct and incorrect options are assembled directly from the students' own past submissions. Large-scale online classroom settings, such as massively open online courses (MOOCs), provide an opportunity to design optimal and adaptive multiple-choice questions that are maximally informative about the students' level of understanding of the material. We deploy a multinomial-logit discrete choice model for the setting of multiple choice testing, derive an optimization objective for selecting optimally discriminative option sets, and demonstrate the effectiveness of our approach via a user study.