Optimal Ranking of Test Items using the Rasch Model

We study the problem of ranking test items, i.e., the ordering of items according to the amount of information they provide on the latent trait of the respondents. We focus on educational applications, where instructors are interested in ranking questions so as to select a small set of informative questions in order to efficiently assess the students' understanding on the course material. Using the Rasch model for modeling student responses, we prove that the simple algorithm of sorting the item level parameters of the Rasch model is optimal in the setting where the goal is to maximize the entropy of the student responses. We demonstrate the optimality of the sorting algorithm using both theoretical results and using empirical results on several real-world datasets. Furthermore, we also demonstrate how the sorting algorithm can be used in a batch adaptive manner for predicting unobserved student responses.