Sequential detection of learning in cognitive diagnosis.

In order to look more closely at the many particular skills examinees utilize to answer items, cognitive diagnosis models have received much attention, and perhaps are preferable to item response models that ordinarily involve just one or a few broadly defined skills, when the objective is to hasten learning. If these fine-grained skills can be identified, a sharpened focus on learning and remediation can be achieved. The focus here is on how to detect when learning has taken place for a particular attribute and efficiently guide a student through a sequence of items to ultimately attain mastery of all attributes while administering as few items as possible. This can be seen as a problem in sequential change-point detection for which there is a long history and a well-developed literature. Though some ad hoc rules for determining learning may be used, such as stopping after M consecutive items have been successfully answered, more efficient methods that are optimal under various conditions are available. The CUSUM, Shiryaev-Roberts and Shiryaev procedures can dramatically reduce the time required to detect learning while maintaining rigorous Type I error control, and they are studied in this context through simulation. Future directions for modelling and detection of learning are discussed.