A Rate Function Approach to Computerized Adaptive Testing for Cognitive Diagnosis

Computerized adaptive testing (CAT) is a sequential experiment design scheme that tailors the selection of experiments to each subject. Such a scheme measures subjects’ attributes (unknown parameters) more accurately than the regular prefixed design. In this paper, we consider CAT for diagnostic classification models, for which attribute estimation corresponds to a classification problem. After a review of existing methods, we propose an alternative criterion based on the asymptotic decay rate of the misclassification probabilities. The new criterion is then developed into new CAT algorithms, which are shown to achieve the asymptotically optimal misclassification rate. Simulation studies are conducted to compare the new approach with existing methods, demonstrating its effectiveness, even for moderate length tests.