Many test-takers do not carefully answer every test question; instead they sometimes quickly answer without thoughtful consideration (rapid guessing, RG). Researchers have not modeled RG when assessing student learning withcognitive diagnostic models(CDMs) to personalize feedback on a set of fine-grained skills (or attributes). Therefore, this study proposes to enhance cognitive diagnosis by modeling RG via an advanced CDM with item response and response time. This study tests the parameter recovery of this new CDM with a series of simulations via Markov chain Monte Carlo methods in JAGS. Also, this study tests the degree to which the standard and proposed CDMs fit the student response data for the Programme for International Student Assessment (PISA) 2015 computer-based mathematics test. This new CDM outperformed the simpler CDM that ignored RG; the new CDM showed less bias and greater precision for both item and person estimates, and greater classification accuracy of test results. Meanwhile, the empirical study showed different levels of student RG across test items and confirmed the findings in the simulations.