Abstract: The Duolingo English Test is a computer adaptive test of English language proficiency. In this paper, a measurement model for the Duolingo English Test is proposed, and its formal characteristics are derived. A scalable real-time rating system, with favorable statistical properties, is proposed and applied to data from the Duolingo English Test to address issues related to differential model fit with respect to item and person characteristics. The results indicate that the signed residual time model fit the test data well, and that there is not evidence of statistical bias toward different groups of test takers.