Disengage when returns diminish: Modeling solution behavior and disengagement in achievement items with a single-process model for responses and response times [Author Accepted Manuscript]

Valid assessments with achievement tests hinge on test-takers being motivated to take the test. Existing latent trait models attempt to disentangle competence and motivational influences, but have theoretical limitations. We propose a single-process accumulator model based on the idea that test-takers accumulate information to solve an item at a continuously decreasing rate. A correct response is generated once the information exceeds a solution threshold. The model incorporates disengagement which is governed by the solution process. Once the accumulation rate falls below a critical level, test-takers stop working on the item. Due to the computational intensity of an analytic solution, we compare maximum likelihood, neural network and Bayesian estimators that use a simulation-based likelihood in a simulation study. Using two empirical examples, the model demonstrates good fit to accuracy and response times of individual items and is able to capture various forms of dependencies between accuracy and response times, including non-linear dependencies.