A latent space accumulator model for response time: Applications to cognitive assessment data

Response time has attracted increased interest in educational and psychological assessment for, for example, measuring test takers' processing speed, improving the measurement accuracy of ability and understanding aberrant response behaviour. Most models for response time analysis are based on a parametric assumption about the response time distribution. The Cox proportional hazard model has been utilized for response time analysis for the advantages of not requiring a distributional assumption of response time and enabling meaningful interpretations with respect to response processes. In this paper, we present a new version of the proportional hazard model, called a latent space accumulator model, for cognitive assessment data based on accumulators for two competing response outcomes, such as correct versus incorrect responses. The proposed model extends a previous accumulator model by capturing dependencies between respondents and test items across accumulators in the form of distances in a two-dimensional Euclidean space. A fully Bayesian approach is developed to estimate the proposed model. The utilities of the proposed model are illustrated with two real data examples.