A Race Model for Responses and Response Times in Tests

Latent trait models for responses and response times in tests are often pure statistical models without a close connection to features of the assumed response process. In the present paper, a new model is presented that is more closely related to assumptions about the response process. The model is based on two increasing stochastic processes. Each stochastic process represents the accumulation of knowledge with respect to one of two response options, the correct and incorrect response. Both accumulators compete and the accumulator that first exceeds a critical level determines the response. General assumptions about the accumulators result in a race between two response times that follow a bivariate Birnbaum Saunders distribution. The model can be calibrated with marginal maximum likelihood estimation. Feasibility of the estimation approach is demonstrated in a simulation study. Additionally, a test of model fit is proposed. Finally, the model will be used for the analysis of an empirical data set.