A Bayesian race model for response times under cyclic stimulus discriminability

Response time (RT) data from psychology experiments are often used to validate theories of how the brain processes information and how long it takes a person to make a decision. When an RT results from a task involving two or more possible responses, the cognitive process that determines the RT may be modeled as the first-passage time of underlying competing (racing) processes with each process describing accumulation of information in favor of one of the responses. In one popular model the racers are assumed to be Gaussian diffusions. Their first-passage times are inverse Gaussian random variables and the resulting RT has a min-inverse Gaussian distribution. The RT data analyzed in this paper were collected in an experiment requiring people to perform a two-choice task in response to a regularly repeating sequence of stimuli. Starting from a min-inverse Gaussian likelihood for the RTs we build a Bayesian hierarchy for the rates and thresholds of the racing diffusions. The analysis allows us to characterize patterns in a person’s sequence of responses on the basis of features of the person’s diffusion rates (the “footprint” of the stimuli) and a person’s gradual changes in speed as trends in the diffusion thresholds. Last, we propose that a small fraction of RTs arise from distinct, noncognitive processes that are included as components of a mixture model. In the absence of sharp prior information, the inclusion of these mixture components is accomplished via a two-stage, empirical Bayes approach. The resulting framework may be generalized readily to RTs collected under a variety of experimental designs.