The Annals of Applied Statistics

A Bayesian race model for response times under cyclic stimulus discriminability

Deborah Kunkel, Kevin Potter, Peter F. Craigmile, Mario Peruggia, and Trisha Van Zandt

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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.

Article information

Ann. Appl. Stat., Volume 13, Number 1 (2019), 271-296.

Received: September 2017
Revised: April 2018
First available in Project Euclid: 10 April 2019

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Cognitive modeling inverse Gaussian distribution Gaussian diffusion harmonic regression predictive diagnostics


Kunkel, Deborah; Potter, Kevin; Craigmile, Peter F.; Peruggia, Mario; Van Zandt, Trisha. A Bayesian race model for response times under cyclic stimulus discriminability. Ann. Appl. Stat. 13 (2019), no. 1, 271--296. doi:10.1214/18-AOAS1192.

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Supplemental materials

  • Supplement A. This supplement provides additional detail on the experimental procedure, displays the RT sequences for all students, and reports the results of the analysis for all students. This supplement also includes a demonstration of the ability of our estimation procedure to recover the parameter values used to generate simulated data for a prototypical experimental participant, a comparison of the performance of our theoretically-motivated modeling framework with that of a descriptive generalized additive model, and an evaluation of the predictive performance of our approach.