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

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1554861649

Digital Object Identifier
doi:10.1214/18-AOAS1192

Mathematical Reviews number (MathSciNet)
MR3937429

Keywords
Cognitive modeling inverse Gaussian distribution Gaussian diffusion harmonic regression predictive diagnostics

Citation

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. https://projecteuclid.org/euclid.aoas/1554861649


Export citation

References

  • Baayen, R. H. and Milin, P. (2010). Analyzing reaction times. International Journal of Psychological Research 3 12–28.
  • Brown, S. D. and Heathcote, A. (2008). The simplest complete model of choice reaction time: Linear ballistic accumulation 57 153–178.
  • Caplin, A. and Martin, D. (2016). The dual-process drift diffusion model: Evidence from response times. Economic Inquiry 54 1274–1282.
  • Craigmile, P. F., Peruggia, M. and Van Zandt, T. (2010). Hierarchical Bayes models for response time data. Psychometrika 75 613–632.
  • Heitz, R. P. and Schall, J. D. (2012). Neural mechanisms of speed-accuracy tradeoff. Neuron 76 616–628.
  • Kim, S., Potter, K., Craigmile, P. F., Peruggia, M. and Van Zandt, T. (2017). A Bayesian race model for recognition memory. J. Amer. Statist. Assoc. 112 77–91.
  • Kunkel, D., Potter, K., Craigmile, P. F., Peruggia, M. and Van Zandt, T. (2019). Supplement to “A Bayesian race model for response times under cyclic stimulus discriminability.” DOI:10.1214/18-AOAS1192SUPP.
  • Logan, G. D., Van Zandt, T., Verbruggen, F. and Wagenmakers, E.-J. (2014). On the ability to inhibit thought and action: General and special theories of an act of control. Psychological Review 121 66–95.
  • Luce, R. D. (1986). Response Times: Their Role in Inferring Elementary Mental Organization. Oxford Univ. Press, Oxford, UK.
  • Nelson, M. J., Murthy, A. and Schall, J. D. (2016). Neural control of visual search by frontal eye field: Chronometry of neural events and race model processes. J. Neurophysiol. 115 1954–1969.
  • Ratcliff, R. (1993). Methods for dealing with reaction time outliers. Psychol. Bull. 114 510–532.
  • Ratcliff, R. and McKoon, G. (2007). The diffusion decision model: Theory and data for two-choice decision tasks. Neural Comput. 20 873–922.
  • Ratcliff, R., Smith, P. L. and McKoon, G. (2015). Modeling regularities in response time and accuracy data with the diffusion model. Curr. Dir. Psychol. Sci. 24 458–470.
  • Ruppert, D., Wand, M. P. and Carroll, R. J. (2003). Semiparametric Regression. Cambridge Series in Statistical and Probabilistic Mathematics 12. Cambridge Univ. Press, Cambridge.
  • Usher, M. and McClelland, J. L. (2001). The time course of perceptual choice: The leaky, competing accumulator model. Psychological Review 108 550–592.
  • Vandekerckhove, J. and Tuerlinckx, F. (2007). Fitting the Ratcliff diffusion model to experimental data. Psychon. Bull. Rev. 14 1011–1026.
  • Van Zandt, T., Colonius, H. and Proctor, R. W. (2000). A comparison of two response time models applied to perceptual matching. Psychon. Bull. Rev. 7 208–256.
  • Wagenmakers, E.-J., Farrell, S. and Ratcliff, R. (2004). Estimation and interpretation of $1/f^{\alpha}$ noise in human cognition. Psychon. Bull. Rev. 11 579–615.
  • Whelan, R. (2008). Effective analysis of reaction time data. Psychological Record 58 475–482.

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.