Modeling Response Times for Two-Choice Decisions
Abstract
The diffusion model for two-choice real-time decisions is applied to four psychophysical tasks. The model reveals how stimulus information guides decisions and shows how the information is processed through time to yield sometimes correct and sometimes incorrect decisions. Rapid two-choice decisions yield multiple empirical measures: response times for correct and error responses, the probabilities of correct and error responses, and a variety of interactions between accuracy and response time that depend on instructions and task difficulty. The diffusion model can explain all these aspects of the data for the four experiments we present. The model correctly accounts for error response times, something previous models have failed to do. Variability within the decision process explains how errors are made, and variability across trials correctly predicts when errors are faster than correct responses and when they are slower.
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The discharge on any one trial resembles a random walk to a threshold representing the level of evidence required to reach a decision, at which point the decision process terminates.
“the discharge on any one trial resembles a random walk to a threshold representing the level of evidence required to reach a decision, at which point the decision process terminates”
From Response of Neurons in the Lateral Intraparietal Area during a Combined Visual Discrimination Reaction Time Task (2002) · cites this paper as Ratcliff and Rouder, 1998
Psychophysical and neural data support a model termed drift diffusion, random walk or race in which a decision is made when the accumulated noisy evidence reaches a criterion level, termed a decision bound.
“Psychophysical and neural data1 support a model termed drift diffusion6, random walk5,7 or race8 in which a decision is made when the accumulated noisy evidence (decision variable) reaches a criterion level, termed a decision bound.”
From Changes of mind in decision-making (2009) · cites this paper as [6]
Several formalisms propose that a representation of noisy evidence is evaluated against a criterion to produce a decision.
“Several formalisms propose that a representation of noisy evidence is evaluated against a criterion to produce a decision4-8.”
From Changes of mind in decision-making (2009) · cites this paper as [6]
Sequential sampling with optional stopping models explains the tradeoff between speed and accuracy in decisions.
“The ensuing tradeoff between speed and accuracy is explained by sequential sampling with optional stopping models in which evidence is accumulated to some stopping criterion or bound (Link, 1975; Ratcliff and Rouder, 1998).”
From A common mechanism underlies changes of mind about decisions and confidence (2016) · cites this paper as Ratcliff and Rouder, 1998
The class of bounded sequential sampling models explains the tradeoff between speed and accuracy, and many of the essential steps have correlates in neurophysiology.
“The class of bounded sequential sampling models, including many variants (Wald, 1947; Stone, 1960; Laming, 1968; Link, 1975; Good, 1979; Luce, 1986; Ratcliff and Rouder, 1998) explains the tradeoff between speed and accuracy, and many of the essential steps have correlates in neurophysiology (Romo et al., 2002; Heekeren et al., 2004; Ploran et al., 2007; Heitz and Schall, 2012; White et al., 2012;”
From A common mechanism underlies changes of mind about decisions and confidence (2016) · cites this paper as Ratcliff and Rouder, 1998
Many models proposed to explain the coordination of reaction time and choice accuracy in 2-choice tasks share a common feature: a termination bound is applied to some form of evidence representation, the decision variable.
“Many models are proposed to explain the coordination of RT and choice accuracy in 2-choice tasks 4,18,25–27. These models share a common feature: a termination bound is applied to some form of evidence representation, the decision variable.”
From Decision-making with multiple alternatives (2008) · cites this paper as [25]
A simple diffusion model provides a plausible account for the stimulation effects in both areas.
“A simple diffusion model provides a plausible account for the stimulation effects in both areas (Fig. 5).”
From Microstimulation of macaque area LIP affects decision-making in a motion discrimination task (2006) · cites this paper as [17]
Human studies commonly report skewed RT distributions with a long right tail, which is well captured by the diffusion model but not the existing neural circuit model.
“On the other hand, human studies commonly report skewed RT distributions with a long right tail, which is well captured by the diffusion model (Ratcliff, 1978; Luce, 1986; Ratcliff and Rouder, 1998; Usher and McClelland, 2001; Sigman and Dehaene, 2005) but not the existing neural circuit model.”
From Decision Making in Recurrent Neuronal Circuits (2008) · cites this paper as Ratcliff and Rouder, 1998
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Nicenboim, B., & Vasishth, S. (2016) · Language and Linguistics Compass · doi:10.1111/lnc3.12207 · Cited by 267 · see citing works
Klinkenberg, S., Straatemeier, M., & van der Maas, H. L. J. (2011) · Computers & Education · doi:10.1016/j.compedu.2011.02.003 · Cited by 261 · see citing works
Good things peak in pairs: a note on the bimodality coefficient
Pfister, R., Schwarz, K. A., Janczyk, M., Dale, R. A. C., & Freeman, J. B. (2013) · Frontiers in Psychology · doi:10.3389/fpsyg.2013.00700 · Cited by 258 · see citing works
The Speed-Accuracy Tradeoff in the Elderly Brain: A Structural Model-Based Approach
Forstmann, B. U., Tittgemeyer, M., Wagenmakers, E., Derrfuß, J., Imperati, D., & Brown, S. D. (2011) · Journal of Neuroscience · doi:10.1523/jneurosci.0309-11.2011 · Cited by 252 · see citing works
Cognitive and sensory declines in old age: Gauging the evidence for a common cause.
Lindenberger, U., & Ghisletta, P. (2009) · Psychology and Aging · doi:10.1037/a0014986 · Cited by 251 · see citing works
Modeling confidence and response time in recognition memory.
Ratcliff, R., & Starns, J. J. (2009) · Psychological Review · doi:10.1037/a0014086 · Cited by 250 · see citing works
Self-citationA diffusion model analysis of the effects of aging on recognition memory
Ratcliff, R., Thapar, A., & McKoon, G. (2004) · Journal of Memory and Language · doi:10.1016/j.jml.2003.11.002 · Cited by 239 · see citing works
Self-citationA diffusion model account of masking in two-choice letter identification.
Ratcliff, R., & Rouder, J. N. (2000) · Journal of Experimental Psychology Human Perception & Performance · doi:10.1037//0096-1523.26.1.127 · Cited by 238 · see citing works
Self-citationIndividual differences, aging, and IQ in two-choice tasks
Ratcliff, R., Thapar, A., & McKoon, G. (2009) · Cognitive Psychology · doi:10.1016/j.cogpsych.2009.09.001 · Cited by 237 · see citing works
Self-citationPratte, M. S., Rouder, J. N., Morey, R. D., & Feng, C. (2010) · Attention Perception & Psychophysics · doi:10.3758/app.72.7.2013 · Cited by 237 · see citing works
Self-citationRatcliff, R., Hasegawa, Y. T., Hasegawa, R. P., Smith, P. L., & Segraves, M. A. (2007) · Journal of Neurophysiology · doi:10.1152/jn.00393.2006 · Cited by 236 · see citing works
Self-citationMicrostimulation of visual cortex affects the speed of perceptual decisions
Ditterich, J., Mazurek, M. E., & Shadlen, M. N. (2003) · Nature Neuroscience · doi:10.1038/nn1094 · Cited by 234 · see citing works
Stochastic models of decisions about motion direction: Behavior and physiology
Ditterich, J. (2006) · Neural Networks · doi:10.1016/j.neunet.2006.05.042 · Cited by 233 · see citing works
Seeing at a glance, smelling in a whiff: rapid forms of perceptual decision making
Uchida, N., Kepecs, Á., & Mainen, Z. F. (2006) · Nature reviews. Neuroscience · doi:10.1038/nrn1933 · Cited by 231 · see citing works
Wagenmakers, E. (2008) · The European Journal of Cognitive Psychology · doi:10.1080/09541440802205067 · Cited by 230 · see citing works
Evidence for time‐variant decision making
Ditterich, J. (2006) · European Journal of Neuroscience · doi:10.1111/j.1460-9568.2006.05221.x · Cited by 229 · see citing works
A ballistic model of choice response time
Brown, S., & Heathcote, A. (2005) · Psychological Review · doi:10.1037/0033-295x.112.1.117 · Cited by 228 · see citing works
Real-Time Strategy Game Training: Emergence of a Cognitive Flexibility Trait
Glass, B. D., Maddox, W. T., & Love, B. C. (2013) · PLoS ONE · doi:10.1371/journal.pone.0070350 · Cited by 227 · see citing works
- Authors
- Ratcliff, R., & Rouder, J. N.
- Affiliations
- Northwestern University (US)
- Venue
- Psychological Science
- Publisher
- SAGE Publications
- Published
- 1998-09
- Volume
- 9
- Issue
- 5
- Pages
- 347-356
- ISSN
- 0956-7976 (ISSN-L)
- 1467-9280
- OpenAlex
- W2100476792
- Cited by
- 1,478
- References
- 24
- Citations by year
- 2026: 45 · 2025: 84 · 2024: 87 · 2023: 88 · 2022: 76 · 2021: 99 · 2020: 94 · 2019: 91 · 2018: 92 · 2017: 79 · 2016: 82 · 2015: 72 · 2014: 68 · 2013: 48 · 2012: 41
- FWCI
- 4.86
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Psychological Science (publishedVersion)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural and Behavioral Psychology Studies
- Social Sciences › Decision Sciences › General Decision Sciences › Decision-Making and Behavioral Economics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Visual perception and processing mechanisms
- Keywords
- diffusion models, reaction time (psychology), decision accuracy, reaction time variability, task difficulty, real-time decision making
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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