Mathematical Psychology
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Drift Diffusion Model

The Drift-Diffusion Model describes two-choice decisions as a noisy evidence accumulation process, simultaneously accounting for response times and accuracy.

dx = v·dt + s·dW

The Drift-Diffusion Model (DDM), developed primarily by Roger Ratcliff beginning in 1978, is the dominant model of speeded two-choice decision making. It describes the decision process as the continuous accumulation of noisy evidence from a starting point toward one of two absorbing boundaries. When the accumulated evidence reaches a boundary, the corresponding response is initiated.

Model Parameters

The DDM has four core parameters, each with a clear psychological interpretation:

Core DDM Parameters v = drift rate (quality of evidence)
a = boundary separation (speed-accuracy tradeoff / caution)
z = starting point (a priori bias)
Ter = non-decision time (encoding + motor execution)

The drift rate (v) reflects the rate of evidence accumulation and maps onto task difficulty and stimulus quality. The boundary separation (a) reflects the amount of evidence required before committing to a response — wider boundaries produce slower but more accurate responses. The starting point (z) captures response bias, and the non-decision time (Ter) captures processes outside the decision itself.

EZ-Diffusion

Wagenmakers, van der Maas, and Grasman (2007) developed the EZ-diffusion method, which provides closed-form estimates of the three main DDM parameters (v, a, Ter) from just three summary statistics: mean RT, RT variance, and accuracy. While less flexible than full model fitting, EZ-diffusion makes the DDM accessible for studies where full RT distributions are unavailable.

Neural Basis

The DDM has received strong neural support. Neurons in the lateral intraparietal area (LIP) of monkeys show ramping activity during perceptual decisions that closely mirrors the accumulation process posited by the model. The drift rate corresponds to the rate of neural firing increase, and the boundary corresponds to the threshold firing rate at which a saccadic eye movement is triggered.

Interactive Calculator

Enter summary statistics from a two-choice RT experiment: mean_rt (mean correct RT in seconds), var_rt (variance of correct RTs), and accuracy (proportion correct). The EZ-diffusion method estimates drift rate (v), boundary separation (a), and non-decision time (Ter).

Click Calculate to see results, or Animate to watch the statistics update one record at a time.

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References

  1. Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85(2), 59–108. https://doi.org/10.1037/0033-295X.85.2.59
  2. Ratcliff, R., & McKoon, G. (2008). The diffusion decision model: Theory and data for two-choice decision tasks. Neural Computation, 20(4), 873–922. https://doi.org/10.1162/neco.2008.12-06-420
  3. Wagenmakers, E.-J., van der Maas, H. L. J., & Grasman, R. P. P. P. (2007). An EZ-diffusion model for response time and accuracy. Psychonomic Bulletin & Review, 14(1), 3–22. https://doi.org/10.3758/BF03194023
  4. Gold, J. I., & Shadlen, M. N. (2007). The neural basis of decision making. Annual Review of Neuroscience, 30, 535–574. https://doi.org/10.1146/annurev.neuro.29.051605.113038

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