Explicit moments of decision times for single- and double-threshold drift-diffusion processes

- Analytic expressions for first three unconditioned and conditioned moments of decision time for pure drift-diffusion model.
- Semi-analytic expressions for first three unconditioned and conditioned moments of decision time for extended drift-diffusion model.
- Thorough analysis of the behavior of moments of decision time as a function of model parameters.
- Analysis of the effect of non-decision time on moments of reaction time.

We derive expressions for the first three moments of the decision time (DT) distribution produced via first threshold crossings by sample paths of a drift-diffusion equation. The “pure” and “extended” diffusion processes are widely used to model two-alternative forced choice decisions, and, while simple formulae for accuracy, mean DT and coefficient of variation are readily available, third and higher moments and conditioned moments are not generally available. We provide explicit formulae for these, describe their behaviors as drift rates and starting points approach interesting limits, and, with the support of numerical simulations, discuss how trial-to-trial variability of drift rates, starting points, and non-decision times affect these behaviors in the extended diffusion model. Both unconditioned moments and those conditioned on correct and erroneous responses are treated. We argue that the results will assist in exploring mechanisms of evidence accumulation and in fitting parameters to experimental data.