The first-passage time distribution for the diffusion model with variable drift

TY - JOUR

T1 - The first-passage time distribution for the diffusion model with variable drift

AU - Blurton, Steven Paul

AU - Kesselmeier, Miriam

AU - Gondan, Matthias

PY - 2017/2/1

Y1 - 2017/2/1

N2 - The Ratcliff diffusion model is now arguably the most widely applied model for response time data. Its major advantage is its description of both response times and the probabilities for correct as well as incorrect responses. The model assumes a Wiener process with drift between two constant absorbing barriers. The first-passage times at the upper and lower boundary describe the responses in simple two-choice decision tasks, for example, in experiments with perceptual discrimination or memory search. In applications of the model, a usual assumption is a varying drift of the Wiener process across trials. This extra flexibility allows accounting for slow errors that often occur in response time experiments. So far, the predicted response time distributions were obtained by numerical evaluation as analytical solutions were not available. Here, we present an analytical expression for the cumulative first-passage time distribution in the diffusion model with normally distributed trial-to-trial variability in the drift. The solution is obtained with predefined precision, and its evaluation turns out to be extremely fast.

AB - The Ratcliff diffusion model is now arguably the most widely applied model for response time data. Its major advantage is its description of both response times and the probabilities for correct as well as incorrect responses. The model assumes a Wiener process with drift between two constant absorbing barriers. The first-passage times at the upper and lower boundary describe the responses in simple two-choice decision tasks, for example, in experiments with perceptual discrimination or memory search. In applications of the model, a usual assumption is a varying drift of the Wiener process across trials. This extra flexibility allows accounting for slow errors that often occur in response time experiments. So far, the predicted response time distributions were obtained by numerical evaluation as analytical solutions were not available. Here, we present an analytical expression for the cumulative first-passage time distribution in the diffusion model with normally distributed trial-to-trial variability in the drift. The solution is obtained with predefined precision, and its evaluation turns out to be extremely fast.

KW - Faculty of Social Sciences

KW - Diffusion model

KW - Response time modeling

U2 - 10.1016/j.jmp.2016.11.003

DO - 10.1016/j.jmp.2016.11.003

M3 - Journal article

SN - 0022-2496

VL - 76

SP - 7

EP - 12

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

IS - Part A

ER -