The Seven-parameter Diffusion Model: an Implementation in Stan for Bayesian Analyses

Diffusion models have been widely used to obtain information about cognitive processes from the analysis of responses and response-time data in two-alternative forced-choice tasks. We present an implementation of the seven-parameter diffusion model, incorporating inter-trial variabilities in drift rate, non-decision time, and relative starting point, in the probabilistic programming language Stan. Stan is a free, open-source software that gives the user much flexibility in defining model properties such as the choice of priors and the model structure in a Bayesian framework. We explain the implementation of the new function and how it is used in Stan. We then evaluate its performance in a simulation study that addresses both parameter recovery and simulation-based calibration. The recovery study shows generally good recovery of the model parameters in line with previous findings. The simulation-based calibration study validates the Bayesian algorithm as implemented in Stan.