An EZ Bayesian hierarchical drift diffusion model for response time and accuracy

The EZ-diffusion model is a simplification of the popular drift diffusion model of choice response times that allows researchers to calculate diffusion model parameters directly from data with no need for expensive computations. The EZ-diffusion model is based on a system of equations in which the diffusion model's drift rate, boundary separation, and nondecision time parameters are jointly used to predict three summary statistics (the accuracy rate and the mean and variance of the correct response times). These equations can then be inverted to obtain estimators for the three parameters from these summary statistics. Here, we describe a probabilistic formulation of the EZ-diffusion model that can serve as a hyper-efficient proxy model to the drift diffusion model. The new formulation is based on sampling distributions of summary statistics and consists only of normal and binomial distributions. It can easily be implemented in any probabilistic programming language. We demonstrate the validity of the proxy model through extensive simulation studies and provide multiple examples (via https://osf.io/bzkpn/ ), including an implementation in JASP. We conclude that, although the recovery of some parameters with the proxy model is biased, the recovery of regression parameters is good, making the method useful for cognitive psychometrics (i.e., explanatory cognitive modeling). Casting the EZ-diffusion model in the broad family of Bayesian generative models allows us to benefit from mature implementations, practical workflows, and powerful extensions that are not possible without a probabilistic implementation and not feasible with the regular drift diffusion model. Code and example applications are provided via https://osf.io/bzkpn/ .