Linking the diffusion model and general recognition theory: Circular diffusion with bivariate-normally distributed drift rates

The circular diffusion model is a model of continuous outcome decisions, which are modeled as evidence accumulation by a two-dimensional Wiener diffusion process on the interior of a disk whose bounding circle represents the decision criterion. When there is across-trial variability in the evidence entering the decision process, represented by variability in drift rates, the model predicts that inaccurate responses will be slower than accurate responses, in agreement with, and generalizing, the slow-error property of the one-dimensional diffusion model of two-choice decisions. A natural generalization of the one-dimensional model’s assumption of normally distributed drift rates is provided by general recognition theory, which represents the perceptual effects of a two-dimensional stimulus as a bivariate distribution with possibly correlated components. Analytic predictions are derived for the joint distributions of decision outcomes and decision times for the circular diffusion model with bivariate-normally distributed drift rates with correlated components. The decision time and accuracy predictions of the model are shown to depend on the relationship between the orientation of the ellipses of equal likelihood of the drift-rate distribution and the orientation of the mean drift rate vector. The analytic expressions for the model can be computed efficiently and are well suited to fitting data.