Diffusion theory of the antipodal "shadow" mode in continuous-outcome, coherent-motion decisions

Continuous-outcome decisions, in which responses are made on continuous scales, are increasingly used to study perception and memory for stimulus attributes like color, orientation, and motion. This interest has led to the development of models of continuous-outcome decision processes like the circular diffusion model that predict joint distributions of decision outcomes and response times (RTs). We use the circular diffusion model and a new spherical generalization of it to model performance in a continuous-outcome version of the random-dot motion task. The task is a benchmark test of decision models because it yields bimodal distributions of decision outcomes: In addition to a peak or mode in the true direction of motion, there is a secondary, antipodal, mode at 180° to the true direction. Models like the circular diffusion model, in which evidence is accumulated by a single process, are thought to be unable to predict bimodality. We compared diffusion models for the continuous motion task in which evidence is accumulated in either a two-dimensional (2D) or a three-dimensional (3D) representational space. We found that performance was well described by a spherical (3D) diffusion model in which the drift rate encodes perceived motion direction and strength and the points on the bounding sphere representing the decision criterion are projected onto a 2D circle to make a response. A model with an antipodal component of drift rate and drift-rate variability successfully predicted bimodal distributions of decision outcomes and the joint distributions of decision outcomes and RT for individual participants. (PsycInfo Database Record (c) 2023 APA, all rights reserved).