Modeling evidence accumulation decision processes using integral equations: Urgency-gating and collapsing boundaries

Diffusion models of evidence accumulation have successfully accounted for the distributions of response times and choice probabilities from many experimental tasks, but recently their assumption that evidence is accumulated at a constant rate to constant decision boundaries has been challenged. One model assumes that decision-makers seek to optimize their performance by using decision boundaries that collapse over time. Another model assumes that evidence does not accumulate and is represented by a stationary distribution that is gated by an urgency signal to make a response. We present explicit, integral-equation expressions for the first-passage time distributions of the urgency-gating and collapsing-bounds models and use them to identify conditions under which the models are equivalent. We combine these expressions with a dynamic model of stimulus encoding that allows the effects of perceptual and decisional integration to be distinguished. We compare the resulting models to the standard diffusion model with variability in drift rates on data from three experimental paradigms in which stimulus information was either constant or changed over time. The standard diffusion model was the best model for tasks with constant stimulus information; the models with time-varying urgency or decision bounds performed similarly to the standard diffusion model on tasks with changing stimulus information. We found little support for the claim that evidence does not accumulate and attribute the good performance of the time-varying models on changing-stimulus tasks to their increased flexibility and not to their ability to account for systematic experimental effects. (PsycInfo Database Record (c) 2022 APA, all rights reserved).