Paradox resolved: stop signal race model with negative dependence

Abstract

The ability to inhibit our responses voluntarily is an important case of cognitive control. The stop-signal paradigm is a popular tool to study response inhibition. Participants perform a response time task (go task) and, occasionally, the go stimulus is followed by a stop signal after a variable delay, indicating subjects to withhold their response (stop task). The main interest of modeling is in estimating the unobservable stop-signal processing time, that is, the covert latency of the stopping process as a characterization of the response inhibition mechanism. In the independent race model the stop-signal task is represented as a race between stochastically independent go and stop processes. Without making any specific distributional assumptions about the processing times, the model allows to estimate the mean time to cancel a response. However, neurophysiological studies on countermanding saccadic eye movements have shown that neural correlates of go and stop processes consist of networks of mutually interacting gaze-shifting and gaze-holding neurons. This poses a major challenge in formulating linking propositions between the behavioral and neural findings. Here we propose a dependent race model that postulates perfect negative stochastic dependence between go and stop activations. The model is consistent with the concept of interacting processes while retaining the simplicity and elegance of the distribution-free independent race model. For mean data, the dependent models predictions remain identical to those of the independent model. The resolution of this apparent paradox advances the understanding of mechanisms of response inhibition and paves the way for modeling more complex situations.