Response inhibition is an important act of control in many domains of psychology and neuroscience. It is often studied in a stop-signal task that requires subjects to inhibit an ongoing action in response to a stop signal. Performance in the stop-signal task is understood as a race between a go process that underlies the action and a stop process that inhibits the action. Responses are inhibited if the stop process finishes before the go process. The finishing time of the stop process is not directly observable; a mathematical model is required to estimate its duration. Logan and Cowan (1984) developed an independent race model that is widely used for this purpose. We present a general race model that extends the independent race model to account for the role of choice in go and stop processes, and a special race model that assumes each runner is a stochastic accumulator governed by a diffusion process. We apply the models to 2 data sets to test assumptions about selective influence of capacity limitations on drift rates and strategies on thresholds, which are largely confirmed. The model provides estimates of distributions of stop-signal response times, which previous models could not estimate. We discuss implications of viewing cognitive control as the result of a repertoire of acts of control tailored to different tasks and situations.
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