Models of response inhibition in the stop-signal and stop-change paradigms

Abstract

The stop-signal paradigm is very useful for the study of response inhibition. Stop-signal performance is typically described as a race between a go process, triggered by a go stimulus, and a stop process, triggered by the stop signal. Response inhibition depends on the relative finishing time of these two processes. Numerous studies have shown that the independent horse-race model of Logan and Cowan [Logan, G.D., Cowan, W.B., 1984. On the ability to inhibit thought and action: a theory of an act of control. Psychological Review 91, 295-327] accounts for the data very well. In the present article, we review the independent horse-race model and related models, such as the interactive horse-race model [Boucher, L., Palmeri, T.J., Logan, G.D., Schall, J.D., 2007. Inhibitory control in mind and brain: an interactive race model of countermanding saccades. Psychological Review 114, 376-397]. We present evidence that favors the independent horse-race model but also some evidence that challenges the model. We end with a discussion of recent models that elaborate the role of a stop process in inhibiting a response.

Figure 1

Depiction of a trial course in the stop-signal paradigm. Tasks and task parameters in this figure are adapted from STOP-IT, which is a free-to-use stop-signal task program (Verbruggen, Logan & Stevens, 2008). In the go task, subjects respond to the shape of a stimulus (a ‘square’ requires a left response and a ‘circle’ requires a right response). On one fourth of the trials, the go stimulus is followed by an auditory stop signal after a variable stop-signal delay (SSD).

Figure 2

(A) Graphic representation of the horse-race idea. The length of the bars represents the duration of the process (SSD = stop-signal delay, SSRT = stop-signal reaction time). (B) Graphic representation of the assumptions of the independent horse-race model of Logan & Cowan (1984), indicating how the probability of responding [p(respond|signal)] and the probability of inhibiting [p(inhibit|signal)] depend on the distribution of go reaction times, stop-signal delay (SSD) and stop-signal reaction time (SSRT).

Figure 3

(A) Graphic representation of the predicted probabilities of responding [p(respond|signal)] based on the independent horse-race model (left panel) and the corresponding inhibition function (right panel), given the go RT distribution and the stop signal reaction time (SSRT). P(respond|signal) is represented by the area under the curve to the left of each dashed line, which increases if SSD increases. (B) Graphic representation of p(respond|signal) for every SSD (left panel) and the corresponding inhibition function (right panel) when the go RT distribution is shifted to the right. The solid line in the right panel is the inhibition function depicted in Figure 3A. (C) Graphic representation of p(respond|signal) for every SSD (left panel) and the corresponding inhibition function (right panel) when SSRT is prolonged. The solid line in the right panel is the inhibition function depicted in Figure 3A.

Figure 4

Graphic representation of the predicted effect of variability in go reaction times on p(respond|signal) (left panel) and the corresponding inhibition function (right panel).

Figure 5

Cumulative RT distributions for signal-respond and no-stop-signal trials predicted by the independent horse-race model. For signal-respond trials, different distributions are predicted for short SSDs, central SSDs and late SSDs.