Modeling response inhibition in the stop signal task: the copula approach

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 should withhold their response (stop task). The main interest for modeling is in estimating the unobservable stop-signal processing time, that is, the covert latency of the stopping process as a characterization of the level of response inhibition mechanism. In the dominant model performance is hypothesized as a race between two stochastically independent random variables representing go and stop signal processing (independent race model, IRM). Different of versions of the IRM including parameter estimation methods have been proposed, in particular classic non-parametric ones by G. D. Logan and colleagues and parametric ones by D. Matzke and colleagues. An important prediction of all independent race models is that the distribution of reaction times to the go signal, without a stop signal being present, lies below the go signal distribution of when a stop signal is presented after a certain time interval (stop signal delay, SSD). On the other hand, consistent violations of this prediction have been observed for certain SSD values (e.g., P.G. Bissett and colleagues). Here we propose non-independent versions of the race model based on the statistical concept of copula. Copulas allow one to study multivariate dependency separately from assuming specific marginal distributions. We investigate under what conditions these new race models are consistent with violations of the distribution inequality stated above.