Modeling trigger failures in the stop signal task

The stop signal task is a popular tool for studying 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 that subjects should withhold their response (stop task). One issue in modeling performance in the task is the issue of potential trigger failures: if a response is given after the stop signal, this may be due either to an unsuccessful inhibition (stop signal processing terminates "too late") or by a failure to trigger processing of the stop signal at all. Up to now, testing for the occurrence of trigger failures and estimating its probability has only been studied in fully-parametrized race models. Here we first suggest a statistical test for the existence of trigger failures. Second, we propose a more general (latent variable) modeling approach using concepts from the statistical theory of copulas that permits estimation of trigger failure probabilities.