A frequentist mixture modeling of stop signal reaction times

The stop signal reaction time (SSRT), a measure of the latency of the stop signal process, has been theoretically formulated using a horse race model of go and stop signal processes by the American scientist Gordon Logan (1994). The SSRT assumes equal impact of the preceding trial type (go/stop) on its measurement. In the case of a violation of this assumption, we consider estimation of SSRT based on the idea of earlier analysis of cluster type go reaction times (GORT) and linear mixed model (LMM) data analysis results. Two clusters of trials were considered including those trials preceded by a go trial and other trials preceded by a stop trial. Given disparities between cluster type SSRTs, we need to consider some new indexes considering the unused cluster type information in the calculations. We introduce mixture SSRT and weighted SSRT as two new distinct indexes of SSRT that address the violated assumption. Mixture SSRT and weighted SSRT are theoretically asymptotically equivalent under special conditions. An example of stop single task (SST) real data is presented to show equivalency of these two new SSRT indexes and their larger magnitude compared to Logan's single 1994 SSRT. Abbreviations: ADHD: attention deficit hyperactivity disorder; ExG: Ex-Gaussiandistribution; GORT: reaction time in a go trial; GORTA: reaction time in a type A gotrial; GORTB: reaction time in a type B go trial; LMM: linear mixed model; SWAN:strengths and weakness of ADHD symptoms and normal behavior rating scale; SSD: stop signal delay; SR: signal respond; SRRT: reaction time in a failedstop trial; SSRT: stop signal reaction times in a stop trial; SST: stop signaltask.