The distribution of single Stop Signal Reaction Times (SSRT) in the stop signal task (SST) as a measurement of the latency of the unobservable stopping process has been modeled with a nonparametric method by Hans Colonius (1990) and with a Bayesian parametric method by Eric-Jan Wagenmakers and colleagues (2012). These methods assume equal impact of the preceding trial type (go/stop) in the SST trials on the SSRT distributional estimation without addressing the case of the violated assumption. This study presents the required model by considering two state mixture model for the SSRT distribution. It then compares the Bayesian parametric single SSRT and mixture SSRT distributions in the usual stochastic order at the individual and the population level under ex-Gaussian distributional format. It shows that compared to a single SSRT distribution, the mixture SSRT distribution is more diverse, more positively skewed, more leptokurtic, and larger in stochastic order. The size of the disparities in the results also depends on the choice of weights in the mixture SSRT distribution. This study confirms that mixture SSRT indices as a constant or distribution are significantly larger than their single SSRT counterparts in the related order. This offers a vital improvement in the SSRT estimations.
The Stop Signal Reaction Time (SSRT) is a latency measurement for the unobservable human brain stopping process, and was formulated by Logan (1994) without consideration of the nature (go/stop) of trials that precede the stop trials. Two asymptotically equivalent and larger indices of mixture SSRT and weighted SSRT were proposed in 2017 to address this issue from time in task longitudinal perspective, but estimation based on the time series perspective has still been missing in the literature. A time series-based state space estimation of SSRT was presented and it was compared with Logan 1994 SSRT over two samples of real Stop Signal Task (SST) data and the simulated SST data. The results showed that time series-based SSRT is significantly larger than Logan’s 1994 SSRT consistent with former Longitudinal-based findings. As a conclusion, SSRT indices considering the after effects of inhibition in their estimation process are larger yielding to hypothesize a larger estimates of SSRT using information on the reactive inhibition, proactive inhibition and their interplay in the SST data.
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