A Bayesian Mixture Modelling of Stop Signal Reaction Time Distributions
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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 the 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.
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