Linking the Ex-Gaussian Parameters to Cognitive Stages: Insights from the Linear Ballistic Accumulator (LBA) Model

The ex-Gaussian distribution has been routinely used by researchers as a descriptive tool to characterize response time data in speeded two-choice tasks. It has also served as a psychological theory of the underlying cognitive processes. The latter practice requires that the ex-Gaussian parameters should map in a one-to-one correspondence to distinct cognitive stages or process model parameters. The current investigation assessed the correspondence between the exGaussian parameters and the parameters of a well-established process model - the linear ballistic accumulator (LBA, Brown & Heathcote, 2008), using simulations and analyses of empirical data. The results showed the ex-Gaussian parameters bear lawful relations with the LBA's parameters, but that these relations are not unique. These results are in accordance with two earlier studies by Matzke and Wagenmakers (2009) and Rieger and Miller (2019), who assessed the relations between the ex-Gaussian and the diffusion's model parameters. The outcome of the current study suggests that researchers should exercise caution when deploying the ex-Gaussian parameters as a means of psychological theorizing.