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Application of the Gaussian Stochastic Multiplicative Cascade Model to Choice Response Time Data

In two experiments involving a four-choice visual task, participants’ response time difference series were shown to be significantly multifractal. This implied that information processing occurred on multiple time scales, and that performance was nonlinear rather than linear early in practice and whenever time constraints were placed on performance. This led to excellent fits to the multifractal spectra of a Gaussian multiplicative cascade model with two parameters, the mean and variance of the Gaussian stochastic process. As mean and variance were positively correlated, Zmu, the mean parameter estimated with reference to its estimate from 30 surrogate series, was used for data analysis. As practice progressed in Experiment 1, Zmu, a measure of the multifractal component of the mean of the Gaussian process, decreased from the first to second practice session. Zmu increased when people were required to respond quickly in Experiment 2, suggesting its possible application as a measure of information processing capacity in a variety of neuropsychological and human factors applications. As a theoretical bonus, Zmu subsumes all of the sequential effects present in the response time series, thus obviating the need for the inclusion of a large number of additional parameters to represent these temporal dependencies.