Statistical mimicking of reaction time data: Single-process models, parameter variability, and mixtures

Abstract

Statistical mimicking issues involving reaction time measures are introduced and discussed in this article. Often, discussions of mimicking have concerned the question of the serial versus parallel processing of inputs to the cognitive system. Wewill demonstrate that there are several alternative structures that mimic various existing models in the literature. In particular, single-process models have been neglected in this area. When parameter variability is incorporated into single-process models, resulting in discrete or continuous mixtures of reaction time distributions, the observed reaction time distribution alone is no longer as useful in allowing inferences to be made about the architecture of the process that produced it. Many of the issues are raised explicitly in examination of four different case studies of mimicking. Rather than casting a shadow over the use of quantitative methods in testing models of cognitive processes, these examples emphasize the importance of examiningreaction time data armed with the tools of quantitative analysis, the importance of collecting data from the context of specific process models, and the importance of expanding the database to include other dependent measures.Since the publication ofDonders's (1868/1969) essay, "On the speed of mental processes," psychologists have measured the time required by experimental subjects to perform various tasks. These reaction times (RTs) and the changes in RT under different experimental manipulations have been used as evidence for or against models of mental architecture-the arrangement of the mental processes underlying the subject's performance (Sternberg, 1969;Townsend & Ashby, 1983; Woodworth, 1938, chapter 14). RT data have played an important role in distinguishing between models and in testing hypotheses about processes and structures. Consequently, considerable effort has been devoted to the refinement of RT measures, from techniques to optimize the accuracy of subsequent statistical analyses of RT summary statistics (Ratcliff, 1993; Townsend, 1990b;Ulrich & Miller, 1994) to the estimation of RT distributions and RT hazard functions (Burbeck & Luce, 1982;Luce, 1986; Ratcliff & Murdock, 1976). The concentration on the RT This project was supported by NIMH Grants HD MH44640 and MH00871 to R.R. and was completed while the first author was a postdoctoral fellow at Northwestern University. The manuscript was greatly improved by helpful comments from Barbara Dosher, Ehtibar Dzhafarov, Thomas Fikes, Rich Schweickert, Saul Sternberg, and Jim Townsend. Correspondence may be addressed to T. Van Zandt, Department of Psychology, Ames Hall, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218-2686 (e-mail: trish@maigret. psy.jhu.edu). distributions can be seen as an advance from the use of less informative summary statistics such as the mean or median. In the distributional approach, the density or distribution functions predicted by various models are fit to the usually unimodal, positively skewed RT densities or dis...

The Weibull distribution, the power law, and the instance theory of automaticity.

“…Logan (1992, Appendix B) showed that the Weibull closely mimicked the ex-Gaussian distribution (a convolution of a normal distribution and an exponential distribution) that provides an excellent approximation to observed reaction time distributions (Ratcliff & Murdock, 1976). Van Zandt and Ratcliff (1995) showed that the Weibull closely mimicked a mixture of gamma distributions. Moreover, a mixture of gammas chosen in the right way could approximate the power function reduction in the scale of the distribution with practice that is characteristic of the Weibull.…”

Selective Influence and Response Time Cumulative Distribution Functions in Serial-Parallel Task Networks

“…One technique, developed by Ashby and Townsend (1980) and Roberts and Sternberg (1992), is a test of whether two factors selectively influence processes whose durations are combined by addition to form the response time. For a critical analysis, see Van Zandt and Ratcliff (1995). A generalization of this technique is presented in Dzhafarov and Schweickert (1995), Dzhafarov and Cortese (1996), and Cortese and Dzhafarov (1996).…”

Rational adaptation under task and processing constraints: Implications for testing theories of cognition and action.

“…All process durations were sampled from gamma distributions (Van Zandt & Ratcliff, 1995), the shape and scale of which were calibrated from the data (more details are provided in the following calibration section below).…”