Abstract

Among the most valuable tools in behavioral science is statistically fitting mathematical models of cognition to data, response time distributions in particular. However, techniques for fitting distributions vary widely and little is known about the efficacy of different techniques. In this article, we assessed several fitting techniques by simulating six widely cited models of response time and using the fitting procedures to recover model parameters. The techniques include the maximization of likelihood and least-squares fits of the theoretical distributions to different empirical estimates of the simulated distributions. A running example was used to illustrate the different estimation and fitting procedures. The simulation studies revealed that empirical density estimates are biased even for very large sample sizes. Some fitting techniques yielded more accurate and less variable parameter estimates than others. Methods that involved least-squares fits to density estimates generally yielded very poor parameter estimates. How to Fit a Response Time Distribution The importance of considering the entire response time (RT) distribution in testing formal models of cognition is now widely appreciated. Fitting a model to mean RT alone can mask important details of the data that examination of the entire distribution would reveal, such as the behavior of fast and slow responses across the conditions of an experiment (e.g., Heathcote, Popiel & Mewhort, 1991), the extent of facilitation between perceptual channels (Miller, 1982), and the effects of practice on RT quantiles (Logan, 1992). Techniques for testing hypotheses based on the RT distribution have been developed (Townsend, 1990). In addition, the RT distribution provides an important meeting ground between theory and da...

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