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How to fit a response time distribution

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 assess 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 is used to illustrate the different estimation and fitting procedures. The simulation studies reveal that empirical density estimates are biased even for very large sample sizes. Some fitting techniques yield more accurate and less variable parameter estimates than do others. Methods that involve least squares fits to density estimates generally yield very poor parameter estimates.

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Portions of this article were presented at the 31st Annual Meeting of the Society for Mathematical Psychology, August 1998, Vanderbilt University, and at the 39th Annual Meeting of the Psychonomic Society, November 1998, Dallas. The project was funded by NSF Grant SBR-9702291. The author gratefully acknowledges the many contributions to this project by Steven Yantis. Thanks also are due Howard Egeth, Andrew Heathcote, and John Wixted for many helpful comments that greatly improved the paper.

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Van Zandt, T. How to fit a response time distribution. Psychon Bull Rev 7, 424–465 (2000). https://doi.org/10.3758/BF03214357

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  • DOI: https://doi.org/10.3758/BF03214357

Keywords

  • Cumulative Distribution Function
  • True Density
  • Race Model
  • Response Time Distribution
  • Histogram Estimate