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A Hierarchical Bayesian Statistical Framework for Response Time Distributions

Published online by Cambridge University Press:  01 January 2025

Jeffrey N. Rouder ,
Dongchu Sun ,
Paul L. Speckman ,
Jun Lu  and
Duo Zhou
Jeffrey N. Rouder*
Affiliation:
University of Missouri-Columbia
Dongchu Sun
Affiliation:
University of Missouri-Columbia
Paul L. Speckman
Affiliation:
University of Missouri-Columbia
Jun Lu
Affiliation:
University of Missouri-Columbia
Duo Zhou
Affiliation:
University of Missouri-Columbia
*
Requests for reprints should be sent to Jeffrey N. Rouder, Department of Psychological Sciences, 210 McAlester Hall, University of Missouri, Columbia, MO 65211. E-Mail: jeff@missouri.edu
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Abstract

This paper provides a statistical framework for estimating higher-order characteristics of the response time distribution, such as the scale (variability) and shape. Consideration of these higher order characteristics often provides for more rigorous theory development in cognitive and perceptual psychology (e.g., Luce, 1986). RT distribution for a single participant depends on certain participant characteristics, which in turn can be thought of as arising from a distribution of latent variables. The present work focuses on the three-parameter Weibull distribution, with parameters for shape, scale, and shift (initial value). Bayesian estimation in a hierarchical framework is conceptually straightforward. Parameter estimates, both for participant quantities and population parameters, are obtained through Markov Chain Monte Carlo methods. The methods are illustrated with an application to response time data in an absolute identification task. The behavior of the Bayes estimates are compared to maximum likelihood (ML) estimates through Monte Carlo simulations. For small sample size, there is an occasional tendency for the ML estimates to be unreasonably extreme. In contrast, by borrowing strength across participants, Bayes estimation “shrinks” extreme estimates. The results are that the Bayes estimators are more accurate than the corresponding ML estimators.

Keywords

Bayesian analysishierarchical modelsresponse timeMCMCWeibull distribution
Type
Theory And Methods
Information
Psychometrika , Volume 68 , Issue 4 , December 2003 , pp. 589 - 606
Copyright
Copyright © 2003 The Psychometric Society

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Footnotes

We are grateful to Michael Stadler who allowed us use of his data. This research is supported by (a) National Science Foundation Grant SES-0095919 to J. Rouder, D. Sun, and P. Speckman, (b) University of Missouri Research Board Grant 00-77 to J. Rouder, (c) National Science Foundation grant DMS-9972598 to Sun and Speckman, and (d) a grant from the Missouri Department of Conservation to D. Sun.

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