Psychometrika

, Volume 68, Issue 4, pp 589–606

A hierarchical bayesian statistical framework for response time distributions

Authors

    • Department of Psychological SciencesUniversity of Missouri
  • Dongchu Sun
    • Department of Psychological SciencesUniversity of Missouri
  • Paul L. Speckman
    • Department of Psychological SciencesUniversity of Missouri
  • Jun Lu
    • Department of Psychological SciencesUniversity of Missouri
  • Duo Zhou
    • Department of Psychological SciencesUniversity of Missouri
Theory And Methods

DOI: 10.1007/BF02295614

Cite this article as:
Rouder, J.N., Sun, D., Speckman, P.L. et al. Psychometrika (2003) 68: 589. doi:10.1007/BF02295614

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.

Key words

Bayesian analysishierarchical modelsresponse timeMCMCWeibull distribution

Copyright information

© The Psychometric Society 2003