Abstract
Queen’s University, Kingston, Ontario, Canada We introduce and evaluate via a Monte Carlo study a robust new estimation technique that fits distribution functions to grouped response time (RT) data, where the grouping is determined by sample quantiles. The new estimator, quantile maximum likelihood (QML), is more efficient and less biased than the best alternative estimation technique when fitting the commonly used ex-Gaussian distribution. Limitations of the Monte Carlo results are discussed and guidance provided for the practical application of the new technique. Because QML estimation can be computationally costly, we make fast open source code for fitting available that can be easily modified
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Andrews, S., &Heathcote, A. (2001). Distinguishing common and task-specific processes in word identification: A matter of some moment?Journal of Experimental Psychology: Human Perception & Performance,27, 514–544.
Balota, D. A., &Spieler, D. H. (1999). Word frequency, repetition, and lexicality effects in word recognition tasks: Beyond measures of central tendency.Journal of Experimental Psychology: General,128, 32–55.
Bassett, G., &Koenker, R. (1978). Asymptotic theory of least absolute error regression.Journal of the American Statistical Association,73, 618–622.
Brown, S., & Heathcote, A. (2001).QMLE: Fast, robust and efficient estimation of distribution functions based on quantiles. Manuscript submitted for publication.
Cleveland, W. S. (1985).The elements of graphing data. Monterey, CA: Wadsworth.
Davison, A. C., &Hinkley, D. V. (1997).Bootstrap methods and their application. New York: Cambridge University Press.
Edwards, A. W. F. (1972).Likelihood. London: Cambridge University Press.
Heathcote, A. (1996). RTSYS: A DOS application for the analysis of reaction time data.Behavioral Research Methods, Instruments, & Computers,28, 427–445.
Heathcote, A., Popiel, S. J., &Mewhort, D. J. K. (1991). Analysis of response time distributions: An example using the Stroop task.Psychological Bulletin,109, 340–347.
Hockley, W. E. (1984). Analysis of response time distributions in the study of cognitive processes.Journal of Experimental Psychology: Learning, Memory, & Cognition,10, 598–615.
Hunter, D. R., &Lange, K. (2000). Quantile regression via an MM algorithm.Journal of Computational & Graphical Statistics,9, 60–77.
Kulldorff, G. (1961).Estimation from grouped and partially grouped samples. Wiley: New York.
Leth-Steensen, C., Elbaz, Z. K., &Douglas, V. I. (2000). Mean response times, variability, and skew in the responding of ADHD children: A response time distributional approach.Acta Psychologica,104, 167–190.
McGill, W. J. (1963). Stochastic latency mechanisms. In R.D. Luce, R. R. Bush, & E. Galanter (Eds.),Handbook of mathematical psychology (pp. 193–199). New York: Wiley.
Mewhort, D. J. K., Braun, J. G., &Heathcote, A. (1992). Response time distributions and the Stroop task: A test of the Cohen, Dunbar, and McClelland (1990) model.Journal of Experimental Psychology: Human Perception & Performance,18, 872–882.
Morgenthaler, S., &Tukey, J. W. (2000). Fitting quantiles: Doubling, HR, HQ, and HHH distributions.Journal of Computational & Graphical Statistics,9, 180–195.
Pollard, A., Mewhort, D. J. K., &Weaver, D. F. (2000).High performance computing systems and applications. Boston: Kluwer.
Press W. H., Teukolsky, S. A., Vetterling, W. T., &Flannery, B. P. (1992). Numerical recipes in FORTRAN: The art of scientific computing (2nd ed). New York: Cambridge University Press.
Ratcliff, R. (1978). A theory of memory retrieval.Psychological Review,85, 59–108.
Ratcliff, R. (1979). Group reaction time distributions and the analysis of distribution statistics.Psychological Bulletin,86, 446–461.
Ratcliff, R., &Murdock, B. B. (1976). Retrieval processes in recognition memory.Psychological Review,83, 190–214.
Roher, D., &Wixted, J. T. (1994). An analysis of latency and interresponse time in free recall.Memory & Cognition,22, 511–524.
Rousseeuw, P. J., &Leroy, A. M. (1987).Robust regression and outlier detection. New York: Wiley.
Smith, D. G., &Mewhort, D. J. K. (1998). The distribution of latencies constrains theories of decision time: A test of the random-walk model using numeric comparison.Australian Journal of Psychology,50, 149–156.
Spieler, D. H., Balota, D. A., &Faust, M. E. (1996). Stroop performance in healthy younger and older adults and in individuals with dementia of the Alzheimer’s type.Journal of Experimental Psychology: Human Perception & Performance,22, 461–479.
Tanner, M. A. (1993).Tools for statistical inference. New York: Springer-Verlag.
Thomas, E. A. C., &Ross, B. H. (1980). On appropriate procedures for combining probability distributions within the same family.Journal of Mathematical Psychology,21, 136–152.
Ulrich, R., &Miller, J. (1994). Effects of outlier exclusion on reaction time analysis.Journal of Experimental Psychology: General,123, 34–80.
Van Zandt, T. (2000). How to fit a response time distribution.Psychonomic Bulletin & Review,7, 424–465.
Van Zandt, T., Colonius, H., &Proctor, R. W. (2000). A comparison of two response time models applied to perceptual matching.Psychonomic Bulletin & Review,7, 208–256.
Wand, M. P., &Jones, M. C. (1995).Kernel smoothing. London: Chapman & Hall.
Wixted, J. T., &Roher, D. (1993). Proactive interference and the dynamics of free recall.Journal of Experimental Psychology: Learning, Memory, & Cognition,19, 1024–1039.
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Heathcote, A., Brown, S. & Mewhort, D.J.K. Quantile maximum likelihood estimation of response time distributions. Psychonomic Bulletin & Review 9, 394–401 (2002). https://doi.org/10.3758/BF03196299
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DOI: https://doi.org/10.3758/BF03196299