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An EZ-diffusion model for response time and accuracy

  • Theoretical and Review Articles
  • Published: February 2007
  • Volume 14, pages 3–22, (2007)
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An EZ-diffusion model for response time and accuracy
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  • Eric-Jan Wagenmakers1,
  • Han L. J. Van Der Maas1 &
  • Raoul P. P. P. Grasman1 
  • 6994 Accesses

  • 397 Citations

  • 7 Altmetric

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Abstract

The EZ-diffusion model for two-choice response time tasks takes mean response time, the variance of response time, and response accuracy as inputs. The model transforms these data via three simple equations to produce unique values for the quality of information, response conservativeness, and nondecision time. This transformation of observed data in terms of unobserved variables addresses the speed—accuracy trade-off and allows an unambiguous quantification of performance differences in two-choice response time tasks. The EZ-diffusion model can be applied to data-sparse situations to facilitate individual subject analysis. We studied the performance of the EZ-diffusion model in terms of parameter recovery and robustness against misspecification by using Monte Carlo simulations. The EZ model was also applied to a real-world data set.

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References

  • Balakrishnan, J. D., Busemeyer, J. R., MacDonald, J. A., &Lin, A. (2002).Dynamic signal detection theory: The next logical step in the evolution of signal detection analysis. (Cognitive Science Tech. Rep. No. 248). Bloomington: Indiana University, Cognitive Science Program.

    Google Scholar 

  • Batchelder, W. H. (1998). Multinomial processing tree models and psychological assessment.Psychological Assessment,10, 331–344.

    Article  Google Scholar 

  • Batchelder, W. H., &Riefer, D. M. (1999). Theoretical and empirical review of multinomial process tree modeling.Psychonomic Bulletin & Review,6, 57–86.

    Article  Google Scholar 

  • Botvinick, M. M., Braver, T. S., Barch, D. M., Carter, C. S., &Cohen, J. D. (2001). Conflict monitoring and cognitive control.Psychological Review,108, 624–652.

    Article  PubMed  Google Scholar 

  • Box, G. E. P. (1979). Robustness in scientific model building. In R. L. Launer & G. N. Wilkinson (Eds.),Robustness in statistics. (pp. 201–236). New York: Academic Press.

    Google Scholar 

  • Browne, M. W. (2000). Cross-validation methods.Journal of Mathematical Psychology,44, 108–132.

    Article  PubMed  Google Scholar 

  • Busemeyer, J. R., &Stout, J. C. (2002). A contribution of cognitive decision models to clinical assessment: Decomposing performance on the Bechara gambling task.Psychological Assessment,14, 253–262.

    Article  PubMed  Google Scholar 

  • Cox, D. R., &Miller, H. D. (1970).The theory of stochastic processes. London: Methuen.

    Google Scholar 

  • D’Agostino, R. B. (1970). Transformation to normality of the null distribution of g1.Biometrika,57, 679–681.

    Google Scholar 

  • Dennis, I., &Evans, J. B. T. (1996). The speed—error trade-off problem in psychometric testing.British Journal of Psychology,87, 105–129.

    Google Scholar 

  • Diederich, A., &Busemeyer, J. R. (2003). Simple matrix methods for analyzing diffusion models of choice probability, choice response time, and simple response time.Journal of Mathematical Psychology,47, 304–322.

    Article  Google Scholar 

  • Efron, B., &Tibshirani, R. J. (1993).An introduction to the bootstrap. New York: Chapman & Hall.

    Google Scholar 

  • Emerson, P. L. (1970). Simple reaction time with Markovian evolution of Gaussian discriminal processes.Psychometrika,35, 99–109.

    Article  Google Scholar 

  • Eriksen, B. A., &Eriksen, C. W. (1974). Effects of noise letters upon the identification of a target letter in a nonsearch task.Perception & Psychophysics,16, 143–149.

    Article  Google Scholar 

  • Gardiner, C. W. (2004).Handbook of stochastic methods. (3rd ed.). Berlin: Springer.

    Google Scholar 

  • Gilden, D. L. (2001). Cognitive emissions of 1/f noise.Psychological Review,108, 33–56.

    Article  PubMed  Google Scholar 

  • Green, D. M., &Swets, J. A. (1966).Signal detection theory and psychophysics. New York: Wiley.

    Google Scholar 

  • Honerkamp, J. (1994).Stochastic dynamical systems: Concepts, numerical methods, data analysis. (K. Lindenberg, Trans.). New York: VCH.

    Google Scholar 

  • Hultsch, D. F., MacDonald, S. W. S., &Dixon, R. A. (2002). Variability in reaction time performance of younger and older adults.Journals of Gerontology,57B, P101-P115.

    Google Scholar 

  • Jones, A. D., Cho, R. Y., Nystrom, L. E., Cohen, J. D., &Braver, T. S. (2002). A computational model of anterior cingulate function in speeded response tasks: Effects of frequency, sequence, and conflict.Cognitive, Affective, & Behavioral Neuroscience,2, 300–317.

    Article  Google Scholar 

  • Laming, D. R. J. (1968).Information theory of choice-reaction times. London: Academic Press.

    Google Scholar 

  • Laming, D. R. J. (1973).Mathematical psychology. London: Academic Press.

    Google Scholar 

  • Li, S.-C. (2002). Connecting the many levels and facets of cognitive aging.Current Directions in Psychological Science,11, 38–43.

    Article  Google Scholar 

  • Link, S. W. (1992).The wave theory of difference and similarity. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Link, S. W., &Heath, R. A. (1975). A sequential theory of psychological discrimination.Psychometrika,40, 77–105.

    Article  Google Scholar 

  • Luce, R. D. (1986).Response times: Their role in inferring elementary mental organization. New York: Oxford University Press.

    Google Scholar 

  • MacDonald, S. W. S., Hultsch, D. F., &Dixon, R. A. (2003). Performance variability is related to change in cognition: Evidence from the Victoria longitudinal study.Psychology & Aging,18, 510–523.

    Article  Google Scholar 

  • Macmillan, N., &Creelman, C. D. (2004).Detection theory: A user’s guide. (2nd ed.). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Meevis, M., Luth, I., vom Kothen, L., Koomen, A., &Verouden, J. (2005).IQ en reactiesnelheid: Een experiment en een wiskundige analyse. (Tech. Rep.). Amsterdam: University of Amsterdam.

    Google Scholar 

  • Myung, I. J., Forster, M. R., & Browne, M. W. (Eds.). (2000). Model selection [Special issue].Journal of Mathematical Psychology,44(1).

  • Oberauer, K. (2005). Binding and inhibition in working memory: Individual and age differences in short-term recognition.Journal of Experimental Psychology: General,134, 368–387.

    Article  Google Scholar 

  • Pachella, R. G. (1974). The interpretation of reaction time in information-processing research. In B. H. Kantowitz (Ed.),Human information processing: Tutorials in performance and cognition. (pp. 41–82). Potomac, MD: Erlbaum.

    Google Scholar 

  • Palmer, J., Huk, A. C., &Shadlen, M. N. (2005). The effect of stimulus strength on the speed and accuracy of a perceptual decision.Journal of Vision,5, 376–404.

    Article  PubMed  Google Scholar 

  • Pew, R. W. (1969). The speed—accuracy operating characteristic.Acta Psychologica,30, 16–26.

    Article  Google Scholar 

  • Ratcliff, R. (1978). A theory of memory retrieval.Psychological Review,85, 59–108.

    Article  Google Scholar 

  • Ratcliff, R. (1981). A theory of order relations in perceptual matching.Psychological Review,88, 552–572.

    Article  Google Scholar 

  • Ratcliff, R. (2002). A diffusion model account of response time and accuracy in a brightness discrimination task: Fitting real data and failing to fit fake but plausible data.Psychonomic Bulletin & Review,9, 278–291.

    Article  Google Scholar 

  • Ratcliff, R., Gomez, P., &McKoon, G. (2004). A diffusion model account of the lexical decision task.Psychological Review,111, 159–182.

    Article  PubMed  Google Scholar 

  • Ratcliff, R., &Rouder, J. N. (1998). Modeling response times for two-choice decisions.Psychological Science,9, 347–356.

    Article  Google Scholar 

  • Ratcliff, R., &Rouder, J. N. (2000). A diffusion model account of masking in two-choice letter identification.Journal of Experimental Psychology: Human Perception & Performance,26, 127–140.

    Article  Google Scholar 

  • Ratcliff, R., &Smith, P. L. (2004). A comparison of sequential sampling models for two-choice reaction time.Psychological Review,111, 333–367.

    Article  PubMed  Google Scholar 

  • Ratcliff, R., Thapar, A., Gomez, P., &McKoon, G. (2004). A diffusion model analysis of the effects of aging in the lexical-decision task.Psychology & Aging,19, 278–289.

    Article  Google Scholar 

  • Ratcliff, R., Thapar, A., &McKoon, G. (2001). The effects of aging on reaction time in a signal detection task.Psychology & Aging,16, 323–341.

    Article  Google Scholar 

  • Ratcliff, R., Thapar, A., &McKoon, G. (2004). A diffusion model analysis of the effects of aging on recognition memory.Journal of Memory & Language,50, 408–424.

    Article  Google Scholar 

  • Ratcliff, R., &Tuerlinckx, F. (2002). Estimating parameters of the diffusion model: Approaches to dealing with contaminant reaction times and parameter variability.Psychonomic Bulletin & Review,9, 438–481.

    Article  Google Scholar 

  • Ratcliff, R., Van Zandt, T., &McKoon, G. (1999). Connectionist and diffusion models of reaction time.Psychological Review,102, 261–300.

    Article  Google Scholar 

  • R Development Core Team. (2004).R: A language and environment for statistical computing. Vienna: Author.

    Google Scholar 

  • Reeves, A., Santhi, N., &Decaro, S. (2005). A random-ray model for speed and accuracy in perceptual experiments.Spatial Vision,18, 73–83.

    Article  PubMed  Google Scholar 

  • Riefer, D. M., Knapp, B. R., Batchelder, W. H., Bamber, D., &Manifold, V. (2002). Cognitive psychometrics: Assessing storage and retrieval deficits in special populations with multinomial processing tree models.Psychological Assessment,14, 184–201.

    Article  PubMed  Google Scholar 

  • Rouder, J. N., &Lu, J. (2005). An introduction to Bayesian hierarchical models with an application in the theory of signal detection.Psychonomic Bulletin & Review,12, 573–604.

    Article  Google Scholar 

  • Rouder, J. N., Lu, J., Speckman, P., Sun, D., &Jiang, Y. (2005). A hierarchical model for estimating response time distributions.Psychonomic Bulletin & Review,12, 195–223.

    Article  Google Scholar 

  • Schouten, J. F., &Bekker, J. A. M. (1967). Reaction time and accuracy.Acta Psychologica,27, 143–153.

    Article  PubMed  Google Scholar 

  • Seber, G. A. F., &Lee, A. J. (2003).Linear regression analysis. (2nd ed.). Hoboken, NJ: Wiley.

    Google Scholar 

  • Shammi, P., Bosman, E., &Stuss, D. T. (1998). Aging and variability in performance.Aging, Neuropsychology, & Cognition,5, 1–13.

    Article  Google Scholar 

  • Slifkin, A. B., &Newell, K. M. (1998). Is variability in human performance a reflection of system noise?Current Directions in Psychological Science,7, 170–177.

    Article  Google Scholar 

  • Smith, P. L. (2000). Stochastic dynamic models of response time and accuracy: A foundational primer.Journal of Mathematical Psychology,44, 408–463.

    Article  PubMed  Google Scholar 

  • Stone, M. (1960). Models for choice-reaction time.Psychometrika,25, 251–260.

    Article  Google Scholar 

  • Stout, J. C., Busemeyer, J. R., Lin, A., Grant, S. J., &Bonson, K. R. (2004). Cognitive modeling analysis of decision-making processes in cocaine abusers.Psychonomic Bulletin & Review,11, 742–747.

    Article  Google Scholar 

  • Townsend, J. T., &Ashby, F. G. (1983).The stochastic modeling of elementary psychological processes. Cambridge: Cambridge University Press.

    Google Scholar 

  • Tuerlinckx, F. (2004). The efficient computation of the cumulative distribution and probability density functions in the diffusion model.Behavior Research Methods, Instruments, & Computers,36, 702–716.

    Article  Google Scholar 

  • Tukey, J. W. (1977).Explanatory data analysis. Reading, MA: Addison-Wesley.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Vickers, D., &Lee, M. D. (1998). Dynamic models of simple judgments: I. Properties of a self-regulating accumulator module.Nonlinear Dynamics, Psychology, & Life Sciences,2, 169–194.

    Article  Google Scholar 

  • Voss, A., Rothermund, K., &Voss, J. (2004). Interpreting the parameters of the diffusion model: An empirical validation.Memory & Cognition,32, 1206–1220.

    Article  Google Scholar 

  • Wagenmakers, E.-J., Farrell, S., &Ratcliff, R. (2004). Estimation and interpretation of 1/fα noise in human cognition.Psychonomic Bulletin & Review,11, 579–615.

    Article  Google Scholar 

  • Wagenmakers, E.-J., Grasman, R. P. P. P., &Molenaar, P. C. M. (2005). On the relation between the mean and the variance of a diffusion model response time distribution.Journal of Mathematical Psychology,49, 195–204.

    Article  Google Scholar 

  • Wagenmakers, E.-J., & Waldorp, L. (Eds.). (2006). Model selection: Theoretical developments and applications [Special issue].Journal of Mathematical Psychology,50(2).

  • Wickelgren, W. A. (1977). Speed—accuracy trade-off and information processing dynamics.Acta Psychologica,41, 67–85.

    Article  Google Scholar 

  • Zaki, S. R., &Nosofsky, R. M. (2001). Exemplar accounts of blending and distinctiveness effects in perceptual old—new recognition.Journal of Experimental Psychology: Learning, Memory, & Cognition,27, 1022–1041.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Psychology, University of Amsterdam, Roetersstraat 15, 1018 WB, Amsterdam, The Netherlands

    Eric-Jan Wagenmakers, Han L. J. Van Der Maas & Raoul P. P. P. Grasman

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  1. Eric-Jan Wagenmakers
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  2. Han L. J. Van Der Maas
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  3. Raoul P. P. P. Grasman
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Corresponding author

Correspondence to Eric-Jan Wagenmakers.

Additional information

This research was funded by a VENI grant from the Dutch Organization for Scientific Research (NWO). Part of this work was presented at the 4th Annual Summer Interdisciplinary Conference, Briançon, France (July 2005), and at the 38th Annual Meeting of the Society for Mathematical Psychology, Memphis, Tennessee (August 2005).

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Wagenmakers, EJ., Van Der Maas, H.L.J. & Grasman, R.P.P.P. An EZ-diffusion model for response time and accuracy. Psychonomic Bulletin & Review 14, 3–22 (2007). https://doi.org/10.3758/BF03194023

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  • Received: 31 October 2005

  • Accepted: 12 June 2006

  • Issue Date: February 2007

  • DOI: https://doi.org/10.3758/BF03194023

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Keywords

  • Diffusion Model
  • Drift Rate
  • Error Response
  • Boundary Separation
  • Parameter Recovery
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