A comparison of two response time models applied to perceptual matching
- 827 Downloads
- 7 Citations
Abstract
Two models, a Poisson race model and a diffusion model, are fit to data from a perceptual matching task. In each model, information about the similarity or the difference between two stimuli accumulates toward thresholds for either response. Stimulus variables are assumed to influence the rate at which information accumulates, and response variables are assumed to influence the level of the response thresholds. Three experiments were conducted to assess the performance of each model. In Experiment 1, observers performed under different response deadlines; in Experiment 2, response bias was manipulated by changing the relative frequency ofsame anddifferent stimuli. In Experiment 3, stimulus pairs were presented at three eccentricities: foveal, parafoveal, and peripheral. We examined whether the race and diffusion models could fit the response time and accuracy data through changes only in response parameters (for Experiments 1 and 2) or stimulus parameters (for Experiment 3). Comparisons between the two models suggest that the race model, which has not been studied extensively, can account for perceptual matching data at least as well as the diffusion model. Furthermore, without the constraints on the parameters provided by the experimental conditions, the diffusion and the race models are indistinguishable. This finding emphasizes the importance of fitting models across several conditions and imposing logical psychological constraints on the parameters of models.
Keywords
Diffusion Model Drift Rate Race Model Predicted Density Perceptual MatchReferences
- Ashby, F. G. (1983). Testing the assumptions of exponential, additive reaction time models.Memory & Cognition,10, 125–134.CrossRefGoogle Scholar
- Audley, R. C., &Pike, A. R. (1965). Some alternative stochastic models of choice.British Journal of Mathematical & Statistical Psychology,18, 207–225.Google Scholar
- Bamber, D. (1969). Reaction times and error rates for “same”-“different” judgments of multidimensional stimuli.Perception & Psychophysics,6, 169–174.CrossRefGoogle Scholar
- Browne, M. W., &Cudeck, R. (1992). Alternative ways of assessing model fit.Sociological Methods & Research,2, 230–258.CrossRefGoogle Scholar
- Colonius, H. (1995). The instance theory of automaticity: Why the Weibull?Psychological Review,102, 744–750.CrossRefGoogle Scholar
- Diederich, A. (1995). Intersensory facilitation of reaction time: Eval uation of counter and diffusion coactivation models.Journal of Mathematical Psychology,39, 197–215.CrossRefGoogle Scholar
- Dzhafarov, E. N. (1992). The structure of simple reaction time to stepfunction signals.Journal of Mathematical Psychology,36, 235–268.CrossRefGoogle Scholar
- Dzhafarov, E. N. (1993). Grice-representability of response time distribution families.Psychometrika,58, 281–314.CrossRefGoogle Scholar
- Eriksen, C. W., &Schultz, D. W. (1977). Retinal locus and acuity in visual information processing.Bulletin of the Psychonomic Society,9, 81–84.Google Scholar
- Farrell, B. (1985). “Same”-“different” judgments: A review of current controversies in perceptual comparisons.Psychological Bulletin,98, 419–456.CrossRefGoogle Scholar
- Feller, W. (1968).An introduction to probability theory and its applications (Vol. 1). New York: Wiley.Google Scholar
- Gallant, A. R. (1987).Nonlinear statistical models. New York: Wiley.CrossRefGoogle Scholar
- Grigelionis, B. (1963). On the convergence of sums of random step processes to a Poisson process.Theory of Probability & Its Applications,8, 177–182.CrossRefGoogle Scholar
- Heath, R. A., &Willcox, C. H. (1990). A stochastic model for interkeypress times in a typing task.Acta Psychologica,75, 13–39.CrossRefPubMedGoogle Scholar
- Hick, W. E. (1952). On the rate of gain of information.Quarterly Journal of Experimental Psychology,4, 11–26.CrossRefGoogle Scholar
- Hockley, W. E. (1984). Analysis of response time distributions in the study of cognitive processes.Journal of Experimental Psychology: Learning, Memory, & Cognition,6, 598–615.CrossRefGoogle Scholar
- Hommel, B. (1998). Event files: Evidence for automatic integration of stimulus-response episodes.Visual Cognition,5, 183–216.CrossRefGoogle Scholar
- Hyman, R. (1953). Stimulus information as a determinant of reaction time.Journal of Experimental Psychology,45, 188–196.CrossRefPubMedGoogle Scholar
- Khintchine, A. Y. (1960).Mathematical methods in the theory of queuing. London: Griffin.Google Scholar
- Krueger, L. E. (1978). A theory of perceptual matching.Psychological Review,85, 278–304.CrossRefPubMedGoogle Scholar
- Krueger, L. E. (1985). Effect of intermixed foveal and parafoveal presentation on same-different judgments: Evidence for a criterioninertia model.Perception & Psychophysics,37, 266–271.CrossRefGoogle Scholar
- Krueger, L. E., &Allen, P. A. (1987). Same-different judgments of foveal and parafoveal letter pairs by older adults.Perception & Psychophysics,38, 188–193.CrossRefGoogle Scholar
- LaBerge, D. A. (1962). A recruitment theory of simple behavior.Psychometrika,27, 375–396.CrossRefGoogle Scholar
- Laming, D. R. (1968).Information theory of choice reaction time. New York: Wiley.Google Scholar
- Link, S. W. (1975). The relative judgement theory of two choice response time.Journal of Mathematical Psychology,12, 114–135.CrossRefGoogle Scholar
- Link, S. W., &Heath, R. A. (1975). A sequential theory of psychological discrimination.Psychometrika,40, 77–105.CrossRefGoogle Scholar
- Logan, G. D. (1988). Toward an instance theory of automatization.Psychological Review,95, 492–527.CrossRefGoogle Scholar
- Logan, G. D. (1992). Shapes of reaction-time distributions and shapes of learning curves: A test of the instance theory of automaticity.Journal of Experimental Psychology: Learning, Memory, & Cognition,18, 883–914.CrossRefGoogle Scholar
- Logan, G. D. (1995). The Weibull distribution, the power law, and the instance theory of automaticity.Psychological Review,102, 751–756.CrossRefGoogle Scholar
- Luce, R. D. (1986).Response times: Their role in inferring elementary mental organization. New York: Oxford University Press.Google Scholar
- Marley, A. A. J., &Colonius, H. (1992). The “horse race” random utility model for choice probabilities and reaction times, and its competing risks interpretation.Journal of Mathematical Psychology,36, 1–20.CrossRefGoogle Scholar
- Mordkoff, J. T., &Yantis, S. (1991). An interactive race model of divided attention.Journal of Experimental Psychology: Human Perception & Performance,17, 520–538.CrossRefGoogle Scholar
- Nelder, J. A., &Mead, R. (1965). A simplex method for function minimization.Computer Journal,7, 308–313.Google Scholar
- Newell, A., &Rosenbloom, P. S. (1981). Mechanisms of skill acquisition and the law of practice. In J. R. Anderson (Ed.),Cognitive skills and their acquisition (pp. 1–55). Hillsdale, NJ: Erlbaum.Google Scholar
- Pachella, R. G. (1974). The interpretation of reaction time in information processing research. In B. Kantowitz (Ed.),Human information processing: Tutorials in performance and cognition (pp. 41–82). Hillsdale, NJ: Erlbaum.Google Scholar
- Pike, R. (1973). Response latency models for signal detection.Psychological Review,80, 53–68.CrossRefPubMedGoogle Scholar
- 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.Google Scholar
- Proctor, R. W. (1981). A unified theory for matching-task phenomena.Psychological Review,88, 291–326.CrossRefGoogle Scholar
- Proctor, R. W. (1986). Response bias, criteria settings, and the fast-same phenomenon: A reply to Ratcliff.Psychological Review,93, 473–477.CrossRefGoogle Scholar
- Proctor, R. W., &Rao, V. K. (1983). Evidence that the same-different disparity in letter matching is not attributable to response bias.Perception & Psychophysics,34, 72–76.CrossRefGoogle Scholar
- Proctor, R. W., Van Zandt, T., &Watson, H. (1990). Effects of background symmetry on same-different pattern matching: A compromise criteria account.Perception & Psychophysics,48, 543–550.Google Scholar
- Ratcliff, R. (1978). A theory of memory retrieval.Psychological Review,85, 59–108.CrossRefGoogle Scholar
- Ratcliff, R. (1981). A theory of order relations in perceptual matching.Psychological Review,88, 552–572.CrossRefGoogle Scholar
- Ratcliff, R. (1985). Theoretical interpretations of the speed and accuracy of positive and negative responses.Psychological Review,92, 212–225.CrossRefPubMedGoogle Scholar
- Ratcliff, R., &Murdock, B. B., Jr. (1976). Retrieval processes in recognition memory.Psychological Review,83, 190–214.CrossRefGoogle Scholar
- Ratcliff, R., Van Zandt, T., &McKoon, G. (1999). Comparing connectionist and diffusion models of reaction time.Psychological Review,106, 261–300.CrossRefPubMedGoogle Scholar
- Roberts, S., &Pashler, H. (in press). How persuasive is a good fit?Psychological Review.Google Scholar
- Rumelhart, D. E. (1970). A multicomponent theory of the perception of briefly exposed visual displays.Journal of Mathematical Psychology,7, 191–218.CrossRefGoogle Scholar
- Schwarz, W. (1990). Stochastic accumulation of information in discrete time: Comparing exact results and Wald approximations.Journal of Mathematical Psychology,34, 229–236.CrossRefGoogle Scholar
- Smith, P. L. (1995). Psychophysically principled models of visual simple reaction time.Psychological Review,102, 567–593.CrossRefGoogle Scholar
- Smith, P. L., &Van Zandt, T. (in press). Time-dependent Poisson counter models of response latency in simple judgment.British Journal of Mathematical & Statistical Psychology.Google Scholar
- Smith, P. L., &Vickers, D. (1988). The accumulator model of two-choice discrimination.Journal of Mathematical Psychology,32, 135–168.CrossRefGoogle Scholar
- Smith, P. L., &Vickers, D. (1989). Modeling evidence accumulation with partial loss in expanded judgment.Journal of Experimental Psychology: Human Perception & Performance,15, 797–815.CrossRefGoogle Scholar
- Steiger, J. H. (1990). Structural model evaluation and modification: An interval estimation approach.Multivariate Behavioral Research,25, 173–180.CrossRefGoogle Scholar
- Stephens, M. A. (1983). Kolmogorov-Smirnov statistics. In S. Kotz & N. L. Johnson (Eds.),Encyclopedia of statistical sciences (Vol. 4, pp. 393–396). New York: Wiley.Google Scholar
- St. James, J. D., &Eriksen, C. W. (1992). Response competition produces a “fast same effect” in same-different judgments. In J. Pomerantz & G. Lockhead (Eds.),The perception of structure (pp. 157–168). Washington, DC: American Psychological Association.Google Scholar
- Stone, M. (1960). Models for choice reaction time.Psychometrika,25, 251–260.CrossRefGoogle Scholar
- Townsend, J. T. (1976). Serial and within-stage independent parallel model equivalence on the minimum completion time.Journal of Mathematical Psychology,14, 219–238.CrossRefGoogle Scholar
- Townsend, J. T., &Ashby, F. G. (1983).Stochastic modeling of elementary psychological processes. New York: Cambridge University Press.Google Scholar
- Van Zandt, T. (in press-a). How to fit a response time distribution.Psychonomic Bulletin & Review.Google Scholar
- Van Zandt, T. (in press-b). ROC curves and confidence judgments in recognition memory.Journal of Experimental Psychology: Learning, Memory, & Cognition.Google Scholar
- Van Zandt, T., &Ratcliff, R. (1995). Statistical mimicking of reaction time distributions: Mixtures and parameter variability.Psychonomic Bulletin & Review,2, 20–54.Google Scholar
- Vickers, D. (1970). Evidence for an accumulator model of psychophysical discrimination.Ergonomics,13, 37–58.CrossRefPubMedGoogle Scholar
- Vickers, D. (1979).Decision processes in visual perception. New York: Academic Press.Google Scholar
- Vickers, D., Caudrey, D., &Willson, R. J. (1971). Discriminating between the frequency of occurrence of two alternative events.Acta Psychologica,35, 151–172.CrossRefGoogle Scholar
- Ward, R., &McClelland, J. L. (1989). Conjunctive search for one and two identical targets.Journal of Experimental Psychology: Human Perception & Performance,15, 664–672.CrossRefGoogle Scholar