Abstract
Recently, Diederich and Busemeyer (2006) evaluated three hypotheses formulated as particular versions of a sequential-sampling model to account for the effects of payoffs in a perceptual decision task with time constraints. The bound-change hypothesis states that payoffs affect the distance of the starting position of the decision process to each decision bound. The drift-rate-change hypothesis states that payoffs affect the drift rate of the decision process. The two-stage-processing hypothesis assumes two processes, one for processing payoffs and another for processing stimulus information, and that on a given trial, attention switches from one process to the other. The latter hypothesis gave the best account of their data. The present study investigated two questions: (1) Does the experimental setting influence decisions, and consequently affect the fits of the hypotheses? A task was conducted in two experimental settings—either the time limit or the payoff matrix was held constant within a given block of trials, using three different payoff matrices and four different time limits—in order to answer this question. (2) Could it be that participants neglect payoffs on some trials and stimulus information on others? To investigate this idea, a further hypothesis was considered, the mixture-of-processes hypothesis. Like the two-stage-processing hypothesis, it postulates two processes, one for payoffs and another for stimulus information. However, it differs from the previous hypothesis in assuming that on a given trial exactly one of the processes operates, never both. The present design had no effect on choice probability but may have affected choice response times (RTs). Overall, the two-stage-processing hypothesis gave the best account, with respect both to choice probabilities and to observed mean RTs and mean RT patterns within a choice pair.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ashby, F. G. (1983). A biased random walk model for two choice reaction times. Journal of Mathematical Psychology, 27, 277–297.
Bohil, C. J., & Maddox, W. T. (2003). A test of the optimal classifier’s independence assumption in perceptual categorization. Perception & Psychophysics, 65, 478–493.
Busemeyer, J. R., & Diederich, A. (2002). Survey of decision field theory. Mathematical Social Sciences, 43, 345–370.
Diederich, A. (1995). Intersensory facilitation of reaction time: Evaluation of counter and diffusion coactivation models. Journal of Mathematical Psychology, 39, 197–215.
Diederich, A. (1997). Dynamic stochastic models for decision making under time constraints. Journal of Mathematical Psychology, 41, 260–274.
Diederich, A. (2003a). Decision making under conflict: Decision time as a measure of conflict strength. Psychonomic Bulletin & Review, 10, 167–175.
Diederich, A. (2003b). MDFT account of decision making under time pressure. Psychonomic Bulletin & Review, 10, 157–166.
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.
Diederich, A., & Busemeyer, J. R. (2006). Modeling the effects of payoff on response bias in a perceptual discrimination task: Bound-change, drift-rate-change, or two-stage-processing hypothesis. Perception & Psychophysics, 68, 194–207.
Edwards, W. (1965). Optimal strategies for seeking information: Models for statistics, choice reaction times, and human information processing. Journal of Mathematical Psychology, 2, 312–329.
Green, D. M., Smith, A. F., & von Gierke, S. M. (1983). Choice reaction time with a random foreperiod. Perception & Psychophysics, 34, 195–208.
Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics. New York: Wiley.
Heath, R. A. (1981). A tandem random walk model for psychological discrimination. British Journal of Mathematical & Statistical Psychology, 34, 76–92.
Heath, R. A. (1992). A general nonstationary diffusion model for two-choice decision-making. Mathematical Social Sciences, 23, 283–309.
Karlin, S., & Taylor, H. M. (1975). A first course in stochastic processes (2nd ed.). New York: Academic Press.
Laming, D. R. J. (1968). Information theory of choice-reaction times. London: Academic Press.
Link, S. W., & Heath, R. A. (1975). A sequential theory of psychological discrimination. Psychometrika, 40, 77–105.
Luce, R. D. (1986). Response times: Their role in inferring elementary mental organization. New York: Oxford University Press.
Maddox W. T. (2002). Toward a unified theory of decision criterion learning in perceptual categorization. Journal of the Experimental Analysis of Behavior, 78, 567–595.
Maddox, W. T., & Bohil, C. J. (2004). Probability matching, accuracy maximization, and a test of the optimal classifier’s independence assumption in perceptual categorization. Perception & Psychophysics, 66, 104–118.
Maddox, W. T., & Dodd J. L. (2001). On the relation between base-rate and cost-benefit learning in simulated medical diagnosis. Journal of Experimental Psychology: Learning, Memory, & Cognition, 27, 1367–1384.
Navarro, D. J., Pitt, M. A., & Myung, I. J. (2004). Assessing the distinguishability of models and the informativeness of data. Cognitive Psychology, 49, 47–84.
Pfanzagl, J. (1978). Allgemeine Methodenlehre der Statistik (Vol. 2). Berlin: Walter de Gruyter.
Rapoport, A., & Burkheimer, G. J. (1971). Models for deferred decision making. Journal of Mathematical Psychology, 8, 508–538.
Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85, 59–108.
Ratcliff, R. (1980). A note on modeling accumulation of information when the rate of accumulation changes over time. Journal of Mathematical Psychology, 21, 178–184.
Ratcliff, R. (1981). A theory of order relations in perceptual matching. Psychological Review, 88, 552–572.
Ratcliff, R. (2006). Modeling response signal and response time data. Cognitive Psychology, 53, 195–237.
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.
Ruthruff, E. (1996). A test of the deadline model for speed-accuracy tradeoffs. Perception & Psychophysics, 58, 56–64.
Swensson, R. G. (1972). The elusive tradeoff: Speed vs. accuracy in visual discrimination tasks. Perception & Psychophysics, 12, 16–32.
Swets, J. A., Tanner, W. P., Jr., & Birdsall, T. G. (1961). Decision processes in perception. Psychological Review, 68, 301–340.
Townsend, J. T., & Ashby, F. G. (1983). The stochastic modeling of elementary psychological processes. Cambridge: Cambridge University Press.
Tuckwell, H. C. (1995). Elementary applications of probability theory: With an introduction to stochastic differential equations (2nd ed.). London: Chapman & Hall.
Wagenmakers, E.-J., Ratcliff, R., Gomez, P., & Iverson, G. J. (2004). Assessing model mimicry using the parametric bootstrap. Journal of Mathematical Psychology, 48, 28–50.
Yellott, J. I. (1971). Correction for fast guessing and the speed-accuracy tradeoff in choice reaction time. Journal of Mathematical Psychology, 8, 159–199.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by Deutsche Forschungsgemeinschaft Grant Di 506/8-3.
Rights and permissions
About this article
Cite this article
Diederich, A. A further test of sequential-sampling models that account for payoff effects on response bias in perceptual decision tasks. Perception & Psychophysics 70, 229–256 (2008). https://doi.org/10.3758/PP.70.2.229
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.3758/PP.70.2.229