Academic journal article Perception and Psychophysics

A Further Test of Sequential-Sampling Models That Account for Payoff Effects on Response Bias in Perceptual Decision Tasks

Academic journal article Perception and Psychophysics

A Further Test of Sequential-Sampling Models That Account for Payoff Effects on Response Bias in Perceptual Decision Tasks

Article excerpt

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.

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What affects response bias? How can response bias be separated from discriminability? An answer to these questions is usually provided by signal detection theory: Response bias is separated from discriminability on the basis of the observed hit and false alarm rates, and the response bias parameter is assumed to be influenced by the prior probability of the signal, as well as by the payoffs for each type of error (Green & Swets, 1966; Swets, Tanner, & Birdsall, 1961; see Maddox, 2002, for a review of numerous tests of these assumptions). A major limitation of the classic signal detection model is that it provides a static (fixed-sample) description of the decision process, and is therefore unable to simultaneously account for choice and response time (RT). Sequential-sampling models (e.g., Laming, 1968; Link & Heath, 1975; Ratcliff, 1978) provide a dynamic extension of signal detection theory that elegantly accounts for the systematic relations between choice and RT. Like the classic signal detection model, sequential-sampling models make a distinction between discriminability and response bias, but they can account for speed-accuracy trade-offs as well. Yet whereas the effects of prior probability on response bias have been examined (see, e.g., Green, Smith, & von Gierke, 1983), the effects of payoffs have rarely been studied within the sequential-sampling framework. Only recently did Diederich and Busemeyer (2006) investigate how payoffs affect response bias in sequential-sampling models of perceptual decision making. They showed how three different hypotheses incorporate response biases into a sequential-sampling decision process. These three hypotheses are as follows.

The bound-change hypothesis states that payoffs affect the distance of the starting position of the decision process to each decision bound. This idea goes back to Edwards (1965; see also Rapoport & Burkheimer, 1971), who derived the optimal stopping rule for the sequentialsampling model-that is, the stopping rule that maximizes expected payoff. …

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