Academic journal article Attention, Perception and Psychophysics

A Comparison of Two Diffusion Process Models in Accounting for Payoff and Stimulus Frequency Manipulations

Academic journal article Attention, Perception and Psychophysics

A Comparison of Two Diffusion Process Models in Accounting for Payoff and Stimulus Frequency Manipulations

Article excerpt

Published online: 6 June 2012

(Q> Psychonomic Society, Inc. 2012

Abstract I analyzed response time and accuracy data from a numerosity discrimination experiment in which both stimulus frequency and payoff structure were manipulated. The numerosity discrimination encompassed responding either "low" or "high" to the number of asterisks in a 10 × 10 grid, on the basis of an experimenter-determined decision cutoff (fixed at 50). In the stimulus frequency condition, there were more low than high stimuli in some blocks and more high than low stimuli in other blocks. In the payoff condition, responses were rewarded such that the relative value of a stimulus mimicked the relative frequency of that stimulus in the previous manipulation. I modeled the data using two sequential-sampling models in which evidence was accumulated until either a "low" or a "high" decision criterion was reached and a response was initiated: a single-stage diffusion model framework and a two-stage diffusion model framework. In using these two frameworks, the goal was to examine their relative merits across stimulus frequency and payoff structure manipulations. I found that shifts in starting point in a single-stage diffusion framework and shifts in the initial drift rate in the two-stage model were able to account for the data. I also found, however, that these two shifts across the two models produced similar changes in the random walk that described the decision process. In conclusion, I found that the similarities in the descriptions of the decision processes make it difficult to choose between the two models and suggested that such a choice should consider model assumptions and parameter estimate interpretations.

Keywords Response time * Diffusion model * Two-stage model * Payoff * Stimulus frequency

(ProQuest: ... denotes formula omitted.)

Studying the effects of payoff manipulations has been of long-standing interest in cognitive psychology (e.g., Edwards, 1965; Fitts, 1966). In manipulations involving payoffs mapped to two choices, for example, participants can be induced to favor the correct response alternative over the incorrect response because of a high reward (or a low cost) value associated with the correct response, or because of a high cost (or a low reward) value associated with the incorrect response. This type of manipulation is often implemented with a performancedriven, variable monetary reward to the participant (see Chiew & Braver, 2011; Dambacher, Hübner, & Schlösser, 2011, for recent studies of the factors that determine under what conditions monetary incentives enhance performance).

Consistent with the description above, Diederich and Busemeyer (2006) used a line length judgment to examine how sequential-sampling models might represent the effects of payoffs on mean response time (RT). They compared three hypotheses: bound change, in which only the starting position of the accumulation process is influenced by the payoffs, but the accumulation of information extracted from the stimuli is not (cf. Link & Heath, 1975); drift rate change, in which the payoffs influence the rate of information accumulation (cf. Ashby, 1983; Ratcliff, 1981); and two-stage processing, in which the decision process consists of two subprocesses, switching from one that processes payoffs to another that processes the stimulus (cf. Heath, 1981, 1992; Laming, 1968; Ratcliff, 1980). Diederich and Busemeyer found that two-stage processing provided a better account of the data than did either drift-rate change or bound change, suggesting that individuals initially process the payoff information, then switch to the stimulus information (p. 206; see also Busemeyer & Diederich, 2002; Diederich, 1995, 1997, 2008).

Like manipulations of payoffs, manipulations of stimulus frequency cause participants to alter their responses, now on the basis of the probability of occurrence of the stimulus, such that they are faster and more acciuate when responding to stimuli that appear more often than to those that appear less often (Falmagne, 1965; Jarvik, 1951; Kirby, 1976; Laming, 1969; Remington, 1969). …

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