A comparison of two diffusion process models in accounting for payoff and stimulus frequency manipulations

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.