Modeling Numerosity Representation With an Integrated Diffusion Model

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Models of the representation of numerosity information used in discrimination tasks are integrated with a diffusion decision model. The representation models assume distributions of numerosity either with means and SD that increase linearly with numerosity or with means that increase logarithmically with constant SD. The models produce coefficients that are applied to differences between two numerosities to produce drift rates and these drive the decision process. The linear and log models make differential predictions about how response time (RT) distributions and accuracy change with numerosity and which model is successful depends on the task. When the task is to decide which of two side-by-side arrays of dots has more dots, the log model fits decreasing accuracy and increasing RT as numerosity increases. When the task is to decide, for dots of two colors mixed in a single array, which color has more dots, the linear model fits decreasing accuracy and decreasing RT as numerosity increases. For both tasks, variables such as the areas covered by the dots affect performance, but if the task is changed to one in which the subject has to decide whether the number of dots in a single array is more or less than a standard, the variables have little effect on performance. Model parameters correlate across tasks suggesting commonalities in the abilities to perform them. Overall, results show that the representation used depends on the task and no single representation can account for the data from all the paradigms.

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