Abstract
One of the most prominent response-time models in cognitive psychology is the diffusion model, which assumes that decision-making is based on a continuous evidence accumulation described by a Wiener diffusion process. In the present paper, we examine two basic assumptions of standard diffusion model analyses. Firstly, we address the question of whether participants adjust their decision thresholds during the decision process. Secondly, we investigate whether so-called Lévy-flights that allow for random jumps in the decision process account better for experimental data than do diffusion models. Specifically, we compare the fit of six different versions of accumulator models to data from four conditions of a number-letter classification task. The experiment comprised a simple single-stimulus task and a more difficult multiple-stimulus task that were both administered under speed versus accuracy conditions. Across the four experimental conditions, we found little evidence for a collapsing of decision boundaries. However, our results suggest that the Lévy-flight model with heavy-tailed noise distributions (i.e., allowing for jumps in the accumulation process) fits data better than the Wiener diffusion model.
Highlights
The diffusion model was introduced four decades ago as a tool to analyze response-time data (Ratcliff, 1978)
It solves a central problem of measuring cognitive performance with response-time tasks: In typical experimental tasks, performance spreads over two metrics, i.e., response latencies and accuracy rates
The present study aimed at comparing the ability of six variants of accumulator models to account for data from four variants of a number-letter classification task: In this paradigm, either one stimulus had to be categorized as a number or a letter or it had to be assessed whether the majority of 16 simultaneously presented moving stimuli were letters or numbers
Summary
The diffusion model was introduced four decades ago as a tool to analyze response-time data (Ratcliff, 1978). Only in the last two decades has the model become widely popular in cognitive psychology (Voss, Nagler, & Lerche, 2013). The diffusion model proved to be a useful tool to test specific psychological hypotheses. Most importantly, it solves a central problem of measuring cognitive performance with response-time tasks: In typical experimental tasks, performance spreads over two metrics, i.e., response latencies and accuracy rates. A diffusion-model analysis solves this problem by providing independent measures for performance and for the adopted speed-accuracy setting (Spaniol, Madden, & Voss, 2006). A third reason for the popularity of the diffusion model is the strong assocation of the model's architecture with neural processes (Gold & Shadlen, 2007)
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