A Ballistic Model of Choice Response Time.

Brown, Scott; Heathcote, Andrew · 2005 · Psychological Review

DOI: 10.1037/0033-295x.112.1.117

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Summary

This paper introduces the Ballistic Accumulation (BA) model, a deterministic framework for explaining choice response times (RT) that challenges the prevailing stochastic accumulation models. While traditional models, such as the diffusion model and the leaky competitive accumulator, rely on within-trial stochastic noise to account for RT variability and the speed–accuracy trade-off (SAT), Brown and Heathcote argue that these complexities are unnecessary. They propose that a simplified, deterministic within-trial process, combined with between-trial variability in input strength and starting points, is sufficient to explain benchmark behavioral phenomena. The motivation stems from the desire to reduce model complexity and offer a distinct psychological interpretation where decisions are not viewed as sequential sampling processes but as ballistic trajectories. The BA model associates each choice response with a unit whose activation follows deterministic dynamics governed by input strength, passive leakage, and mutual competition. Crucially, the model incorporates two sources of between-trial variability: Gaussian noise in input strength and uniform variability in the starting point of accumulation. Unlike stochastic models, the accumulation trajectory within a single trial is smooth and deterministic. The authors derived analytical solutions for the two-choice case, showing that the model’s dynamics are governed by total leakage and the balance between leakage and competition. To validate the model, the authors fitted it to empirical data from Ratcliff and Rouder (1998), which included approximately 10,000 observations from three participants in a two-alternative forced-choice perceptual categorization task. This dataset represents an information-controlled paradigm, allowing for rigorous testing of the model’s ability to predict both RT distributions and accuracy. The results demonstrate that the BA model successfully accounts for the benchmark phenomena observed in the data, including the speed–accuracy trade-off and RT distributions for both correct and error responses. The model explains SAT by showing that increased integration time allows the input signal to overcome variability in starting points; however, asymptotic accuracy remains imperfect due to persistent variability in input strength. The fitted BA model exhibited "winner-takes-all" behavior driven by strong response competition, a dynamic distinct from the fitted stochastic versions of similar models. The authors found that the deterministic nature of the within-trial process did not hinder the model's fit, confirming that between-trial variability alone can generate the necessary RT variability. The significance of this work lies in its challenge to the assumption that within-trial stochasticity is essential for modeling decision processes. By demonstrating that a ballistic model can replicate the performance of more complex stochastic models, the authors suggest a fundamental shift in the psychological interpretation of choice RT. The BA model offers a simpler, analytically tractable alternative that retains explanatory power for both time-controlled and information-controlled paradigms. This finding implies that the variability in human decision-making may be largely attributable to trial-to-trial fluctuations in initial conditions and input strength, rather than moment-to-moment noise during evidence accumulation.

Key finding

A deterministic ballistic accumulation model with between-trial variability in starting points and rates can accurately account for choice response time data and benchmark phenomena previously explained only by stochastic models.

Methodology

theoretical

Provenance

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Topics

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• time perception