The simplest complete model of choice response time: Linear ballistic accumulation
DOI: 10.1016/j.cogpsych.2007.12.002
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Summary
This paper introduces the Linear Ballistic Accumulator (LBA) model, a simplified theoretical framework for modeling choice response times (RT) and decision-making. The authors address the historical trade-off in cognitive psychology between model complexity and completeness. While previous sequential sampling models, such as the diffusion model or leaky competing accumulator, are complex and often restricted to binary choices, simpler models often fail to account for empirical phenomena like the distribution of error responses. The LBA aims to provide the simplest complete model that accommodates both binary and multiple-choice scenarios while maintaining analytical tractability. The LBA model posits that decisions are made by independent evidence accumulators racing toward a common response threshold. Unlike stochastic models, evidence accumulation in the LBA is linear and deterministic (ballistic) within a trial. Variability in response times and choices arises solely from between-trial randomness in two parameters: the starting point of evidence accumulation, drawn from a uniform distribution, and the drift rate (speed of accumulation), drawn from a normal distribution. The first accumulator to reach the threshold determines the response and the decision time. This architecture allows for closed-form analytic solutions for choices involving any number of alternatives, a significant advantage over models restricted to two options. The authors validate the LBA by fitting it to data from five previously published experiments, including lexical decision tasks, brightness discrimination, and absolute identification tasks. In lexical decision experiments, the LBA successfully modeled response accuracy and the shapes of RT distributions for both correct and incorrect responses using fewer parameters than the diffusion model. Specifically, the model accounted for "fast errors" (where incorrect responses are faster than correct ones) by setting the response threshold near the upper limit of the start-point distribution. Conversely, it explained "slow errors" in accuracy-emphasis conditions by setting the threshold well above the start-point distribution, allowing drift rate variability to dominate. The model also accurately predicted speed-accuracy trade-off curves and extended effectively to a ten-alternative absolute identification task, demonstrating its utility in multiple-choice contexts. The significance of the LBA lies in its balance of simplicity and descriptive power. It resolves the inadequacies of earlier simplified models, which often produced unrealistic predictions for error response times, while avoiding the computational complexity of stochastic sequential sampling models. By providing analytic solutions for multiple alternatives, the LBA opens new avenues for modeling complex decision-making processes. The results suggest that linear, independent accumulation is sufficient to explain a wide range of empirical phenomena in choice RT, challenging the necessity of more complex mechanisms like mutual inhibition or within-trial stochasticity.
Key finding
The linear ballistic accumulator model provides a simple, analytically tractable account of choice response times that successfully fits empirical data from binary and multiple-choice tasks, including complex patterns of fast and slow errors.
Methodology
modeling
Provenance
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| Stage | Outcome | Tool | Model | Prompt | Attempts | Completed |
|---|---|---|---|---|---|---|
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| verify | success | — | — | — | 2 | 2026-06-10 |
Summary generated by qwen3.6-27b-prismaquant on 2026-06-10; verification: verified.
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