The overconstraint of response time models: Rethinking the scaling problem
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Summary
This paper addresses a fundamental methodological issue in the application of evidence accumulation (sequential sampling) models to choice response time (RT) data. The authors argue that these models, which dominate the field of cognitive psychology, suffer from a mathematical "scaling property" where multiplying a subset of parameters by a constant does not change model predictions. To resolve this identifiability issue, researchers must fix one parameter. The authors contend that the field has universally adopted an "overconstrained" approach by not only fixing a scaling parameter but also holding it constant across all experimental conditions. This practice imposes implicit, untested psychological assumptions that unnecessarily restrict the models' ability to account for empirical data. To demonstrate the impact of this overconstraint, the authors reanalyzed data from Gould, Wolfgang, and Smith (2007), who investigated stimulus detection under varying contrast levels. They compared two major classes of evidence accumulation models: the single-accumulator diffusion model and the multiple-accumulator linear ballistic accumulator (LBA) model. In the conventional approach, the diffusion coefficient (for the diffusion model) or the sum of drift rates (for the LBA) was fixed across all five contrast conditions. The authors then applied a "minimally constrained" approach, where the scaling parameter was fixed in only one condition (e.g., the highest contrast or easiest condition) and freely estimated in the others. Model fits were evaluated using quantile probability plots and the Bayesian Information Criterion (BIC), which penalizes model complexity. The results showed that the conventionally constrained models provided poor accounts of the data. Specifically, the diffusion model underpredicted the shift in RT distributions across conditions, while the LBA failed to capture faster errors in easy conditions. In contrast, the minimally constrained versions of both models significantly improved the fit to the data. The BIC analysis indicated strong evidence favoring the minimally constrained models, demonstrating that the improvement in fit outweighed the penalty for adding four additional parameters. The minimally constrained diffusion model better predicted the RT shifts and reduced extreme skewness for difficult decisions, while the minimally constrained LBA better accommodated fast errors. Furthermore, the estimated scaling parameters decreased with decreasing stimulus contrast, suggesting a dependency between decision signal and noise that the conventional approach obscured. The significance of these findings lies in challenging the standard practice of fixing scaling parameters across conditions. The authors conclude that this overconstraint is not theoretically justified and can lead to misleading psychological interpretations, such as assuming that evidence variability is independent of the mean rate of accumulation. By adopting minimal constraints, researchers can achieve better model fits and more accurate psychological inferences. The authors assert that this issue applies to all evidence accumulation models, including variants of the leaky competing accumulator and Poisson counter models, urging the field to rethink how scaling problems are handled to avoid implicit assumptions that limit model utility.
Key finding
Allowing scaling parameters in evidence accumulation models to vary across experimental conditions, rather than fixing them conventionally, yields significantly better fits to response time data.
Methodology
theoretical
Provenance
The full processing record for this entry. Every stage of this paper's journey through the pipeline is logged — what ran, with which tool and model, how many attempts it took, and when it last completed. Discovered via author_sweep_intake on 2026-05-28.
| Stage | Outcome | Tool | Model | Prompt | Attempts | Completed |
|---|---|---|---|---|---|---|
| discover | success | author_sweep | — | — | 2 | 2026-05-28 |
| archive | success | canonical_url | — | — | 1 | 2026-06-04 |
| extract | success | cached | — | — | 3 | 2026-06-10 |
| clean | success | clean | — | — | 1 | 2026-06-04 |
| chunk | success | chunk | — | — | 1 | 2026-06-04 |
| embed | success | embed | Qwen/Qwen3-Embedding-8B | — | 1 | 2026-06-04 |
| enrich | failed | — | — | — | 4 | 2026-07-02 |
| promote | success | — | — | — | 1 | 2026-06-04 |
| summarize | success | llm | qwen3.6-27b-prismaquant | summ-v5 | 2 | 2026-06-10 |
| tag | success | vector_similarity | — | — | 15 | 2026-06-11 |
| verify | success | — | — | — | 2 | 2026-06-10 |
Summary generated by qwen3.6-27b-prismaquant on 2026-06-10; verification: verified.
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