Parameter identifiability in evidence-accumulation models: The effect of error rates on the diffusion decision model and the linear ballistic accumulator

Lüken, Malte; Heathcote, Andrew; Haaf, Julia M.; Matzke, Dóra · 2025 · Psychonomic Bulletin & Review

DOI: 10.3758/s13423-024-02621-1

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Summary

This study investigates parameter identifiability in evidence-accumulation models (EAMs), specifically the diffusion decision model (DDM) and the linear ballistic accumulator (LBA), focusing on how error rates affect the reliability of parameter estimates. While EAMs are widely used to decompose response time and accuracy data into cognitive components, their utility depends on the ability to uniquely estimate parameters from observed data. Previous research indicated that identifiability degrades at low error rates but lacked systematic comparisons across models. This paper addresses this gap by determining optimal error rate ranges for robust parameter recovery and explaining the mathematical mechanisms behind identifiability issues. The authors conducted three simulation studies using synthetic data generated from empirically observed parameter distributions. They manipulated error rates (ranging from 0% to 50%) and trial numbers (150 to 1200 trials) across simple designs, difficulty manipulations, and speed-accuracy trade-off instructions. Parameter estimation was performed using Bayesian differential-evolution Markov chain Monte Carlo sampling. Identifiability was assessed by comparing estimated parameters to true data-generating values using root mean squared deviation (RMSD) and Pearson correlations, while parameter trade-offs were analyzed via pairwise and partial correlations within posterior distributions. Results demonstrated that both models suffer from poor identifiability at low error rates, though the DDM performed better than the LBA. In the DDM, estimates for decision threshold ($a$) and drift rate ($v$) increasingly overestimated true values as error rates dropped, driven by a near-perfect positive correlation between these parameters at low error rates. This trade-off allows simultaneous increases in $a$ and $v$ to produce identical model predictions. The LBA exhibited more extreme correlations and poorer recovery overall, particularly for threshold and drift parameters. Increasing the number of trials improved identifiability for both models, but the DDM maintained superior performance even with fewer trials in speed-accuracy designs. The study concludes that experimental designs should aim for error rates between 15% and 35% for small sample sizes and between 5% and 35% for large sample sizes to ensure reliable parameter estimation. The authors attribute identifiability failures to high correlations between decision-threshold and accumulation-rate parameters, which create ambiguous solutions when error data is scarce. These findings provide concrete guidelines for experimental design in cognitive psychology, warning against interpreting parameters from datasets with extremely low error rates and highlighting the DDM’s relative robustness compared to the LBA under such conditions.

Key finding

Low error rates cause poor parameter identifiability in both the diffusion decision model and the linear ballistic accumulator due to parameter trade-offs, with the diffusion decision model showing superior recovery properties.

Methodology

simulation_modeling

Provenance

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• dbq psychometrics