Estimating across-trial variability parameters of the Diffusion Decision Model: Expert advice and recommendations

Boehm, Udo; Annis, Jeffrey; Frank, Michael J.; Hawkins, Guy E.; Heathcote, Andrew; Kellen, David; Krypotos, Angelos‐Miltiadis; Lerche, Veronika; Logan, Gordon D.; Palmeri, Thomas J.; Ravenzwaaij, Don van; Servant, Mathieu; Singmann, Henrik; Starns, Jeffrey J.; Voß, Andreas; Wiecki, Thomas V.; Matzke, Dóra; Wagenmakers, Eric‐Jan · 2018 · Journal of Mathematical Psychology

DOI: 10.1016/j.jmp.2018.09.004

archive: archived pipeline: cataloged verified

Get this paper ↗ (DOI — opens at the source; we link to it, we don't host it)

Summary

This paper addresses the challenge of estimating across-trial variability parameters in the Diffusion Decision Model (DDM), a widely used framework for analyzing response time and accuracy data. While the DDM’s main parameters (boundary separation, drift rate, starting point, and non-decision time) are generally well-established, estimating the variability of these parameters across trials is difficult yet crucial for accurately modeling response time distributions, particularly error responses. Previous research indicated that these variability parameters often exhibit low retest reliability and are poorly constrained by data, especially in designs with limited trials, such as those common in functional neuroimaging. To provide expert guidance, the authors conducted a collaborative project inviting researchers from the DDM community to apply their preferred fitting methods to simulated datasets and offer recommendations. The study utilized three synthetic datasets of increasing complexity, generated using the `rtdists` R package. Level 1 involved a single participant with 1,000 trials per condition, where main DDM parameters were known, isolating the estimation of variability parameters. Level 2 also involved a single participant with 1,000 trials per condition but required estimating all DDM parameters from the data. Level 3 simulated data for 20 participants, allowing for the assessment of hierarchical Bayesian methods that pool data across individuals to estimate group-level variability parameters. Nine groups of collaborators applied various estimation techniques, including conventional maximum likelihood methods and hierarchical Bayesian approaches (using software like HDDM, JAGS, and Stan). Collaborators provided parameter estimates, measures of uncertainty (e.g., 95% highest density intervals), and practical advice on overcoming estimation difficulties. The results demonstrated that all estimation methods could accurately recover across-trial variability in non-decision time ($s_{Ter}$). However, estimates for across-trial variability in drift rate ($s_v$) and starting point ($s_z$) were associated with large uncertainty and frequently missed the true parameter values by a wide margin. This difficulty persisted even when using hierarchical Bayesian methods, which theoretically leverage group data to improve individual estimates. The authors noted that while main DDM parameters were estimated with high precision, the variability parameters remained challenging due to the limited information provided by error response times, which are often sparse. The significance of this work lies in its provision of a comprehensive reference resource for researchers using the DDM. It highlights that while across-trial variability in non-decision time is robustly estimable, variability in drift rate and starting point requires careful handling. The authors recommend that prior restrictions on parameters can improve estimation performance and that users should be cautious when interpreting variability estimates, particularly in studies with limited trial counts. By synthesizing expert advice and empirical results from multiple fitting methods, the paper offers practical solutions and warnings for navigating the complexities of DDM parameter estimation in real-world applications.

Key finding

Estimation methods accurately recovered across-trial variability in non-decision time, but estimates for across-trial variability in drift rate and starting point were associated with considerable uncertainty and often deviated significantly from true values.

Methodology

simulation_modeling

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.

Summary generated by qwen3.6-27b-prismaquant on 2026-06-10; verification: verified.

Topics

Ranked by relevance to this paper. Hover a topic for its definition.

• expert witness methodology