Drift-Diffusion Model (DDM)

Purpose

This skill encodes expert knowledge for applying drift-diffusion models (DDMs) to two-choice reaction time data. DDMs decompose observed accuracy and RT distributions into latent cognitive processes — evidence accumulation rate, response caution, and non-decision time. This skill guides researchers through model variant selection, parameter fitting, and result evaluation, encoding domain-specific judgment that requires specialized training in computational cognitive modeling.

When to Use This Skill

Designing a study where two-alternative forced choice (2AFC) RT data will be collected and you want to decompose behavior into latent cognitive components
Choosing between DDM variants (classic DDM, full DDM, EZ-diffusion, HDDM, LBA) for a given dataset and research question
Setting up model fitting: selecting fitting method, preparing data, configuring software tools
Evaluating model fit quality: checking parameter recovery, running posterior predictive checks, comparing nested models
Interpreting DDM parameters in terms of cognitive processes (e.g., drift rate as evidence quality, boundary separation as response caution)
Troubleshooting fitting problems: convergence failures, implausible parameter estimates, poor fits to RT quantiles

When NOT to Use This Skill

Tasks with more than two response options require multi-accumulator models (see Racing Diffusion Model or LBA in references/model-variants.md)
Go/No-Go tasks violate the two-boundary assumption; use single-boundary models or SSP models instead (Ratcliff et al., 2018)
Tasks where speed-accuracy tradeoff is not a meaningful dimension (e.g., pure accuracy tasks with unlimited time)
If you only need a coarse summary of RT effects and do not need process-level decomposition, standard ANOVA on mean RT may suffice

Research Planning Protocol

Before executing the domain-specific steps below, you MUST:

State the research question — What cognitive process decomposition question is this DDM addressing?
Justify the method choice — Why DDM (not simple RT analysis, Bayesian models, etc.)? What alternatives were considered?
Declare expected outcomes — Which parameter(s) do you expect to differ across conditions, and in what direction?
Note assumptions and limitations — What does the DDM assume (e.g., 2AFC, stationary drift)? Where could it mislead?
Present the plan to the user and WAIT for confirmation before proceeding.

For detailed methodology guidance, see the research-literacy skill.

⚠️ Verification Notice

This skill was generated by AI from academic literature. All parameters, thresholds, and citations require independent verification before use in research. If you find errors, please open an issue.

Core Concepts

What the DDM Models

The DDM assumes that on each trial, noisy evidence accumulates over time from a starting point toward one of two decision boundaries. The key insight: observed RT = decision time + non-decision time, and accuracy depends on which boundary is reached first (Ratcliff, 1978).

The Four Core Parameters

Parameter	Symbol	Cognitive Interpretation	Typical Range	Source
Drift rate	v	Quality/strength of evidence accumulation	0.1 – 5.0 (commonly 0.5–3.0)	Ratcliff & McKoon, 2008; Voss et al., 2004, Table 2
Boundary separation	a	Response caution (speed-accuracy tradeoff)	0.5 – 2.5 (commonly 0.8–2.0)	Ratcliff & McKoon, 2008; Voss et al., 2004, Table 2
Non-decision time	t0 (or Ter)	Encoding + motor execution time	0.1 – 0.6 s (commonly 0.2–0.5 s)	Ratcliff & McKoon, 2008; Matzke & Wagenmakers, 2009, Table 1
Starting point	z	Response bias (relative to boundaries)	a/2 (unbiased) ± 20%	Ratcliff & McKoon, 2008; Voss et al., 2013

Trial-to-Trial Variability Parameters (Full DDM)

Parameter	Symbol	Interpretation	Typical Range	Source
Drift rate variability	sv	Cross-trial variation in evidence quality	0 – 2.0	Ratcliff & McKoon, 2008
Starting point variability	sz	Cross-trial variation in bias	0 – 0.3 × a	Ratcliff & McKoon, 2008
Non-decision time variability	st0	Cross-trial variation in encoding/motor time	0 – 0.3 s	Ratcliff & McKoon, 2008

Decision Logic: Choosing a Model Variant

Step 1: Assess Your Research Question

Is the goal to decompose RT data into cognitive components?
├── YES → Continue to Step 2
└── NO → DDM may not be needed; consider simpler analyses

Step 2: Assess Data Characteristics

How many trials per condition do you have?
├── < 20 trials → Insufficient for any DDM variant (Ratcliff & Childers, 2015)
├── 20-40 trials → Use EZ-diffusion only (Wagenmakers et al., 2007)
├── 40-100 trials → Classic 4-parameter DDM or EZ-diffusion
├── 100-200 trials → Full DDM possible but fix some variability parameters
└── > 200 trials → Full DDM with all 7 parameters estimable

(Trial count thresholds: Ratcliff & Childers, 2015, simulation study)

Step 3: Choose Variant

Are you comparing groups or conditions at the population level?
├── YES, with moderate sample size (N > 15 participants)
│ └── Consider HDDM for hierarchical/Bayesian estimation (Wiecki et al., 2013)
├── YES, with large trial counts per person
│ └── Classic or Full DDM per participant, then group-level tests on parameters
└── Exploratory / individual differences focus
 └── HDDM or hierarchical Bayesian approach

How many response alternatives?
├── 2 → Standard DDM variants
├── > 2 → LBA or Racing Diffusion Model (see references/model-variants.md)
└── Go/No-Go → Single-boundary model (not covered here)

See references/model-variants.md for detailed comparison of all variants.

Step 4: Select Fitting Method

What variant did you choose?
├── EZ-diffusion → Closed-form solution, no fitting needed (Wagenmakers et al., 2007)
├── Classic/Full DDM → Use fast-dm (Voss & Voss, 2007) or PyDDM (Shinn et al., 2020)
│ ├── MLE: Best for large trial counts (>100 per condition)
│ ├── Chi-square: Robust for moderate trial counts (Ratcliff & Tuerlinckx, 2002)
│ └── Quantile-based (QMP): Most robust to outliers (Heathcote et al., 2002)
└── HDDM → Use HDDM Python package, Bayesian estimation (Wiecki et al., 2013)

See references/fitting-guide.md for the complete fitting workflow.

Fitting Workflow Summary

Data Preparation: Clean RTs, apply cutoffs (remove < 200 ms and > 3000-5000 ms; Ratcliff, 1993; Ratcliff & Tuerlinckx, 2002), code accuracy
Model Specification: Choose parameters to estimate vs. fix; decide which parameters vary across conditions
Parameter Estimation: Run fitting with chosen method and tool
Convergence Check: Verify optimizer converged; run multiple starting points
Model Comparison: Use BIC (for MLE-fitted models) or DIC/WAIC (for Bayesian; Spiegelhalter et al., 2002) to compare nested models
Posterior Predictive Check: Simulate data from fitted parameters; compare predicted vs. observed RT quantiles (Ratcliff & McKoon, 2008, Fig. 2)
Parameter Recovery: Simulate data with known parameters; verify your pipeline can recover them (Heathcote et al., 2015)

See references/fitting-guide.md for detailed guidance on each step.

Interpreting Parameters

Drift Rate (v)

Higher v = faster, more accurate decisions
Sensitive to: stimulus difficulty, attention, perceptual quality
Manipulations that typically affect v: stimulus contrast, coherence (motion dots), word frequency (Ratcliff et al., 2004)
If v is near 0 for a condition, participants are essentially guessing

Boundary Separation (a)

Higher a = more cautious (slower but more accurate)
Sensitive to: speed-accuracy instructions, emphasis conditions
Manipulations that typically affect a: speed vs. accuracy instruction (Ratcliff & McKoon, 2008), reward structure
If a changes across stimulus conditions (rather than instruction conditions), reconsider the model specification

Non-Decision Time (t0)

Reflects encoding + response execution time
Sensitive to: stimulus degradation, response modality (key press vs. voice)
Manipulations that typically affect t0: stimulus masking, response complexity (Ratcliff & McKoon, 2008)
If t0 > 0.5 s, check for unusually slow motor responses or task-specific encoding demands

Starting Point (z)

Reflects a priori bias toward one response
Sensitive to: prior probability, payoff asymmetry
When z = a/2, no bias; z > a/2 = bias toward upper boundary
Manipulations that typically affect z: unequal base rates, cue validity (Ratcliff & McKoon, 2008; Voss et al., 2004)

Common Pitfalls

Fitting too many free parameters with too few trials: The full 7-parameter DDM requires >200 trials per condition for stable estimates (Ratcliff & Childers, 2015). With fewer trials, fix variability parameters or use EZ-diffusion.
Ignoring RT outliers: Extremely fast (< 200 ms) or slow (> 3000–5000 ms) RTs likely reflect non-decision processes (guesses, lapses). Include these and they distort parameter estimates (Ratcliff, 1993; Ratcliff & Tuerlinckx, 2002). Apply cutoffs BEFORE fitting.
Not checking parameter recovery: Always simulate data with known parameters using your exact pipeline and verify you can recover them. Poor recovery means your results are uninterpretable (Heathcote et al., 2015; White et al., 2018).
Confusing drift rate and boundary effects: Speed-accuracy tradeoff instructions should primarily affect boundary separation (a), not drift rate (v). If both change, the model may be misspecified or the manipulation has multiple effects (Ratcliff & McKoon, 2008).
Using mean RT instead of full RT distributions: DDMs leverage the shape of the entire RT distribution. Analyzing only mean RT discards the information DDMs are designed to capture (Ratcliff, 1978; Wagenmakers et al., 2007).
Neglecting error RT distributions: Correct and error RT distributions are jointly constrained by the DDM. Fitting only correct RTs loses critical information about the generative process (Ratcliff & McKoon, 2008).
Treating HDDM posterior modes as point estimates: Bayesian models yield posterior distributions. Report and interpret the full posterior, including credible intervals, rather than treating the mode as a frequentist point estimate (Wiecki et al., 2013).

Key References

Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85(2), 59–108.
Ratcliff, R., & McKoon, G. (2008). The diffusion decision model: Theory and data for two-choice decision tasks. Neural Computation, 20(4), 873–922.
Wagenmakers, E.-J., van der Maas, H. L. J., & Grasman, R. P. P. P. (2007). An EZ-diffusion model for response time and accuracy. Psychonomic Bulletin & Review, 14(1), 3–22.
Voss, A., Nagler, M., & Lerche, V. (2013). Diffusion models in experimental psychology: A practical introduction. Experimental Psychology, 60(6), 385–402.
Wiecki, T. V., Sofer, I., & Frank, M. J. (2013). HDDM: Hierarchical Bayesian estimation of the drift-diffusion model in Python. Frontiers in Neuroinformatics, 7, 14.
See references/model-variants.md for DDM family details.
See references/fitting-guide.md for the complete fitting workflow.