AI agent skill · by @NeuroAIHub

Evidence Accumulation Selector

Advises on when to use DDM vs. LBA vs. race models for choice-RT data based on experimental design and research goals

Archived 2026-10-23 · Source updated 2026-10-02 · License: AGPL-3.0. Check the original repository for the latest version.

SKILL.md instructions

# Evidence Accumulation Model Selector

## Purpose

This skill encodes expert knowledge for selecting among evidence accumulation models (EAMs) when analyzing choice response-time (RT) data. A competent programmer without cognitive science training would typically analyze only mean RT and accuracy separately, missing the critical insight that RT distributions and speed-accuracy tradeoffs carry rich information about latent cognitive processes. Selecting the wrong EAM -- or applying one when the data violate its assumptions -- leads to uninterpretable or misleading parameter estimates.

## When to Use

Use this skill when:

- You have choice-time data (both accuracy and full RT distributions, not just means)
- You want to decompose observed performance into latent cognitive processes (evidence quality, response caution, non-decision time)
- You need to distinguish speed-accuracy tradeoff effects from genuine sensitivity changes
- You are deciding which model class (DDM, LBA, EZ-diffusion, race model) is appropriate for your experimental design

Do **not** use this skill when:

- You only have accuracy data without RTs (use signal detection theory instead)
- RTs are from simple detection (single response option) rather than choice tasks
- The task involves continuous tracking or free response without discrete choice points

## Research Planning Protocol

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

1. **State the research question** -- What specific question is this analysis/paradigm addressing?
2. **Justify the method choice** -- Why is this approach appropriate? What alternatives were considered?
3. **Declare expected outcomes** -- What results would support vs. refute the hypothesis?
4. **Note assumptions and limitations** -- What does this method assume? Where could it mislead?
5. **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](https://github.com/HaoxuanLiTHUAI/awesome_cognitive_and_neuroscience_skills/issues).

## Core Concepts: What EAMs Do

All evidence accumulation models share a common framework: on each trial, noisy evidence is accumulated over time until a decision boundary is reached, triggering a response. The models differ in their assumptions about accumulation architecture.

### Key Parameters Across Models

| Parameter | Cognitive Interpretation | Typical Manipulation |
|-----------|------------------------|---------------------|
| **Drift rate (v)** | Quality/rate of evidence extraction | Stimulus difficulty, S/N ratio (Ratcliff & McKoon, 2008) |
| **Boundary separation (a)** | Speed-accuracy tradeoff / response caution | Speed vs. accuracy instructions (Ratcliff & Rouder, 1998) |
| **Non-decision time (Ter / t0)** | Encoding + motor execution time | Response modality, stimulus quality (Ratcliff & McKoon, 2008) |
| **Starting point (z)** | Prior bias toward one response | Prior probability, payoff asymmetry (Ratcliff, 1985) |
| **Drift rate variability (eta/sv)** | Across-trial variability in evidence quality | Individual or item differences (Ratcliff, 1978) |
| **Non-decision time variability (st0)** | Variability in encoding/motor processes | (Ratcliff & Tuerlinckx, 2002) |

## Decision Tree: Selecting a Model

```
How many response alternatives does the task have?
|
+-- TWO alternatives
| |
| +-- Do you need full distributional analysis?
| | |
| | +-- YES --> Do you have sufficient trial counts (>50/condition)?
| | | |
| | | +-- YES --> Use the FULL DIFFUSION MODEL (DDM)
| | | | (Ratcliff, 1978; Ratcliff & McKoon, 2008)
| | | |
| | | +-- NO (fewer trials) --> Use EZ-DIFFUSION
| | | (Wagenmakers et al., 2007)
| | |
| | +-- NO (means/summaries sufficient)
| | --> Use EZ-DIFFUSION for simplicity
| | (Wagenmakers et al., 2007)
| |
| +-- Is response bias (starting point) a key research question?
| |
| +-- YES --> Use FULL DDM with z parameter free
| | (Ratcliff, 1985; White & Poldrack, 2014)
| |
| +-- NO --> DDM with z fixed at a/2 (unbiased)
|
+-- MORE THAN TWO alternatives
| |
| +-- Use the LINEAR BALLISTIC ACCUMULATOR (LBA)
| | (Brown & Heathcote, 2008)
| | or RACING DIFFUSION MODEL
| | (Tillman et al., 2020)
| |
| +-- Do accumulators need to be independent?
| |
| +-- YES --> LBA (independent accumulators by design)
| |
| +-- NO (competition matters) --> Racing diffusion
| or leaky competing accumulator (LCA; Usher & McClelland, 2001)
|
+-- SPECIAL CASES
 |
 +-- Extremely fast RTs (<200 ms median)?
 | --> EAMs are likely inappropriate; these may be anticipatory
 | responses (Luce, 1986)
 |
 +-- No speed pressure at all (untimed)?
 | --> EAMs are inappropriate; use accuracy-based models
 |
 +-- Go/no-go task?
 --> Use the DDM with absorbing boundary modifications
 or the SSRT framework (Verbruggen & Logan, 2008)
```

## Model Descriptions

### Drift Diffusion Model (DDM)

The canonical EAM for two-choice tasks (Ratcliff, 1978; Ratcliff & McKoon, 2008).

**Architecture**: A single accumulator drifts between two absorbing boundaries. Evidence for option A moves the process toward the upper boundary; evidence for option B moves it toward the lower boundary.

**Full DDM parameters** (7 parameters; Ratcliff & Tuerlinckx, 2002):

| Parameter | Symbol | Typical Range | Role |
|-----------|--------|---------------|------|
| Drift rate | v | -5 to 5 (Ratcliff & McKoon, 2008) | Evidence quality |
| Boundary separation | a | 0.5 to 2.5 (Ratcliff & McKoon, 2008) | Response caution |
| Non-decision time | Ter | 0.1 to 0.5 s (Ratcliff & McKoon, 2008) | Encoding + motor |
| Starting point | z | 0 to a (typically a/2) | Prior bias |
| Drift variability | eta (sv) | 0 to 2 (Ratcliff, 1978) | Cross-trial drift noise |
| Starting point variability | sz | 0 to a | Cross-trial bias noise |
| Non-decision variability | st0 | 0 to 0.3 s | Cross-trial Ter noise |

**When to use DDM**:
- Two-choice tasks with speed-accuracy tradeoff
- At least **40-50 trials per condition** for the full model (Ratcliff & Childers, 2015), though **200+ recommended** for stable individual parameter estimates (Lerche et al., 2017)
- RTs in the typical range: **200 ms to 2000 ms** (Ratcliff & McKoon, 2008)

**Key assumption**: Only two response options. The DDM cannot natively handle >2 choices.

### EZ-Diffusion

A simplified closed-form estimator for three DDM parameters (Wagenmakers et al., 2007).

**Estimated parameters**: v (drift rate), a (boundary separation), Ter (non-decision time).

**Input**: Only three summary statistics per condition -- mean RT for correct responses (MRT), variance of RT for correct responses (VRT), and accuracy (Pc).

**Closed-form equations** (Wagenmakers et al., 2007, Eq. 1-3; see `references/ez-diffusion-formulas.md`):

**When to use EZ-diffusion**:
- Quick exploration before committing to full DDM fitting
- Low trial counts where full DDM is unstable (as few as **~10 trials per condition**; Wagenmakers et al., 2007)
- When only summary-level data are available (e.g., published means and variances)
- When the research question does not require starting point bias or cross-trial variability parameters

**Limitations**:
- Assumes no starting point variability (sz = 0) and no cross-trial drift variability (sv = 0)
- Cannot estimate response bias
- The "edge correction" is needed when accuracy is 0.5 or 1.0 (Wagenmakers et al., 2007)

### Linear Ballistic Accumulator (LBA)

A multi-alternative accumulator model (Brown & Heathcote, 2008).

**Architecture**: N independent linear accumulators (one per response option) race to a common threshold. The first accumulator to reach threshold triggers the corresponding response. Accumulation is ballistic (no within-trial noise) -- all variability comes from across-trial variation in drift rates and starting points.

**Parameters per accumulator** (Brown & Heathcote, 2008):

| Parameter | Symbol | Role |
|-----------|--------|------|
| Mean drift rate | vi | Evidence accumulation rate for option i |
| Drift rate variability | s | Across-trial standard deviation of drift (often fixed to 1 for scaling) |
| Response threshold | b | Evidence needed to trigger response |
| Maximum starting point | A | Upper bound of uniform start-point distribution [0, A] |
| Non-decision time | t0 | Encoding + motor time |

**When to use LBA**:
- Tasks with **2 or more** response alternatives (Brown & Heathcote, 2008)
- When you need a mathematically tractable multi-choice model
- When accumulators can be assumed independent (no lateral inhibition)
- Minimum **~100 trials per condition** recommended (Donkin et al., 2011)

### Race Models

**Classical race model** (Pike, 1966; Townsend & Ashby, 1983): Multiple accumulators race independently; first to finish wins. Unlike DDM, there is no competition between accumulators.

**When to use**:
- As a baseline/null model to test against more complex models
- When inhibitory competition between responses is not theoretically expected

**Limitation**: The standard race model cannot account for speed-accuracy tradeoff without additional assumptions (Ratcliff & McKoon, 2008).

## Model Comparison Methods

When comparing model fits, use information criteria that penalize complexity:

| Method | When to Use | Citation |
|--------|-------------|----------|
| **BIC** | Frequentist model comparison; favors parsimony; appropriate for large N | Schwarz, 1978 |
| **AIC** | Less conservative than BIC; better for prediction | Akaike, 1974 |
| **DIC** | Bayesian hierarchical models (e.g., HDDM) | Spiegelhalter et al., 2002 |
| **WAIC** | Bayesian; more stable than DIC for hierarchical models | Watanabe, 2010 |
| **Bayes factor** | Direct comparison of model evidence; interpretable strength | Kass & Raftery, 1995 |

**Preferred approach**: Fit competing models and compare using WAIC or Bayes factors in a Bayesian framework (Annis et al., 2017). Lower WAIC = better fit.

## Parameter Recovery Check

Before interpreting fitted parameters, **always** conduct a parameter recovery study (Heathcote et al., 2015):

1. Simulate data from known parameter values matching your design
2. Fit the model to simulated data
3. Check that recovered parameters correlate highly (r > 0.90) with generating parameters
4. If recovery fails, the model is too complex for your data or trial counts are insufficient

## Software Recommendations

| Software | Model | Language | Citation |
|----------|-------|----------|----------|
| **HDDM** | DDM (hierarchical Bayesian) | Python | Wiecki et al., 2013 |
| **fast-dm** | DDM (frequentist, fast) | C / R wrapper | Voss & Voss, 2007 |
| **EZ-diffusion** | EZ | R / any | Wagenmakers et al., 2007 |
| **rtdists** | DDM, LBA | R | Singmann et al., 2016 |
| **PyDDM** | DDM (flexible extensions) | Python | Shinn et al., 2020 |
| **DMC** | LBA, DDM, racing diffusion | R | Heathcote et al., 2019 |

## Common Pitfalls

1. **Analyzing mean RT only**: Mean RT conflates drift rate, boundary separation, and non-decision time. Two conditions with identical mean RTs can have very different latent processes (Ratcliff & McKoon, 2008).

2. **Applying DDM to >2-choice tasks**: The standard DDM is defined for two-choice tasks only. For 3+ alternatives, use LBA, racing diffusion, or the multi-alternative DDM extension (Ratcliff & Starns, 2013).

3. **Insufficient trial counts**: The full DDM requires at least **40-50 trials per condition** for group-level estimates and **200+ for stable individual estimates** (Ratcliff & Childers, 2015; Lerche et al., 2017). With fewer trials, use EZ-diffusion or hierarchical Bayesian fitting.

4. **Ignoring RT distribution shape**: EAMs predict specific distributional forms (right-skewed). If your RT distribution is bimodal or has a long left tail, check for contaminant processes (e.g., fast guesses) before fitting (Ratcliff & Tuerlinckx, 2002).

5. **Not trimming outlier RTs**: Extremely fast (<200 ms) or slow (>3000 ms for speeded tasks) RTs likely reflect processes outside the model. Standard practice: trim RTs below **200 ms** and above a task-appropriate upper bound (Ratcliff & McKoon, 2008).

6. **Fitting too many free parameters**: The full 7-parameter DDM is often overparameterized. Fix parameters that are not theoretically relevant (e.g., fix sz = 0 and st0 = 0 as a starting point; Ratcliff & Childers, 2015).

7. **Confusing EZ-diffusion limitations**: EZ-diffusion assumes no across-trial variability in drift or starting point. If your design manipulates prior probability (affecting starting point bias), EZ cannot capture this (Wagenmakers et al., 2007).

8. **Skipping parameter recovery**: Without recovery checks, you cannot know whether your data are informative for the parameters you want to interpret (Heathcote et al., 2015).

## Minimum Reporting Checklist

Based on Dutilh et al. (2019) and current best practices:

- [ ] Model selected and justification (why DDM vs. LBA vs. EZ)
- [ ] Number of trials per condition per participant
- [ ] RT trimming criteria and percentage of data excluded
- [ ] Complete list of free vs. fixed parameters with rationale
- [ ] Fitting method (MLE, chi-square, Bayesian) and software (with version)
- [ ] Model fit assessment (quantile probability plots, AIC/BIC/WAIC)
- [ ] Parameter recovery results (simulated data check)
- [ ] All parameter estimates with uncertainty (SE or credible intervals)
- [ ] Model comparison results if multiple models were fit
- [ ] Diagnostic plots: observed vs. predicted RT quantiles (0.1, 0.3, 0.5, 0.7, 0.9) for correct and error responses

## References

- Akaike, H. (1974). A new look at the statistical model identification. *IEEE Transactions on Automatic Control*, 19, 716-723.
- Annis, J., Miller, B. J., & Palmeri, T. J. (2017). Bayesian inference with Stan: A tutorial on adding custom distributions. *Behavior Research Methods*, 49, 863-886.
- Brown, S. D., & Heathcote, A. (2008). The simplest complete model of choice response time: Linear ballistic accumulation. *Cognitive Psychology*, 57, 153-178.
- Donkin, C., Averell, L., Brown, S., & Heathcote, A. (2011). Getting more from accuracy and response time data: Methods for fitting the linear ballistic accumulator. *Behavior Research Methods*, 43, 332-343.
- Dutilh, G., et al. (2019). The quality of response time data inference: A blinded, collaborative assessment of the validity of cognitive models. *Psychonomic Bulletin & Review*, 26, 1051-1069.
- Heathcote, A., Brown, S. D., & Wagenmakers, E.-J. (2015). An introduction to good practices in cognitive modeling. In B. U. Forstmann & E.-J. Wagenmakers (Eds.), *An introduction to model-based cognitive neuroscience*. New York: Springer.
- Heathcote, A., Lin, Y.-S., Reynolds, A., Strickland, L., Gretton, M., & Matzke, D. (2019). Dynamic models of choice. *Behavior Research Methods*, 51, 961-985.
- Kass, R. E., & Raftery, A. E. (1995). Bayes factors. *Journal of the American Statistical Association*, 90, 773-795.
- Lerche, V., Voss, A., & Nagler, M. (2017). How many trials are required for parameter estimation in diffusion modeling? *Behavior Research Methods*, 49, 513-537.
- Luce, R. D. (1986). *Response times: Their role in inferring elementary mental organization*. New York: Oxford University Press.
- Pike, R. (1966). Stochastic models of choice behaviour: Response probabilities and latencies of finite Markov chain systems. *British Journal of Mathematical and Statistical Psychology*, 19, 15-32.
- Ratcliff, R. (1978). A theory of memory retrieval. *Psychological Review*, 85, 59-108.
- Ratcliff, R. (1985). Theoretical interpretations of the speed and accuracy of positive and negative responses. *Psychological Review*, 92, 212-225.
- Ratcliff, R., & Childers, R. (2015). Individual differences and fitting methods for the two-choice diffusion model of decision making. *Decision*, 2, 237-279.
- Ratcliff, R., & McKoon, G. (2008). The diffusion decision model: Theory and data for two-choice decision tasks. *Neural Computation*, 20, 873-922.
- Ratcliff, R., & Rouder, J. N. (1998). Modeling response times for two-choice decisions. *Psychological Science*, 9, 347-356.
- Ratcliff, R., & Starns, J. J. (2013). Modeling response times, accuracy, and confidence in two-choice tasks. *Psychological Review*, 120, 510-560.
- Ratcliff, R., & Tuerlinckx, F. (2002). Estimating parameters of the diffusion model. *Psychonomic Bulletin & Review*, 9, 438-481.
- Schwarz, G. (1978). Estimating the dimension of a model. *Annals of Statistics*, 6, 461-464.
- Shinn, M., Lam, N. H., & Murray, J. D. (2020). A flexible framework for simulating and fitting generalized drift-diffusion models. *eLife*, 9, e56938.
- Singmann, H., Brown, S., Gretton, M., & Heathcote, A. (2016). rtdists: Response time distributions. R package.
- Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & van der Linde, A. (2002). Bayesian measures of model complexity and fit. *Journal of the Royal Statistical Society B*, 64, 583-639.
- Tillman, G., Van Zandt, T., & Logan, G. D. (2020). Sequential sampling models without random between-trial variability: The racing diffusion model with its competing risks. *Psychonomic Bulletin & Review*, 27, 1170-1190.
- Townsend, J. T., & Ashby, F. G. (1983). *Stochastic modeling of elementary psychological processes*. Cambridge University Press.
- Usher, M., & McClelland, J. L. (2001). The time course of perceptual choice: The leaky, competing accumulator model. *Psychological Review*, 108, 550-592.
- Verbruggen, F., & Logan, G. D. (2008). Response inhibition in the stop-signal paradigm. *Trends in Cognitive Sciences*, 12, 418-424.
- Voss, A., & Voss, J. (2007). Fast-dm: A free program for efficient diffusion model analysis. *Behavior Research Methods*, 39, 767-775.
- 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, 3-22.
- Watanabe, S. (2010). Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. *Journal of Machine Learning Research*, 11, 3571-3594.
- White, C. N., & Poldrack, R. A. (2014). Decomposing bias in different types of simple decisions. *Journal of Experimental Psychology: Learning, Memory, and Cognition*, 40, 385-398.
- 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/ez-diffusion-formulas.md` for EZ-diffusion closed-form equations and worked examples.