Fitting the full drift diffusion model requires estimating multiple parameters from entire RT distributions, typically using computationally intensive methods like maximum likelihood estimation or chi-square fitting. The EZ-diffusion model dramatically simplifies this process by providing closed-form algebraic equations that map three easily computed summary statistics — proportion correct (Pc), mean RT for correct responses (MRT), and variance of correct RT (VRT) — directly onto the three core DDM parameters.
The Closed-Form Equations
Drift rate: v = sign(Pc − 0.5) × s × √(L × (Pc² × L − Pc × L + Pc − 0.5) / VRT)
Boundary: a = s² × L / v
Non-decision time: Ter = MRT − (a/(2v)) × (1 − e^(−vL)) / (1 + e^(−vL))
These equations are derived by inverting the analytical expressions for the DDM's predicted accuracy, mean RT, and RT variance (assuming no across-trial variability in parameters and a symmetric starting point). The key mathematical move is expressing the three DDM equations in terms of three unknowns and solving the system algebraically.
Advantages
The EZ-diffusion model has several compelling advantages over full DDM fitting:
Simplicity: No iterative optimization is needed; parameters are computed in a single pass. This eliminates convergence failures, local minima, and the need for starting values that plague full DDM fitting.
Minimal data requirements: EZ works with as few as ~50 trials per condition (compared to hundreds for the full DDM), making it suitable for clinical, developmental, and individual-differences applications where trial counts are limited.
Transparency: The closed-form equations make it clear exactly how each summary statistic maps onto each parameter. Higher accuracy maps onto higher drift rate. Greater RT variance (relative to accuracy) maps onto lower boundary separation. Mean RT minus the predicted decision time gives non-decision time.
The simplification comes at a cost. EZ assumes no across-trial variability in drift rate, starting point, or non-decision time — variability parameters that the full DDM includes and that are important for explaining certain empirical patterns (e.g., the relationship between error RT and correct RT). EZ also assumes an unbiased starting point, so it cannot model response bias. For applications where these features matter, the full DDM or intermediate models (like EZ2) should be used instead.
Validation and Impact
Wagenmakers et al. (2007) validated EZ through extensive simulations, showing that EZ parameter recovery is excellent when the generating model matches EZ's assumptions and remains reasonable even with moderate violations. Van Ravenzwaaij, Donkin, and Vandekerckhove (2017) conducted a large-scale comparison and found that EZ performs surprisingly well even when the generating model includes across-trial variability, particularly for drift rate and boundary separation.
The EZ-diffusion model has been widely adopted in cognitive aging research (where it reveals that older adults primarily differ in non-decision time and boundary separation, not drift rate for many tasks), clinical neuropsychology (decomposing ADHD deficits into specific cognitive components), and individual-differences research (relating DDM parameters to personality traits and cognitive abilities). Its accessibility has made diffusion model analysis available to researchers without specialized computational expertise.