Source
Wiecki, Sofer & Frank (2013), “HDDM: Hierarchical Bayesian Estimation of the Drift-Diffusion Model in Python”, LIT-563, read in NOTE-466 from the PMC full text. Code listings and the online supplement were not seen.
What was actually shown
The method. Subject parameters are draws from group distributions, all estimated together by MCMC, with informative priors set from published DDM estimates (e.g. μ_a ~ Gamma(1.5, 0.75), μ_v ~ N(2, 3)) and the Navarro–Fuss likelihood. Inter-trial variabilities are estimated at group level only.
Experiment 1 (Fig. 6). Group parameters drawn uniformly, v₂ = 2v₁, sz = st = 0, 12 subjects, 20 to 150 trials. Trimmed mean absolute error was lowest for HB for every parameter, with the largest gains for threshold and both drifts at few trials. Paired against ML on the same data sets, HB was significantly better in every condition.
Experiments 2–3 (Figs. 7–8). At 75 trials and 8 to 28 subjects, HB detected the drift difference most often at every sample size. For a trial-by-trial covariate on drift, HB raised detection by up to 20% for the larger effects (0.3, 0.5) with few trials, and modestly for 0.1.
Why it helps. Where a parameter varies little across people, each estimate is pulled toward the group’s, which leaves more of the data to fix the parameters that do vary. The gain is largest where trials are few.
What could have come out otherwise: per-subject ML could have recovered some parameter better, for instance where the informative priors were off. It did not in these simulations.
What this does not say
- That HB is better when the data are not a DDM. Every data set was generated from the fitted family, with sz and st set to zero. Robustness to a leaky or competing accumulator is untested (NOTE-466, Open questions).
- That the power gain comes from the hierarchy. HB used a posterior-interval test, the others t-tests. The authors attribute the gain to the hierarchy on the strength of a t-test on HB’s estimates, which they then omit as invalid (C3, weak).
- That the DDM is the right model of the choices. The tool measures DDM parameters; it does not test the model.
- Anything about theta and threshold under deep brain stimulation. Fig. 5 reanalyses Cavanagh et al. (2011) as an illustration (C4).
Connections
- The model HDDM implements is Ratcliff & McKoon’s (LIT-576), and the account of its parameters as controlled quantities is THEORY-061 (Bogacz et al., LIT-569), which HDDM would let one test in individuals.
- THEORY-068 (balanced leak and inhibition) concerns accumulators HDDM does not implement; its race option is the linear ballistic accumulator.
- QUESTION-062 asks whether a goal sets threshold, starting point or drift within one decision. HDDM is the measuring instrument such a test would use; this THEORY does not answer it.