Hierarchical drift–diffusion model (HDDM)

HDDM falls under the class of sequential sampling methods which utilise Bayesian methods to estimate the DDM parameters such as the threshold (a) and the drift rate (v), response bias (z), and non-decision time (t) (Fig. 1e, f). We focus our analysis on the first three parameters as t primarily concerns motor and non-decision-making processes. The Bayesian-based HDDM estimates parameters as posterior probability distributions with the mean of the distribution representing the group’s average. The model utilises the Markov Chain Monte Carlo sampling method to estimate the distributions. The prior distribution for each parameter was based on 23 studies that reported the best fitting DDM parameters for multiple cognitive tasks¹⁹. The pre-analysis code was written in MATLAB version 2017a and the built-in HDDM python package by¹⁹ was used for parameter estimation.

Trials with response times less than 50 ms were discarded from the analysis to ensure model convergence and to constrain the data to realistic response times. The parameters were estimated by drawing 120,000 samples with the first 10,000 samples being discarded as burn-in and saving only every 10^th sample. The convergence of the model was assessed by both visual inspection and computation of the Gelman-Rubin statistic, which indicated convergence (R^{^} < 1.1)²⁰.

Additionally, we also estimated the parameters for accuracy (see⁷ for details on methods). We estimated all the three HDDM parameters (a, v, and z) in HV and ADHD in placebo and MPH conditions.