Fitting drift-diffusion models in a hierarchical Bayesian framework: methods and applications
Thomas V. Wiecki (Brown University), Imri Sofer (Brown University), Michael J. Frank (Brown University)
We present an open-source software suite written in Python called HDDM (Hierarchical Drift Diffusion Modelling) that allows users to easily perform hierarchical Bayesian inference on drift-diffusion decision making models. Drift-diffusion models (DDM) account for the full reaction time (RT) distributions of correct and error responses in 2-alternative-forced-choice tasks. The parameters of the DDM have a direct mapping onto psychological processes underlying decision-making. Classically, finding the set of parameters that best explain a subjects RT distribution is done via maximum likelihood (ML) methods. However, hierarchical Bayesian parameter estimation offers some critical advantages compared to ML: (i) subject parameters are not fit separately but are constrained by group level parameters, thereby sharing statistical strength; and (ii) the procedure offers a principled approach for estimating the full posterior distribution of parameter values (for both subjects and groups) instead of just the single maximum likelihood value. Current software packages for fitting DDMs such as fast-dm and DMAT are constrained to ML or other related optimization techniques. HDDM is a novel software package with focus on ease-of-use, flexibility and computational efficacy that relies on Markov-Chain Monte Carlo sampling methods implemented by PyMC. In addition to the software package we present the extension of the DDM to a novel domain unrelated to decision making: by fitting the HDDM to simulated data from a biological constrained computational model of the antisaccade task we find a direct link between neurobiological and psychological processes.
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