HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python

Abstract

The diffusion model is a commonly used tool to infer latent psychological processes underlying decision-making, and to link them to neural mechanisms based on response times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of response time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model), which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject/condition than non-hierarchical methods, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g., fMRI) influence decision-making parameters. This paper will first describe the theoretical background of the drift diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the χ2-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs/

Refresh my memory: Episodic memory reinstatements intrude on working memory maintenance

“…Specifically, we used the Diffusion Decision Model (DDM; Ratcliff 1978). We used a hierarchical Bayesian model fitting procedure (hDDM; Wiecki et al, 2013) to simultaneously estimate participant and group-level parameters. We fit two main classes of models: the behavioral model, and the neural model.…”

Caution follows fear: Evidence from hierarchical drift diffusion modelling.

“…This was carried out because Diffusion Modelling estimates can be biased by fast responses (Voss, Voss, & Lerche, 2015) and also, because the Hierarchical Drift Diffusion Modelling software (Wiecki et al, 2013) requires RTs greater 100 ms in duration to find initial sampling values.…”

“…I used Hierarchical Drift Diffusion Modelling (Vandekerckhove, Tuerlinckx, & Lee, 2008, 2011bWiecki et al, 2013) to isolate the psychological processes responsible for the effects of facial expressions on visual perception. Hierarchical Bayesian estimation is particularly suited to studies with relatively small number of observations (<48) per cell of the design because subject and group-level posterior estimates can reciprocally influence each other leading to greater statistical precision.…”

“…Here, I use Hierarchical Drift Diffusion Modelling (Vandekerckhove et al, 2011a;Wiecki et al, 2013) to test for both impaired perception and increased caution following fearful, happy and sad facial expressions.…”

Rapid temporal accumulation in spider fear: Evidence from hierarchical drift diffusion modelling.

“…To estimate drift diffusion parameters I used a Hierarchical Drift Diffusion Modelling procedure (Vandekerckhove et al, 2008(Vandekerckhove et al, , 2011Wiecki et al, 2013) implemented in Python (Wiecki et al, 2013). In brief, HDDM uses Markov Chain Monte Carlo simulations to estimate a range of probable values for diffusion parameters -a posterior distribution of values for each parameter.…”