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

Michael J Frank,Imri Sofer,Thomas V Wiecki

doi:10.3389/fninf.2013.00014

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/

Highlights

Sequential sampling models (SSMs) (Townsend and Ashby, 1983) have established themselves as the de-facto standard for modeling response-time data from simple two-alternative forced choice decision making tasks (Smith and Ratcliff, 2004)
The purpose of this report is two-fold; (1) we briefly introduce the toolbox and provide a tutorial on a real-world data set; and (2) characterize its success in recovering model parameters by performing a parameter recovery study using simulated data to compare the hierarchical model used in HDDM to non-hierarchical or non-Bayesian methods as a function of the number of subjects and trials
While demonstrating core features this is by no means a complete overview of all the functionality in HDDM

Summary

Introduction

Sequential sampling models (SSMs) (Townsend and Ashby, 1983) have established themselves as the de-facto standard for modeling response-time data from simple two-alternative forced choice decision making tasks (Smith and Ratcliff, 2004). Models of this class have been used successfully in mathematical psychology since the 60’s and more recently adopted in cognitive neuroscience investigations These studies are typically interested in neural mechanisms associated with the accumulation process or for regulating the decision threshold (e.g., Forstmann et al, 2008; Ratcliff et al, 2009; Cavanagh et al, 2011). One issue in such model-based cognitive neuroscience approaches is that the trial numbers in each condition are often low, making it difficult to estimate model parameters. Efficient and reliable estimation methods that take advantage of the full statistical structure available in the data across subjects and conditions are critical to the success of these endeavors

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Conclusion