Computing Bayes factors for evidence-accumulation models using Warp-III bridge sampling

Quentin F Gronau,Dora Matzke,Andrew Heathcote

doi:10.3758/s13428-019-01290-6

Abstract

Over the last decade, the Bayesian estimation of evidence-accumulation models has gained popularity, largely due to the advantages afforded by the Bayesian hierarchical framework. Despite recent advances in the Bayesian estimation of evidence-accumulation models, model comparison continues to rely on suboptimal procedures, such as posterior parameter inference and model selection criteria known to favor overly complex models. In this paper, we advocate model comparison for evidence-accumulation models based on the Bayes factor obtained via Warp-III bridge sampling. We demonstrate, using the linear ballistic accumulator (LBA), that Warp-III sampling provides a powerful and flexible approach that can be applied to both nested and non-nested model comparisons, even in complex and high-dimensional hierarchical instantiations of the LBA. We provide an easy-to-use software implementation of the Warp-III sampler and outline a series of recommendations aimed at facilitating the use of Warp-III sampling in practical applications.

Highlights

Cognitive models of response times and accuracy canonically assume an accumulation process, where evidence favoring different options is summed over time until a threshold is reached that triggers an associated response
We have found that the improvement afforded by Warp-III can be crucial for efficient application of bridge sampling to evidenceaccumulation models, in situations where the
The Warp-III, Savage–Dickey, and reversible jump MCMC (RJMCMC) methods resulted in stable Bayes factor estimates already with 1000 samples

Summary

Introduction

Cognitive models of response times and accuracy canonically assume an accumulation process, where evidence favoring different options is summed over time until a threshold is reached that triggers an associated response. The two most prominent types of evidence-accumulation models, the diffusion decision model (DDM; Ratcliff, 1978; Ratcliff & McKoon, 2008) and the linear ballistic accumulator (LBA; Brown & Heathcote, 2008) have been widely applied across animal and human research in biology, psychology, economics, and the neurosciences to topics including vision, attention, language, memory, cognition, emotion, development, aging, and clinical disorders (for reviews, see Mulder, Van Maanen, & Forstmann, 2014; Ratcliff, Smith, Brown, & McKoon, 2016; Donkin & Brown, 2018). Our recent literature review indicated that 19% and 21% of the 262 and 53 papers that used the DDM and the LBA, respectively, relied on Bayesian methods to estimate

Objectives

Results

Discussion

Conclusion