Abstract
Drift-diffusion models or DDMs are becoming a standard in the field of computational neuroscience. They extend models from signal detection theory by proposing a simple mechanistic explanation for the observed relationship between decision outcomes and reaction times (RT). In brief, they assume that decisions are triggered once the accumulated evidence in favor of a particular alternative option has reached a predefined threshold. Fitting a DDM to empirical data then allows one to interpret observed group or condition differences in terms of a change in the underlying model parameters. However, current approaches only yield reliable parameter estimates in specific situations (c.f. fixed drift rates vs drift rates varying over trials). In addition, they become computationally unfeasible when more general DDM variants are considered (e.g., with collapsing bounds). In this note, we propose a fast and efficient approach to parameter estimation that relies on fitting a “self-consistency” equation that RT fulfill under the DDM. This effectively bypasses the computational bottleneck of standard DDM parameter estimation approaches, at the cost of estimating the trial-specific neural noise variables that perturb the underlying evidence accumulation process. For the purpose of behavioral data analysis, these act as nuisance variables and render the model “overcomplete,” which is finessed using a variational Bayesian system identification scheme. However, for the purpose of neural data analysis, estimates of neural noise perturbation terms are a desirable (and unique) feature of the approach. Using numerical simulations, we show that this “overcomplete” approach matches the performance of current parameter estimation approaches for simple DDM variants, and outperforms them for more complex DDM variants. Finally, we demonstrate the added-value of the approach, when applied to a recent value-based decision making experiment.
Highlights
Over the past two decades, neurocognitive processes of decision making have been extensively studied under the framework of so-called drift-diffusion models or DDMs
We report the results of a recovery analysis, in which data was simulated under the above generalized DDM
We have described an overcomplete approach to fitting the DDM to trial-by-trial reaction times (RT) data
Summary
Over the past two decades, neurocognitive processes of decision making have been extensively studied under the framework of so-called drift-diffusion models or DDMs. The joint distribution of response times and decision outcomes depends upon the DDM parameters, which include: the drift rate v, the bound’s height b, the noise’s standard deviation σ and the initial condition x0. Under such simple DDM variant, variability in response times and decision outcomes derive from stochastic terms η These are typically thought of as neural noise that perturb the evidence accumulation process within the brain’s decision system (Gold and Shadlen, 2007; Turner et al, 2015; Guevara Erra et al, 2019). This follows from fitting a self-consistency equation that, under a broad class of DDM variants, response times have to obey
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