Preprintgreen2017

Recurrent Auto-Encoding Drift Diffusion Model

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Decision-Making and Behavioral Economics Neural and Behavioral Psychology Studies Statistical Methods and Bayesian Inference

Abstract

Abstract The Drift Diffusion Model (DDM) is a popular model of behaviour that accounts for patterns of accuracy and reaction time data. In the Full DDM implementation, parameters are allowed to vary from trial-to-trial, making the model more powerful but also more challenging to fit to behavioural data. Current approaches yield typically poor fitting quality, are computationally expensive and usually require assuming constant threshold parameter across trials. Moreover, in most versions of the DDM, the sequence of participants’ choices is considered independent and identically distributed (i.i.d .), a condition often violated in real data. Our contribution to the field is threefold: first, we introduce Variational Bayes as a method to fit the full DDM. Second, we relax the i.i.d . assumption, and propose a data-driven algorithm based on a Recurrent Auto-Encoder (RAE-DDM), that estimates the local posterior probability of the DDM parameters at each trial based on the sequence of parameters and data preceding the current data point. Finally, we extend this algorithm to illustrate that the RAE-DDM provides an accurate modelling framework for regression analysis. An important result of the approach we propose is that inference at the trial level can be achieved efficiently for each and every parameter of the DDM, threshold included. This data-driven approach is highly generic and self-contained, in the sense that no external input (e.g. regressors or physiological measure) is necessary to fit the data. Using simulations, we show that this method outperforms i.i.d .-based approaches (either Markov Chain Monte Carlo or i.i.d .-VB) without making any assumption about the nature of the between-trial correlation of the parameters.

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References

1951A Stochastic Approximation Method 2016Numerical solution of stochastic differential equations 2013HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python 2002Estimating parameters of the diffusion model: Approaches to dealing with contaminant reaction times and parameter variability 2000How to fit a response time distribution 2011Hierarchical diffusion models for two-choice response times.2010The Drift Diffusion Model can account for the accuracy and reaction time of value-based choices under high and low time pressure 1997Dynamic Stochastic Models for Decision Making under Time Constraints

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