Bayesian Inference for Evidence Accumulation Models with Regressors

Evidence accumulation models (EAMs) are an important class of cognitive models used to analyse both response time and response choice data. The linear ballistic accumulation model (LBA) and the diffusion decision model (DDM) are two common EAMs, with modern applications employing hierarchical Bayesian versions. The first contribution of the paper is to propose EAMs having covariates, which we call Regression Evidence Accumulation Models (RegEAMs). The second contribution is to develop efficient exact and approximate Bayesian methods for estimating RegEAMs, including a simulation consistent particle Metropolis-within-Gibbs sampler and two variational Bayes approximate methods. The constrained VB method assumes that the posterior distribution of the subject level parameters are independent, but it is much faster than the regular VB for a dataset with many subjects. Initialising the VB method for complex EAMs can be very challenging, and two initialisation methods for the VB method are proposed. The initialisation method based on maximum a posteriori estimation (MAP) is shown to be scalable in the number of subjects. The new estimation methods are illustrated by applying them to simulated and real data, and through pseudo code. The code implementing the methods is freely available.