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Evidence accumulation models (EAMs) are an important class of cognitive
models used to analyze both response time and response choice data recorded
from decision-making tasks. Developments in estimation procedures have helped
EAMs become important both in basic scientific applications and
solution-focussed applied work. Hierarchical Bayesian estimation frameworks for
the linear ballistic accumulator model (LBA) and the diffusion decision model
(DDM) have been widely used, but still suffer from some key limitations,
particularly for large sample sizes, for models with many parameters, and when
linking decision-relevant covariates to model parameters. We extend upon
previous work with methods for estimating the LBA and DDM in hierarchical
Bayesian frameworks that include random effects which are correlated between
people, and include regression-model links between decision-relevant covariates
and model parameters. Our methods work equally well in cases where the
covariates are measured once per person (e.g., personality traits or
psychological tests) or once per decision (e.g., neural or physiological data).
We provide methods for exact Bayesian inference, using particle-based MCMC, and
also approximate methods based on variational Bayesian (VB) inference. The VB
methods are sufficiently fast and efficient that they can address large-scale
estimation problems, such as with very large data sets. We evaluate the
performance of these methods in applications to data from three existing
experiments. Detailed algorithmic implementations and code are freely available
for all methods.