  The Linear Ballistic Accumulator (Brown & Heathcote, 2008) model is used as a
measurement tool to answer questions about applied psychology. The analyses
based on this model depend upon the model selected and its estimated
parameters. Modern approaches use hierarchical Bayesian models and Markov chain
Monte-Carlo (MCMC) methods to estimate the posterior distribution of the
parameters. Although there are several approaches available for model
selection, they are all based on the posterior samples produced via MCMC, which
means that the model selection inference inherits the properties of the MCMC
sampler. To improve on current approaches to LBA inference we propose two
methods that are based on recent advances in particle MCMC methodology; they
are qualitatively different from existing approaches as well as from each
other. The first approach is particle Metropolis-within-Gibbs; the second
approach is density tempered sequential Monte Carlo. Both new approaches
provide very efficient sampling and can be applied to estimate the marginal
likelihood, which provides Bayes factors for model selection. The first
approach is usually faster. The second approach provides a direct estimate of
the marginal likelihood, uses the first approach in its Markov move step and is
very efficient to parallelize on high performance computers. The new methods
are illustrated by applying them to simulated and real data, and through pseudo
code. The code implementing the methods is freely available.
