Bayesian Graphical Modeling with the Circular Drift Diffusion Model.

The circular drift-diffusion model (CDDM) is a sequential sampling model designed to account for decisions and response times in decision-making tasks with a circular set of choice alternatives. We present and demonstrate a fully Bayesian implementation and extension of the CDDM. This development allows researchers to apply the CDDM to data from complex experiments and draw conclusions about targeted hypotheses. The Bayesian implementation relies on a custom JAGS module. We describe the module and demonstrate its adequacy through a simulation study. We then illustrate the advantages of the implementation by revisiting data from a continuous orientation judgment task. We develop a graphical model for the analysis that is based on the CDDM but extends it with hierarchical and latent-mixture structures. We then demonstrate how these extensions are used to accommodate the design of the experiment and to implement psychological assumptions about individual differences, the difficulty of different stimulus conditions, and the impact of cues on decision making. Finally, we demonstrate how the computational Bayesian inference enabled by JAGS allows these assumptions to be tested and addresses psychological research questions about people's decision making.