A Bayesian hierarchical implementation of the circular drift diffusion model
The circular drift diffusion model (CDDM; Smith, 2016, Psychological Review) is a sequential-sampling decision-making model used to describe the choices and response times observed in scenarios where participants have to make decisions on a circular space (i.e., the decision space is a bounded continuum that can be mapped onto a circle). Much like in Ratcliff’s (1978, Psychological Review) diffusion model, a core assumption is that evidence is accumulated over time until a response threshold is reached. The parameters of the CDDM can be mapped to relevant psychological processes such as response caution and information processing speed. We developed a custom JAGS module to facilitate working with the CDDM in a Bayesian framework. We present results from a parameter recovery study showing that the module is well suited to infer the parameter values used to generate bivariate datasets. The implementation in JAGS facilitates a number of useful model extensions: hierarchical models that capture different levels of variation across parameters (e.g., per individual, condition, experimental manipulation, etc.); latent variable models that identify their underlying factorial structure; mixture models that discern responses attributable to different simultaneously active processes; explanatory models that consider exogenous predictors; and so on. We present an application of our CDDM JAGS module to data collected by Kvam (2019, Journal of Experimental Psychology: Human Perception and Performance) in a continuous orientation judgment task. In this study, participants were asked to indicate the mean orientation of a rapid sequence of Gabor patches shown on every trial. The task design included manipulations of boundary distance through speed vs. accuracy instructions, and manipulations of drift magnitude and drift angle variability through different difficulty conditions. We built a hierarchical Bayesian model with a latent mixture structure to test four hypotheses: (1) The response boundary was higher when instructions prompted participants to favor accuracy rather than speed; (2) The drift magnitude decreased with task difficulty; (3) The variability in drift angle increased with task difficulty; and (4) Positive and negative deflections of the cue with respect to the true mean orientation had equivalent effects on the responses observed. We found evidence in support of all four hypotheses. We will present results and discuss further extensions of the model.