Abstract
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.
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Availability of Data and Materials
The data set from Kvam (2019) is available on the Open Science Framework at https://osf.io/px274/.
Code Availability
The jags-cddm module is available at https://github.com/joachimvandekerckhove/jags-cddm. Code for the application is available at https://github.com/ManuelVU/application-jags-cddm.
Notes
For computational reproducibility, the GitHub repository also includes instructions for setting up a virtual machine—a curated computational environment—that includes an operating system with appropriate compilers and software versions that support the module.
The bottom right panel of Fig. 5 excludes cases where the drift length \(\delta \) true value was close to 0 (i.e., \(\delta = 0.01\)), as the drift angle is unidentified in that case.
Other assumptions are possible, such as drift angle being some weighted combination of cue and stimulus information. While these more complicated possibilities could certainly be implemented, we consider just the simplest case in which the drift angle is determined by one or the other.
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Funding
MV, AFCP, PKM, VM, and MDL were supported by National Science Foundation grant #2024856. AFCP and JV were supported by National Science Foundation grants #1230118, #1658303, #1850849, and #2051186.
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AFCP and JV developed the JAGS module. MV and MDL led the development of the graphical modeling application. All authors contributed to the interpretation of results and writing the paper.
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Villarreal, M., Chávez De la Peña, A.F., Mistry, P.K. et al. Bayesian Graphical Modeling with the Circular Drift Diffusion Model. Comput Brain Behav 7, 181–194 (2024). https://doi.org/10.1007/s42113-023-00191-4
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DOI: https://doi.org/10.1007/s42113-023-00191-4