To achieve the above objectives, we propose a hierarchical Bayesian model. Our model takes the underlying hierarchical structure (i.e., subjects are nested within sites, and there are multiple observations per subject) of the data into account. This approach provides a simple modular scheme for measuring group, load, gender, hemisphere, age, visit, and handedness effects, which can be easily updated with future experimental observations (Gelman et al., 2003). The hierarchical Bayesian model also provides information about run, subject, and site variation, which are in turn used to estimate the efficacy of the multi-center study compared to the single-center studies with the same sample size. Using both posterior predictive model checking and model selection based on the deviance information criterion (DIC), we show that the fit of our proposed model to the observed data is substantially better than an alternative model that ignores between-site variation.
