Untangling the relatedness among correlations, part III: Inter-subject correlation analysis through Bayesian multilevel modeling for naturalistic scanning.

While inter-subject correlation (ISC) analysis is a powerful tool for naturalistic scanning data, drawing appropriate statistical inferences is difficult due to the daunting task of accounting for the intricate relatedness in data structure as well as handling the multiple testing issue. Although the linear mixed-effects (LME) modeling approach (Chen et al., 2017a) is capable of capturing the relatedness in the data and incorporating explanatory variables, there are a few challenging issues: 1) it is difficult to assign accurate degrees of freedom for each testing statistic, 2) multiple testing correction is potentially over-penalizing due to model inefficiency, and 3) thresholding necessitates arbitrary dichotomous decisions. Here we propose a Bayesian multilevel (BML) framework for ISC data analysis that integrates all regions of interest into one model. By loosely constraining the regions through a weakly informative prior, BML dissolves multiplicity through conservatively pooling the effect of each region toward the center and improves collective fitting and overall model performance. In addition to potentially achieving a higher inference efficiency, BML improves spatial specificity and easily allows the investigator to adopt a philosophy of full results reporting. A dataset of naturalistic scanning is utilized to illustrate the modeling approach with 268 parcels and to showcase the modeling capability, flexibility and advantages in results reporting. The associated program will be available as part of the AFNI suite for general use.