Multi-subject stochastic blockmodels with mixed effects for adaptive analysis of individual differences in human brain network cluster structure

Recently, there has been a renewed interest in the class of stochastic blockmodels (SBM) and their applications to multi-subject brain networks. In our most recent work, we have considered an extension of the classical SBM, termed heterogeneous SBM (Het-SBM), that models subject variability in the cluster-connectivity profiles through the addition of a logistic regression model with subject-specific covariates on the level of each block. Although this model has proved to be useful in both the clustering and inference aspects of multi-subject brain network data, including fleshing out differences in connectivity between patients and controls, it does not account for dependencies that may exist within subjects. To overcome this limitation, we propose an extension of Het-SBM, termed Het-Mixed-SBM, in which we model the within-subject dependencies by adding subject- and block-level random intercepts in the embedded logistic regression model. Using synthetic data, we investigate the accuracy of the partitions estimated by our proposed model as well as the validity of inference procedures based on the Wald and permutation tests. Finally, we illustrate the model by analyzing the resting-state fMRI networks of 99 healthy volunteers from the Human Connectome Project (HCP) using covariates like age, gender, and IQ to explain the clustering patterns observed in the data.