Connectivity Regression.

Assessing how brain functional connectivity networks vary across individuals promises to uncover important scientific questions such as patterns of healthy brain aging through the lifespan or dysconnectivity associated with disease. In this article, we introduce a general regression framework, Connectivity Regression (ConnReg), for regressing subject-specific functional connectivity networks on covariates while accounting for within-network inter-edge dependence. ConnReg utilizes a multivariate generalization of Fisher's transformation to project network objects into an alternative space where Gaussian assumptions are justified and positive semidefinite constraints are automatically satisfied. Penalized multivariate regression is fit in the transformed space to simultaneously induce sparsity in regression coefficients and in covariance elements, which capture within network inter-edge dependence. We use permutation tests to perform multiplicity-adjusted inference to identify covariates associated with connectivity, and stability selection scores to identify network edges that vary with selected covariates. Simulation studies validate the inferential properties of our proposed method and demonstrate how estimating and accounting for within-network inter-edge dependence leads to more efficient estimation, more powerful inference, and more accurate selection of covariate-dependent network edges. We apply ConnReg to the Human Connectome Project Young Adult study, revealing insights into how connectivity varies with language processing covariates and structural brain features.