Estimating Effective Connectivity from fMRI Data Using Factor-based Subspace Autoregressive Models

We consider the problem of identifying large-scale effective connectivity of brain networks from fMRI data. Standard vector autoregressive (VAR) models fail to estimate reliably networks with large number of nodes. We propose a new method based on factor modeling for reliable and efficient high-dimensional VAR analysis of large networks. We develop a subspace VAR (SVAR) model from a factor model (FM), where observations are driven by a lower-dimensional subspace of common latent factors with an AR dynamics. We consider two variants of principal components (PC) methods that provide consistent estimates for the FM hence the implied SVAR model, even of large dimensions. Information criterion is used to select the optimal subspace dimension. We established asymptotic normality and convergence rates for the estimated SVAR coefficients matrix. Evaluation on simulated resting-state fMRI shows that the SVAR models are more robust and produce better connectivity estimates than the classical model for a moderately-large network analysis. Results on real data by varying the subspace dimensions identify strong connections in the default mode network and reveal hierarchical connectivity of resting-state networks with distinct functional relevance.