Mediation analysis with graph mediator.

This study introduces a mediation analysis framework when the mediator is a graph. A Gaussian covariance graph model is assumed for graph presentation. Causal estimands and assumptions are discussed under this presentation. With a covariance matrix as the mediator, a low-rank representation is introduced and parametric mediation models are considered under the structural equation modeling framework. Assuming Gaussian random errors, likelihood-based estimators are introduced to simultaneously identify the low-rank representation and causal parameters. An efficient computational algorithm is proposed and asymptotic properties of the estimators are investigated. Via simulation studies, the performance of the proposed approach is evaluated. Applying to a resting-state fMRI study, a brain network is identified within which functional connectivity mediates the sex difference in the performance of a motor task.