This study introduces a mediation analysis framework when the mediator is a graph. A Gaussian covariance graph model is assumed for graph representation. Causal estimands and assumptions are discussed under this representation. With a covariance matrix as the mediator, parametric mediation models are imposed based on matrix decomposition. Assuming Gaussian random errors, likelihood-based estimators are introduced to simultaneously identify the decomposition 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.

翻译：本研究提出了一种以图结构为中介变量的中介分析框架。采用高斯协方差图模型对图表示进行建模，并基于该表示讨论了因果估计量及假设条件。以协方差矩阵作为中介变量时，通过矩阵分解建立了参数化中介模型。在假设高斯随机误差的前提下，提出了基于似然的估计方法，可同时识别矩阵分解结果与因果参数。本文设计了高效的计算算法，并探究了估计量的渐近性质。通过模拟研究评估了所提方法的性能。将其应用于静息态功能磁共振成像研究，识别出一个脑网络，在该网络内功能连接中介了运动任务表现中的性别差异。