Abstract
A primary goal of task-based functional magnetic resonance imaging (fMRI) studies is to quantify the effective connectivity between brain regions when stimuli are presented. Assessing the dynamics of effective connectivity has attracted increasing attention. Causal mediation analysis serves as a widely implemented tool aiming to delineate the mechanism between task stimuli and brain activations. However, the case, where the treatment, mediator, and outcome are continuous functions, has not been studied. Causal mediation analysis for functional data is considered. Semiparametric functional linear structural equation models are introduced and causal assumptions are discussed. The proposed models allow for the estimation of individual effect curves. The models are applied to a task-based fMRI study, providing a new perspective of studying dynamic brain connectivity. The R package cfma for implementation is available on CRAN.