Granger Mediation Analysis of Multiple Time Series with an Application to fMRI
This provides a method for researchers in neuroscience and related fields to analyze causal pathways in time series data, addressing individual variability and correlated errors, but it is incremental as it builds on existing mediation and time series models.
The authors tackled the problem of performing causal mediation analysis for multiple time series data, such as fMRI, where traditional assumptions are unrealistic, by developing Granger Mediation Analysis (GMA), which integrates mediation and vector autoregressive models to reduce estimation bias and improve statistical power in simulations and accurately capture feedback effects in real data.
It becomes increasingly popular to perform mediation analysis for complex data from sophisticated experimental studies. In this paper, we present Granger Mediation Analysis (GMA), a new framework for causal mediation analysis of multiple time series. This framework is motivated by a functional magnetic resonance imaging (fMRI) experiment where we are interested in estimating the mediation effects between a randomized stimulus time series and brain activity time series from two brain regions. The stable unit treatment assumption for causal mediation analysis is thus unrealistic for this type of time series data. To address this challenge, our framework integrates two types of models: causal mediation analysis across the variables and vector autoregressive models across the temporal observations. We further extend this framework to handle multilevel data to address individual variability and correlated errors between the mediator and the outcome variables. These models not only provide valid causal mediation for time series data but also model the causal dynamics across time. We show that the modeling parameters in our models are identifiable, and we develop computationally efficient methods to maximize the likelihood-based optimization criteria. Simulation studies show that our method reduces the estimation bias and improve statistical power, compared to existing approaches. On a real fMRI data set, our approach not only infers the causal effects of brain pathways but accurately captures the feedback effect of the outcome region on the mediator region.