Confounding effects of indirect connections on causality estimation.

Addressing the issue of effective connectivity, this study focuses on effects of indirect connections on inferring stable causal relations: partial transfer entropy. We introduce a Granger causality measure based on a multivariate version of transfer entropy. The statistic takes into account the influence of the rest of the network (environment) on observed coupling between two given nodes. This formalism allows us to quantify, for a specific pathway, the total amount of indirect coupling mediated by the environment. We show that partial transfer entropy is a more sensitive technique to identify robust causal relations than its bivariate equivalent. In addition, we demonstrate the confounding effects of the variation in indirect coupling on the detectability of robust causal links. Finally, we consider the problem of model misspecification and its effect on the robustness of the observed connectivity patterns, showing that misspecifying the model may be an issue even for model-free information-theoretic approach.