The effect of latent confounding processes on the estimation of the strength of causal influences in chain-type networks

Reliable recognition of casual interactions between processes is an issue particularly prevalent in the Neurosciences. When the structure of a network is not a priori known it is almost impossible to observe and measure all components of a system, and missing certain components could potentially lead to the inference of spurious interactions. The aim of this study is to demonstrate the effect of missing components of a network on the inferred strength of a spurious interaction. Our novel method uses vector autoregressive modelling and renormalised partial directed coherence to show how and why the inferred strength of causal interactions between processes changes when components in a network are missed. In cases where a latent confounder is influencing a network and consequently a spurious interaction appears, it is not possible to rely on estimates of the strength of this link as strength estimation methods are influenced by the noise of the latent confounder. Our novel approach demonstrates precisely how a latent confounder can affect the strength measure using analysis of vector autoregressive models. While it is possible to measure the strength of directed causal influences between processes the estimation of strength can be confounded if not all components of a system have been observed during measurement.