Adjusting for Unmeasured Confounding Variables in Dynamic Networks

Abstract

This letter presents a technique to identify a certain transfer function in a dynamic network when the input and the output of the transfer function are influenced by an unmeasured confounding variable. It is assumed that in an observational framework, only a subset of the variables of the network are measured and the topology of the interconnections between the variables is partially known. The focus of this letter is the challenging scenario where it is not possible to measure any variables on the directed paths from the confounding variable to either the input or the output of the transfer function of interest. Sufficient conditions are derived to determine a set of instrumental variables and a set of auxiliary variables that guarantee consistent identification of the transfer function using an algorithm based on prediction error method for the class of acyclic networks. It is also shown that similar ideas could be applied to cyclic networks. In particular, we show how consistent estimates of some transfer functions in a network with feedback loops could be used to identify some other transfer functions whose inputs and outputs are influenced by unmeasured confounding variables.