Structural Equation Models and Directed Networks

Abstract

Undirected networks (encoded in symmetric adjacency matrices) cannot be used to describe causal relationships between random variables. Instead, causal information is encoded by directed networks where the arrow A → B indicates that variable A causally influences variable B. We refer to the process of assigning a causal direction to edges in an association network as “edge orienting”. We review structural equation model (SEM)-based approaches for constructing directed networks between random variables. SEMs lead to predictions about the variance–covariance matrices of the observed variables, which is why they are also known as covariance structure models. We review likelihood-based approaches for evaluating the fit of a structural equation model. We provide a short review of SEMs and show how these techniques can be used for defining directed networks. In particular, we describe how local structural equations based on causal anchors can be used to infer causal networks among variables. Causal networks have been used in systems genetics applications for inferring causal relationships based on genetic markers. The network edge orienting (NEO) R software and method can be used to orient the edges of correlation networks (aka. quantitative trait networks) if the edges can be anchored to causal anchors (e.g., genetic polymorphisms). This section reviews and extends work with Jason Aten and Jake Lusis.