Structural factor equation models for causal network construction via directed acyclic mixed graphs

Directed acyclic mixed graphs (DAMGs) provide a useful representation of network topology with both directed and undirected edges subject to the restriction of no directed cycles in the graph. This graphical framework may arise in many biomedical studies, for example, when a directed acyclic graph (DAG) of interest is contaminated with undirected edges induced by some unobserved confounding factors (eg, unmeasured environmental factors). Directed edges in a DAG are widely used to evaluate causal relationships among variables in a network, but detecting them is challenging when the underlying causality is obscured by some shared latent factors. The objective of this paper is to develop an effective structural equation model (SEM) method to extract reliable causal relationships from a DAMG. The proposed approach, termed structural factor equation model (SFEM), uses the SEM to capture the network topology of the DAG while accounting for the undirected edges in the graph with a factor analysis model. The latent factors in the SFEM enable the identification and removal of undirected edges, leading to a simpler and more interpretable causal network. The proposed method is evaluated and compared to existing methods through extensive simulation studies, and illustrated through the construction of gene regulatory networks related to breast cancer.