Structural Factor Equation Models for Causal Network Construction via Acyclic Directed Mixed Graphics

• Activity Number: 432
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Graphics
• Author(s): Yan Zhou* and Peter X.K. Song and Xiaoquan William Wen
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: Directed acyclic graph ; Factor analysis model ; Network data ; Regularization ; Semi-Markov model

Abstract

Acyclic directed mixed graph(ADMG) provides a useful representation for the network topology with both directed and undirected edges subject to the restriction of no directed cycles being allowed in the graph. Such a graphical framework may arise from many biomedical studies, such as the situation where a directed acyclic graph(DAG) of interest is contaminated with numerous undirected edges induced by some unobserved confounding factors (e.g. unmeasured environmental factors). Directed edges in a DAG are widely used to evaluate causal relationships among variables in a network, which may become a great challenge when the underlying causality is obscured by shared latent factors. The objective of this paper is to develop an effective structural equation modeling (SEM) method to extract the part of DAG from an ADMG. The resulting model is termed as the structural factor equation model (SFEM), in which the utility of latent factors enables us to identify and remove undirected edges, leading to a simpler and more interpretable causal network. The proposed method is evaluated and compared to the existing methods through extensive simulation studies, as well as a real data example.