Directed acyclic mixed graphs (DAMG) 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 (e.g., 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 (FA) 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. This article is protected by copyright. All rights reserved.

中文翻译：

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通过有向无环混合图构建因果网络的结构因子方程模型

有向无环混合图 (DAMG) 提供了一种有用的网络拓扑表示，其中有向边和无向边都受到图中无有向循环的限制。这种图形框架可能出现在许多生物医学研究中，例如，当感兴趣的有向无环图 (DAG) 被一些未观察到的混杂因素（例如，未测量的环境因素）引起的无向边污染时。DAG 中的有向边被广泛用于评估网络中变量之间的因果关系，但是当潜在的因果关系被一些共享的潜在因素掩盖时，检测它们是具有挑战性的。本文的目的是开发一种有效的结构方程模型 (SEM) 方法，以从 DAMG 中提取可靠的因果关系。建议的方法，称为结构因子方程模型 (SFEM)，使用 SEM 捕获 DAG 的网络拓扑，同时使用因子分析 (FA) 模型考虑图中的无向边。SFEM 中的潜在因素能够识别和去除无向边，从而形成更简单、更可解释的因果网络。通过广泛的模拟研究对所提出的方法进行评估并与现有方法进行比较，并通过构建与乳腺癌相关的基因调控网络来说明。本文受版权保护。版权所有。导致更简单和更可解释的因果网络。通过广泛的模拟研究对所提出的方法进行评估并与现有方法进行比较，并通过构建与乳腺癌相关的基因调控网络来说明。本文受版权保护。版权所有。导致更简单和更可解释的因果网络。通过广泛的模拟研究对所提出的方法进行评估并与现有方法进行比较，并通过构建与乳腺癌相关的基因调控网络来说明。本文受版权保护。版权所有。