In applications, quantities of interest are often modelled in equilibrium or an equilibrium solution is sought. The presence of confounding makes causal inference in this setting challenging. We provide interpretable graphical models for equilibrium systems with confounding using anterial graphs (Lauritzen and Sadeghi, 2018), a class of graphs containing directed acyclic graphs, ancestral graphs, and chain graphs. In this setting, we provide valid graphical representations of both counterfactual variables and observational variables, which we relate to counterfactual graphs (Shpitser and Pearl, 2007) and single-world intervention graphs (Richardson and Robins,2013). As an application of this graphical representation, we provide an element-wise procedure of selecting adjustment sets that flexibly include and exclude given covariates.

翻译：在应用中，感兴趣的量通常以均衡态建模，或寻求均衡解。混杂因素的存在使该情境下的因果推断充满挑战。我们利用前向图（Lauritzen和Sadeghi，2018）——一类包含有向无环图、祖先图和链图的图结构——为含混杂项的均衡系统提供了可解释图模型。在该框架下，我们给出了反事实变量和观测变量的有效图表示，并将其与反事实图（Shpitser和Pearl，2007）及单世界干预图（Richardson和Robins，2013）建立关联。作为该图表示的应用，我们提出了一种逐元素选择调整集的程序，可灵活地纳入或排除给定协变量。