Single World Intervention Graphs: A Primer

Abstract

We present a simple graphical theory unifying causal directed acyclic graphs (DAGs) and potential (aka counter-factual) outcomes via a node-splitting transformation. We introduce a new graph, the Single-World Intervention Graph (SWIG). The SWIG encodes the counterfactual independences associated with a specific hypothetical intervention on the set of treatment variables. The nodes on the SWIG are the correspond-ing counterfactual random variables. We illustrate the theory with a number of examples. Our graphical theory of SWIGs may be used to infer the coun-terfactual independence relations that hold among the SWIG variables under the FFRCISTG model of Robins (1986) and the NPSEM model with Indepen-dent Errors of Pearl (2000, 2009). Fur-thermore, in the absence of hidden vari-ables, the joint distribution of the coun-terfactuals is identified; the identifying formula is the extended g-computation formula introduced in (Robins et al., 2004). As an illustration of the benefit of reasoning with SWIGs, we use SWIGs to correct an error regarding Example 11.3.3 presented in (Pearl, 2009)