Causal Diagrams

From their inception in the early 20th century, causal systems models (more commonly known as structural-equations models) were accompanied by graphical representations or path diagrams that provided compact summaries of qualitative assumptions made by the models. Figure 1 provides a graph that would correspond to any system of five equations encoding these assumptions:

• 1.
  Independence of A and B
• 2.
  Direct dependence of C on A and B
• 3.
  Direct dependence of E on A and C
• 4.
  Direct dependence of F on C
• 5.
  Direct dependence of D on B, C, and E

The interpretation of ‘direct dependence’ was kept rather informal and usually conveyed by causal intuition, for example, that the entire influence of A on F is ‘mediated’ by C.

By the 1980s, it was recognized that these diagrams could be reinterpreted formally as probability models, which opened the visual power of graph theory for use in probabilistic inference and allowed easy deduction of other independence conditions implied by the assumptions. By the 1990s, it was further recognized that these diagrams could also be [Page 150]used as a formal tool for causal inference, such as predicting the effects of external interventions. Given that the graph is correct, one can see whether the causal effects of interest (target effects, or causal estimands) can be estimated from available data, or what additional observations are needed to validly estimate those effects. One can also see how to represent the effects as familiar standardized effect measures.

Figure 1 Example of a Directed Acrylic Graph

This entry gives an overview of (1) components of causal graph theory, (2) probability interpretations of graphical models, and (3) the methodological implications of the causal and probability structures encoded in the graph.