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:

  • Independence of A and B
  • Direct dependence of C on A and B
  • Direct dependence of E on A and C
  • Direct dependence of F on C
  • 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 ...

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