Pub. date: 2008 | Online Pub. Date: November 27, 2007 | DOI: 10.4135/9781412953948 | Print ISBN: 9781412928168 | Online ISBN: 9781412953948| Publisher:SAGE Publications, Inc.About this encyclopedia
Sander Greenland & Judea Pearl
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 ...