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Chain graph models and their causal interpretations
Author(s) -
Lauritzen Steffen L.,
Richardson Thomas S.
Publication year - 2002
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00340
Subject(s) - directed acyclic graph , conditional independence , simple (philosophy) , generalization , interpretation (philosophy) , chain (unit) , computer science , mathematical economics , mathematics , epistemology , combinatorics , artificial intelligence , philosophy , mathematical analysis , physics , astronomy , programming language
Chain graphs are a natural generalization of directed acyclic graphs and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are many simple and apparently plausible, but ultimately fallacious, interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to flawed methods for applying background knowledge to model selection. We present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated from the equilibrium distributions of dynamic models with feed‐back. These dynamic interpretations lead to a simple theory of intervention, extending the theory developed for directed acyclic graphs. Finally, we contrast chain graph models under this interpretation with simultaneous equation models which have traditionally been used to model feed‐back in econometrics.