Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume 64, Issue -, Pages 321-348Publisher
WILEY
DOI: 10.1111/1467-9868.00340
Keywords
causal model; chain graph; feed-back system; Gibbs sampler; intervention theory; structural equation model
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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.
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