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Abstract:
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Confounding is a fundamental concept in statistical inference; however, clear definitions of what constitutes confounding have sometimes been elusive. This has caused confusion about whether some quantities, such as time-varying covariates, should be controlled for or ignored. Mixed graphical models, that is graphs with more than one type of edge, have done much to clarify the relationships between confounding, mediation, and other forms of bias.
We review the history of graphs and graphical models of confounding, including Sewall Wright's path diagrams, summary graphs, ancestral graphs, nested Markov models, and models with inequalities. Markov equivalence results for models that include confounding are available, and show that ordinary mixed graphs are not rich enough to represent all non-parametric confounding structures. We also provide a class of hypergraphs, mDAGs, which are in one-to-one correspondence with causal models of confounding.
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