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Factorization of the Partial Covariance in Singly-Connected Path Diagrams. (arXiv:2002.05226v6 [stat.ME] UPDATED)
We extend path analysis by showing that, for a singly-connected path diagram,
the partial covariance of two random variables factorizes over the nodes and
edges in the path between the variables. This result allows us to determine the
contribution of each node and edge to the partial covariance. It also allows us
to show that Simpson's paradox cannot occur in singly-connected path diagrams.