Using d-separation to calculate zero partial correlations in linear models with correlated errors

It has been shown in Spirtes(1995) that X and Y are d-separated given Z in a directed graph associated with a recursive or non-recursive linear model without correlated errors if and only if the model entails that ρXY.Z = 0. This result cannot be directly applied to a linear model with correlated errors, however, because the standard graphical representation of a linear model with correlated errors is not a directed graph. The main result of this paper is to show how to associate a directed graph with a linear model L with correlated errors, and then use d-separation in the associated directed graph to determine whether L entails that a particular partial correlation is zero.
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