Technical Report CMUPhil72
Using Dseparation to Calculate Zero Partial Correlations in
Linear Models with Correlated Errors
It has been shown in Spirtes(1995) that X and Y are dseparated given Z in a directed
graph associated with a recursive or nonrecursive linear model without correlated errors if
and only if the model entails that r XY.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 dseparation in the associated directed graph to determine whether L entails that a
particular partial correlation is zero.
In a linear structural equation model (SEM) some partial correlations may be equal to zero
for all values of the model's free parameters (for which the partial correlation is defined).