 
Summary: 1
Technical Report CMUPhil72
Using Dseparation to Calculate Zero Partial Correlations in
Linear Models with Correlated Errors
Peter Spirtes
Thomas Richardson
Christopher Meek
Richard Scheines
Clark Glymour
Abstract
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).
