Finds a basis set for the conditional independencies
implied by a directed acyclic graph, that is a minimal set of
independencies that imply all the other ones.
Usage
basiSet(amat)
Value
a list of vectors representing several conditional independence
statements. Each vector contains the names of two non adjacent
nodes followed by the names of nodes in the conditioning set (which
may be empty).
Arguments
amat
a square matrix with dimnames representing the adjacency matrix
of a DAG.
Author
Giovanni M. Marchetti
Details
Given a DAG and a pair of non adjacent nodes
\((i,j)\) such that \(j\) has higher causal order than \(i\),
the set of independency statements \(i\) independent of
\(j\) given the union of the parents of both \(i\) and \(j\)
is a basis set (see Shipley, 2000). This basis set has the property
to lead to independent test statistics.
References
Shipley, B. (2000). A new inferential test
for path models based on directed acyclic graphs. Structural
Equation Modeling, 7(2), 206--218.