basiSet function

Basis set of a DAG

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.

basiSet(amat)

Arguments

• amat: a square matrix with dimnames representing the adjacency matrix of a DAG.

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.

Returns

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).

References

Shipley, B. (2000). A new inferential test for path models based on directed acyclic graphs. Structural Equation Modeling, 7(2), 206--218.

Author(s)

Giovanni M. Marchetti

See Also

shipley.test, dSep, DAG

Examples

## See Shipley (2000), Figure 2, p. 213
A <- DAG(x5~ x3+x4, x3~ x2, x4~x2, x2~ x1)
basiSet(A)