ggm (version 0.5)

basiSet: Basis set of a DAG

Description

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(A)

Arguments

A

a square Boolean matrix with dimnames representing the edge matrix of a DAG.

Value

• a list of vectors representing several conditional independence statements. Each vector contains the names of two non adjacent nodes plus the names of the nodes in the conditioning set (which may be empty).

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 (cfr. 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.

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)