visibleEdge {pcalg}

Check visible edge.

Description

Check if the directed edge from x to z in a MAG or in a PAG is visible or not.

Usage

visibleEdge(amat, x, z)

Arguments

amat

Adjacency matrix of type amat.pag

x, z

(integer) position of variable x and z, respectively, in the adjacency matrix.

Details

All directed edges in DAGs and CPDAGs are said to be visible. Given a MAG M / PAG P, a directed edge A -> B in M / P is visible if there is a vertex C not adjacent to B, such that there is an edge between C and A that is into A, or there is a collider path between C and A that is into A and every non-endpoint vertex on the path is a parent of B. Otherwise A -> B is said to be invisible. (see Maathuis and Colombo (2015), Def. 3.1)

Value

TRUE if edge is visible, otherwise FALSE.

Author(s)

Diego Colombo

References

M.H. Maathuis and D. Colombo (2015). A generalized backdoor criterion. Annals of Statistics 43 1060-1088.

See Also

backdoor

Examples

amat <- matrix(c(0,3,0,0, 2,0,2,3, 0,2,0,3, 0,2,2,0), 4,4)
colnames(amat) <- rownames(amat) <- letters[1:4]
if(require(Rgraphviz)) {
plotAG(amat)
}

visibleEdge(amat, 3, 4) ## visible
visibleEdge(amat, 2, 4) ## visible
visibleEdge(amat, 1, 2) ## invisible