Find possible descendants on definite status paths.

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Description

In a DAG, CPDAG, MAG or PAG determine which nodes are possible descendants of x on definite status paths.

Usage

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possibleDe(amat, x)

Arguments

amat

adjacency matrix of type amat.pag

x

(integer) position of node x (node of interest) in the adjacency matrix.

Details

A non-endpoint vertex X on a path p in a partial mixed graph is said to be of a definite status if it is either a collider or a definite non-collider on p. The path p is said to be of a definite status if all non-endpoint vertices on the path are of a definite status (see e.g. Maathuis and Colombo (2015), Def. 3.4).

A possible descendent of x can be reached moving to adjacent nodes of x but never going against an arrowhead.

Value

Vector with possible descendents.

Author(s)

Diego Colombo

References

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

See Also

backdoor, amatType

Examples

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amat <- matrix( c(0,3,0,0,0,0, 2,0,2,0,0,0, 0,3,0,0,0,0, 0,0,0,0,1,0,
0,0,0,1,0,1, 0,0,0,0,1,0), 6,6)
colnames(amat) <- rownames(amat) <- letters[1:6]
if(require(Rgraphviz)) {
plotAG(amat)
}

possibleDe(amat, 1) ## a, b are poss. desc. of a
possibleDe(amat, 4) ## d, e, f are poss. desc. of d

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