dreach {pcalg}

Compute D-SEP(x,y,G)

Description

Let x and y be two distinct vertices in a mixed graph G. This function computes D-SEP(x,y,G), which is defined as follows:

A node v is in D-SEP(x,y,G) iff v is not equal to x and there is a collider path between x and v in G such that every vertex on this path is an ancestor of x or y in G.

See p.136 of Sprirtes et al (2000) or Definition 4.1 of Maathuis and Colombo (2015).

Usage

  dreach(x, y, amat, verbose = FALSE)

Arguments

x

First argument of D-SEP, given as the column number of the node in the adjacency matrix.

y

Second argument of D-SEP, given as the column number of the node in the adjacency matrix (y must be different from x).

amat

Adjacency matrix of type amat.pag.

verbose

Logical specifying details should be on output

Value

Vector of column positions indicating the nodes in D-SEP(x,y,G).

Author(s)

Diego Colombo and Markus Kalisch ([e-mail])

References

P. Spirtes, C. Glymour and R. Scheines (2000) Causation, Prediction, and Search, 2nd edition, The MIT Press.

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

See Also

backdoor uses this function; pag2magAM.