qreach function

Compute Possible-D-SEP(x,G) of a node x in a PDAG G

Let G be a graph with the following edge types: o-o, o-> or <->, and let x be a vertex in the graph. Then this function computes Possible-D-SEP(x,G), which is defined as follows:

v is in Possible-D-SEP(x,G) iff there is a path p between x and v in G such that for every subpath <s,t,u> of p, t is a collider on this subpath or <s,t,u> is a triangle in G.

See Spirtes et al (2000) or Definition 3.3 of Colombo et al (2012).

qreach(x, amat, verbose = FALSE)

Arguments

• x: (integer) position of vertex $x$ in the adjacency matrix of which Possible-D-SEP set is to be computed.
• amat: Adjacency matrix of type amat.pag .
• verbose: Logical, asking for details on output

Returns

Vector of column positions indicating the nodes in Possible-D-SEP of x.

References

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

D. Colombo, M.H. Maathuis, M. Kalisch, T.S. Richardson (2012). Learning high-dimensional directed acyclic graphs with latent and selection variables. Annals of Statistics 40 , 294--321.

Author(s)

Markus Kalisch (kalisch@stat.math.ethz.ch )

See Also

fci and pdsep which both use this function.