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pcalg (version 2.0-3)

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

Description

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 of p, t is a collider on this subpath or is a triangle in G.

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

Usage

qreach(x, amat, verbose = FALSE)

Arguments

x
Integer: column position of node in adjacency matrix, of which Possible-D-SEP set is to be computed.
amat
Adjacency matrix (coding 0,1,2,3 for no edge, circle, arrowhead, tail; e.g., amat[a,b] = 2 and amat[b,a] = 3 implies a -> b)
verbose
Logical, asking for details on output

Value

  • 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.

See Also

fci and pdsep which both use this function.