pcalg (version 2.7-12)

dsepAM: Test for d-separation in a MAG

Description

This function tests for d-separation (also known as m-separation) of nodes X and nodes Y given nodes S in a MAG.

Usage

dsepAM(X, Y, S = NULL, amat, verbose=FALSE)

Value

TRUE if X and Y are d-separated by S in the MAG encoded by amat, otherwise FALSE.

Arguments

X

Vector of column numbers of nodes X in the adjacency matrix

Y

Vector of column numbers of nodes Y in the adjacency matrix

S

Vector of column numbers of nodes S in the adjacency matrix (may be empty)

amat

The Maximal Ancestral Graph encoded as adjacency matrix of type amatType

verbose

If true, more detailed output is provided.

Author

Markus Kalisch (), Joris Mooij

Details

This function checks separation in the moralized graph as explained in Richardson and Spirtes (2002).

References

T.S. Richardson and P. Spirtes (2002). Ancestral graph Markov models. Annals of Statistics 30 962-1030.

See Also

dsepAMTest for a wrapper of this function that can easily be included into skeleton, fci or fciPlus. dsep for a similar function for DAGs.

Examples

# Y-structure MAG
# Encode as adjacency matrix
p <- 4 # total number of variables
V <- c("X1","X2","X3","X4") # variable labels
# amat[i,j] = 0 iff no edge btw i,j
# amat[i,j] = 1 iff i *-o j
# amat[i,j] = 2 iff i *-> j
# amat[i,j] = 3 iff i *-- j
amat <- rbind(c(0,0,2,0),
              c(0,0,2,0),
              c(3,3,0,2),
              c(0,0,3,0))
rownames(amat)<-V
colnames(amat)<-V

## d-separated
cat('X1 d-separated from X2? ', dsepAM(1,2,S=NULL,amat),'\n')
## not d-separated given node 3
cat('X1 d-separated from X2 given X4? ', dsepAM(1,2,S=4,amat),'\n')
## not d-separated by node 3 and 4
cat('X1 d-separated from X2 given X3 and X4? ', dsepAM(1,2,S=c(3,4),amat),'\n')