dsepAMTest {pcalg}

Test for d-separation in a MAG

Description

This function tests for d-separation (also known as m-separation) of node x and node y given nodes S in a MAG. dsepAMTest() is written to be easily used in skeleton, fci, fciPlus.

Usage

dsepAMTest(x, y, S = NULL, suffStat)

Arguments

x

Column number of node x in the adjacency matrix

y

Column number of node y in the adjacency matrix

S

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

suffStat

a list with two elements,

amat

The Maximal Ancestral Graph encoded as adjacency matrix of type amatType

verbose

If true, more detailed output is provided.

Details

The function is a wrapper for dsepAM, which checks separation in the moralized graph as explained in Richardson and Spirtes (2002).

Value

Returns 1 if x and y are d-separated by S in the MAG encoded by amat, otherwise 0.

This is analogous to the p-value of an ideal (without sampling error) conditional independence test on any distribution that is faithful to the MAG.

Author(s)

Markus Kalisch ([e-mail]), Joris Mooij

References

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

See Also

dsepTest for a similar function for DAGs. gaussCItest, disCItest and binCItest for similar functions for a conditional independence test for gaussian, discrete and binary variables, respectively.

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

suffStat<-list(g=amat,verbose=FALSE)
## d-separated
cat('X1 d-separated from X2? ', dsepAMTest(1,2,S=NULL,suffStat),'\n')
## not d-separated given node 3
cat('X1 d-separated from X2 given X4? ',
dsepAMTest(1,2,S=4,suffStat),'\n')
## not d-separated by node 3 and 4
cat('X1 d-separated from X2 given X3 and X4? ', dsepAMTest(1,2,S=c(3,4),
suffStat),'\n')

# Derive PAG that represents the Markov equivalence class of the MAG with the FCI algorithm
# Make use of d-separation oracle as "independence test"
indepTest <- dsepAMTest
fci.pag <- fci(suffStat,indepTest,alpha = 0.5,labels = V,verbose=FALSE)
cat('True MAG:\n')
print(amat)
cat('PAG output by FCI:\n')
print(fci.pag@amat)