pcalg (version 2.7-12)

dsepTest: Test for d-separation in a DAG

Description

Tests for d-separation of nodes in a DAG. dsepTest() is written to be easily used in skeleton, pc, fci.

Usage

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

Value

If x and y are d-separated by S in DAG G the result is 1, otherwise it is 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 DAG G.

Arguments

x,y

(integer) position of variable \(X\) and \(Y\), respectively, in the adjacency matrix.

S

(integer) positions of zero or more conditioning variables in the adjacency matrix.

suffStat

a list with two elements,

"g"

Containing the Directed Acyclic Graph (object of class "graph", see graph-class from the package graph), and

"jp"

Containing the shortest path distance matrix for all pairs of nodes as computed by johnson.all.pairs.sp from package RBGL.

Author

Markus Kalisch ()

Details

The function is based on dsep. For details on d-separation see the reference Lauritzen (2004).

References

S.L. Lauritzen (2004), Graphical Models, Oxford University Press.

See Also

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

Examples

p <- 8
set.seed(45)
myDAG <- randomDAG(p, prob = 0.3)

if (require(Rgraphviz)) {
## plot the DAG
plot(myDAG, main = "randomDAG(10, prob = 0.2)")
}

## define sufficient statistics (d-separation oracle)
suffStat <- list(g = myDAG, jp = RBGL::johnson.all.pairs.sp(myDAG))

dsepTest(1,6, S= NULL,  suffStat) ## not d-separated
dsepTest(1,6, S= 3,     suffStat) ## not d-separated by node 3
dsepTest(1,6, S= c(3,4),suffStat) ## d-separated by node 3 and 4