pcalg (version 2.7-12)

searchAM: Search for certain nodes in a DAG/CPDAG/MAG/PAG

Description

Searches for all ancestors, descendants, anteriors, spouses, neighbors, parents, children or possible descendants of a (set of) node(s) in a DAG, CPDAG, MAG or PAG.

Usage

searchAM(amat,x,
	 type = c("an", "de", "ant", "sp", "nb", "pa", "ch", "pde"))

Value

Vector of column numbers of the nodes related to x as specified by type.

Arguments

amat

Adjacency matrix of type amat.pag.

x

Target node(s), given as (a vector of) column number(s) of the node(s) in the adjacency matrix.

type

Character string specifying which relation to the target nodes in x is asked for. It can be one of:

"an"

ancestors: nodes y s.t. y-->...-->x;

"de"

descendants: nodes y s.t. y<--...<--x;

"ant"

anteriors: nodes y s.t. y---...---z-->...-->x, i.e. there is an undirected path from y to a node z followed by a directed path from z to x;

"sp"

spouses: nodes y s.t. y<->x;

"nb"

neighbors: nodes y s.t. y---x;

"pa"

parents: nodes y s.t. y-->x;

"ch"

children: nodes y s.t. y<--x;

"pde"

possible descendants: nodes y s.t. there is a possibly directed path from y to x: y {o,-}--{o,>} ... {o,-}--{o,>} x.

For the precise definitions of these concepts, see the references.

Author

Joris Mooij.

Details

This function performs a search for nodes related to the set of target nodes x in the way specified by type in adjacency matrix amat of type amat.pag.

References

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

J. Zhang (2008). Causal Reasoning with Ancestral Graphs. Journal of Machine Learning Research 9 1437-1474.

Examples

# Y-structure MAG
# Encode as adjacency matrix
p <- 10 # total number of variables
V <- c("X1","X2","X3","X4","X5","X6","X7","X8","X9","X10") # 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(0,3,0,0,0,0,0,0,0,0),
              c(3,0,3,0,0,0,0,0,0,0),
              c(0,3,0,2,0,0,0,0,0,0),
              c(0,0,3,0,2,0,0,0,0,0),
              c(0,0,0,3,0,2,0,2,2,1),
              c(0,0,0,0,3,0,2,0,0,0),
              c(0,0,0,0,0,3,0,0,0,0),
              c(0,0,0,0,2,0,0,0,0,0),
              c(0,0,0,0,1,0,0,0,0,0),
              c(0,0,0,0,1,0,0,0,0,0))
rownames(amat)<-V
colnames(amat)<-V

stopifnot(all.equal(searchAM(amat,5,type = "an"), c(3,4,5))) # ancestors of X5
stopifnot(all.equal(searchAM(amat,5,type = "de"), c(5,6,7))) # descendants of X5
stopifnot(all.equal(searchAM(amat,5,type = "ant"), c(1,2,3,4,5))) # anteriors of X5
stopifnot(all.equal(searchAM(amat,5,type = "sp"), c(8))) # spouses of X5
stopifnot(all.equal(searchAM(amat,2,type = "nb"), c(1,3))) # neighbors of X2
stopifnot(all.equal(searchAM(amat,c(4,6),type = "pa"), c(3,5))) # parents of {X4,X6}
stopifnot(all.equal(searchAM(amat,c(3,5),type = "ch"), c(4,6))) # children of {X3,X5}
stopifnot(all.equal(searchAM(amat,5,type = "pde"), c(5,6,7,9,10))) # possible descendants of X5