pcalg (version 1.1-4)

udag2pag: Extend a pcAlgo-object containing a skeleton to a PAG

Description

This function extends a pcAlgo-object containing a skeleton and corresponding conditional independence information to a Partial Ancestral Graph (PAG). The pcAlgo-object must have been estimated with the option psepset=TRUE. The result is an adjacency matrix indicating also the edge marks.

Usage

udag2pag(gInput, rules, verbose, unfVect = NULL)

Arguments

gInput

pcAlgo-object containing skeleton and cond. ind. information; must have been estimated with psepset=TRUE

rules

array of length 10 containing TRUE or FALSE for each rule. TRUE in position i means that rule i (Ri) will be used. Per default, all rules are set to TRUE.

verbose

0: No output; 1: Details. Default is 0.

unfVect

Vector containing numbers that encode the unfaithful triple (as returned by pc.cons.intern). This is needed in the conservative FCI.

Value

• The output is an adjacency matrix M with edge marks. The edge marks are coded in the following way: M[i,j]=M[j,i]=0: no edge; M[i,j]=1, M[j,i] != 0: i *-o j; M[i,j]=2, M[j,i]!=0: i*->j; M[i,j]=3, M[j,i]!=0: i*-j.

Details

The skeleton is extended to a PAG using rules by Zhang (see References). Note that the algorithm works with columns' position of the adjacency matrix and not with the names of the variables.

References

J. Zhang (2008). On the completeness of orientation rules for causal discovery in the presence of latent confounders and selection bias. Artificial Intelligence 172 1873-1896.

See Also

pc

Examples

## generate and draw random DAG
## this example is taken from Zhang (2008), Fig. 6, p.1882 (see references)
amat <- t(matrix(c(0,1,0,0,1, 0,0,1,0,0, 0,0,0,1,0, 0,0,0,0,0, 0,0,0,1,0),5,5))
colnames(amat) <- rownames(amat) <- as.character(1:5)
V <- as.character(1:5)
edL <- vector("list",length=5)
names(edL) <- V
edL[[1]] <- list(edges=c(2,4),weights=c(1,1))
edL[[2]] <- list(edges=3,weights=c(1))
edL[[3]] <- list(edges=5,weights=c(1))
edL[[4]] <- list(edges=5,weights=c(1))
g <- new("graphNEL", nodes=V, edgeL=edL,edgemode="directed")
if (require(Rgraphviz)) {
plot(g)
}

## define the latent variable
L <- 1

## generate 100000 samples of DAG using standard normal error distribution
n <- 100000
d.mat <- rmvDAG(n, g, errDist = "normal")

## delete rows and columns corresponding to the latent variable
d.mat <- d.mat[-L,-L]

## estimate the skeleton of given data using psepset=TRUE
(resD <- pcAlgo(d.mat, alpha=0.05, psepset=TRUE))

## extend the pcalgo-object into a PAG using all 10 rules
rules <- rep(TRUE,10)
resP <- udag2pag(resD, rules=rules, verbose=1)
colnames(resP) <- rownames(resP) <- graph::nodes(g)[-L]

if (require(Rgraphviz)) {
  ## plot the original DAG and the PAG
  op <- par(mfrow=c(1,2))
  plot(g, main="original (random) DAG")
  plotAG(resP)
  par(op)
}