R Under development (unstable) (2024-09-06 r87103 ucrt) -- "Unsuffered Consequences"
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> library(pcalg)
> 
> # 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)
> 
> cat('X1 d-separated from X2? ', dsepAMTest(1,2,S=NULL,suffStat),'\n') ## d-separated
X1 d-separated from X2?  1 
> cat('X1 d-separated from X2 given X4? ', dsepAMTest(1,2,S=4,suffStat),'\n') ## not d-separated given node 3
X1 d-separated from X2 given X4?  0 
> cat('X1 d-separated from X2 given X3 and X4? ', dsepAMTest(1,2,S=c(3,4),suffStat),'\n') ## not d-separated by node 3 and 4
X1 d-separated from X2 given X3 and X4?  0 
> 
> # 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)
> 
> true.pag <- rbind(c(0,0,2,0),
+                   c(0,0,2,0),
+                   c(1,1,0,2),
+                   c(0,0,3,0))
> rownames(true.pag)<-V
> colnames(true.pag)<-V
> 
> cat('True MAG:\n')
True MAG:
> print(amat)
   X1 X2 X3 X4
X1  0  0  2  0
X2  0  0  2  0
X3  3  3  0  2
X4  0  0  3  0
> cat('PAG output by FCI:\n')
PAG output by FCI:
> print(fci.pag@amat)
   X1 X2 X3 X4
X1  0  0  2  0
X2  0  0  2  0
X3  1  1  0  2
X4  0  0  3  0
> cat('True PAG:\n')
True PAG:
> print(true.pag)
   X1 X2 X3 X4
X1  0  0  2  0
X2  0  0  2  0
X3  1  1  0  2
X4  0  0  3  0
> 
> stopifnot(identical(true.pag,fci.pag@amat))
> 
> proc.time()
   user  system elapsed 
   1.06    0.17    1.21