R Under development (unstable) (2024-02-05 r85863 ucrt) -- "Unsuffered Consequences"
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> library(pcalg)
> (doExtras <- pcalg:::doExtras())
[1] FALSE
> 
> suppressWarnings(RNGversion("3.5.0"))
> set.seed(123)
> nreps <- 100
> res.local <- logical(nreps)
> res.opt <- logical(nreps)
> all.eff.true <- res.local
> Rnd <- function(e) round(e, 14)## get 14 digits accuracy, as we use true (DAG, cov)
> Rnd7 <- function(e) round(e, 7)## get 14 digits accuracy, as we use true (DAG, cov)
> for (i in 1:nreps) {
+   p <- 2 + rpois(1, lambda = 8) # ==>  p >= 2, E[p] = 10
+   ## generate and draw random DAG :
+   myDAG <- randomDAG(p, prob = 0.2)
+   myCPDAG <- dag2cpdag(myDAG)
+   mcov <- trueCov(myDAG)
+   
+   ## x != y  in {1,2,...p} ;
+   xy <- sample.int(p, 2); x <- xy[1]; y <- xy[2]
+   
+   ## plot(myCPDAG)
+   eff.true <- Rnd(causalEffect(myDAG, y, x))
+   all.eff.true[i] <- eff.true
+   ## cat("x=",x," y=",y," eff=",eff.true,"\n")
+   
+   eff.est.local <- Rnd(ida(x,y, mcov, myCPDAG, method="local"))
+   eff.est.opt <- Rnd(ida(x,y, mcov, myCPDAG, method="optimal"))
+   res.local[i] <- (eff.true %in% eff.est.local)
+   res.opt[i] <- (eff.true %in% eff.est.opt)
+ }
> ## cat('Time elapsed: ', (.pt <- proc.time()),"\n")
> 
> ## stem(all.eff.true)
> if (!all(res.local)) stop("Test ida: True effects were not recovered by local method!")
> if (!all(res.opt)) stop("Test ida: True effects were not recovered by optimal method!")
> 
> ## *one* test for  method="global" :
> eff.g.est <- Rnd(ida(x,y, mcov, myCPDAG, method="global", verbose=TRUE))
Fit - y: 4 x: 5 |b.hat= 0 
> stopifnot(eff.est.local == eff.g.est)
> 
> ## cat('Time elapsed additionally: ', proc.time() - .pt,"\n")
> if (doExtras) {
+ ## another special case (from Raphael Gervais)
+ set.seed(123)
+ p <- 7
+ myDAG <- randomDAG(p, prob = 0.2) ## true DAG
+ amatT <- as(myDAG, "matrix") # weighted adjacency matrix of true DAG
+ effT <- Rnd(amatT[2,3]*amatT[3,5]) # Causal effect of 2 on 5 from true DAG weighted matrix
+ myCPDAG <- dag2cpdag(myDAG) ## true CPDAG
+ covTrue <- trueCov(myDAG) ## true covariance matrix
+ effG <- Rnd(ida(2,5, covTrue,myCPDAG,method = "global"))
+ 
+ if (!(effT %in% effG)) stop("Test ida special case: True effects were not recovered!")
+ 
+ ##################################################
+ ## Tests for method = optimal; sets x
+ ##################################################
+ set.seed(1)
+ V <- sample(c("C1","C2","C3","X","C4","C5","C6","C7","Y","C8","C9","C10"))
+ myDAG <- randomDAG(20, 0.3)
+ mcov <- trueCov(myDAG)
+ amat <- t(as(myDAG,"matrix"))
+ graphEst <- dag2cpdag(myDAG)
+ amat.cpdag <- t(as(graphEst,"matrix"))
+ 
+ opt <- ida(c(4,6),12,trueCov(myDAG),graphEst,method="optimal",type="cpdag") 
+ RRC <- jointIda(c(4,6),12,trueCov(myDAG),graphEst,technique="RRC")
+ stopifnot(all.equal(opt,RRC, tolerance = 0.01))
+ 
+ opt <- ida(c(4,6),c(10,19),trueCov(myDAG),graphEst,method="optimal",type="cpdag")
+ RRC <- jointIda(c(4,6),c(10,19),trueCov(myDAG),graphEst,technique="MCD")
+ stopifnot(all.equal(opt,RRC, tolerance = 0.01))
+ 
+ opt <- ida(c(5,10),c(3),trueCov(myDAG),graphEst,method="optimal",type="cpdag")
+ RRC <- jointIda(c(5,10),c(3),trueCov(myDAG),graphEst,technique="RRC")
+ stopifnot(all.equal(opt,RRC, tolerance = 0.01))
+ 
+ ## sometimes they differ
+ ## ida(c(5,20),c(10),trueCov(myDAG),graphEst,method="optimal",type="cpdag")
+ ## jointIda(c(5,20),c(10),trueCov(myDAG),graphEst,technique="RRC")
+ 
+ ##################################################
+ ## Tests related to examples (use dontrun for slow global option there)
+ ##################################################
+ set.seed(123)
+ p <- 10
+ myDAG <- randomDAG(p, prob = 0.2) ## true DAG
+ myCPDAG <- dag2cpdag(myDAG) ## true CPDAG
+ myPDAG <- addBgKnowledge(myCPDAG,2,3) ## true PDAG with background knowledge 2 -> 3
+ covTrue <- trueCov(myDAG) ## true covariance matrix
+ 
+ ## simulate Gaussian data from the true DAG
+ n <- 10000
+ dat <- rmvDAG(n, myDAG)
+ 
+ ## estimate CPDAG and PDAG -- see  help(pc)
+ suffStat <- list(C = cor(dat), n = n)
+ pc.fit <- pc(suffStat, indepTest = gaussCItest, p=p, alpha = 0.01)
+ pc.fit.pdag <- addBgKnowledge(pc.fit@graph,2,3)
+ 
+ ## Supppose that we know the true CPDAG and covariance matrix
+ (l.ida.cpdag <- ida(3,10, covTrue, myCPDAG, method = "local", type = "cpdag"))
+ (o.ida.cpdag <- ida(3,10, covTrue, myCPDAG, method = "optimal", type = "cpdag"))
+ (g.ida.cpdag <- ida(3,10, covTrue, myCPDAG, method = "global", type = "cpdag"))
+ ## All three methods produce the same unique values.
+ stopifnot(all.equal(sort(unique(Rnd7(g.ida.cpdag))),
+                     sort(unique(Rnd7(l.ida.cpdag)))))
+ stopifnot(all.equal(sort(unique(Rnd7(g.ida.cpdag))),
+                     sort(unique(Rnd7(as.vector(o.ida.cpdag))))))
+ 
+ ## Supppose that we know the true PDAG and covariance matrix
+ (l.ida.pdag <- ida(3,10, covTrue, myPDAG, method = "local", type = "pdag"))
+ (o.ida.pdag <- ida(3,10, covTrue, myPDAG, method = "optimal", type = "pdag"))
+ (g.ida.pdag <- ida(3,10, covTrue, myPDAG, method = "global", type = "pdag"))
+ ## All three methods produce the same unique values.
+ stopifnot(all.equal(sort(unique(Rnd7(g.ida.pdag))),
+                     sort(unique(Rnd7(l.ida.pdag)))))
+ stopifnot(all.equal(sort(unique(Rnd7(g.ida.pdag))),
+                     sort(unique(Rnd7(as.vector(o.ida.pdag))))))
+ 
+ ## From the true DAG, we can compute the true causal effect of 3 on 10
+ (ce.3.10 <- causalEffect(myDAG, 10, 3))
+ ## Indeed, this value is contained in the values found by all methods
+ 
+ ## When working with data we have to use the estimated CPDAG and
+ ## the sample covariance matrix
+ (l.ida.est.cpdag <- ida(3,10, cov(dat), pc.fit@graph, method = "local", type = "cpdag"))
+ (o.ida.est.cpdag <- ida(3,10, cov(dat), pc.fit@graph, method = "optimal", type = "cpdag"))
+ (g.ida.est.cpdag <- ida(3,10, cov(dat), pc.fit@graph, method = "global", type = "cpdag"))
+ ## The unique values of the local and the global method are still identical.
+ stopifnot(all.equal(sort(unique(Rnd7(g.ida.est.cpdag))), sort(unique(Rnd7(l.ida.est.cpdag)))))
+ ## While not identical, the values of the optimal method are very similar.
+ stopifnot(all.equal(sort(o.ida.est.cpdag), sort(l.ida.est.cpdag), tolerance = 0.025))
+ ## The true causal effect is contained in all three sets, up to a small
+ ## estimation error (0.118 vs. 0.112 with true value 0.114) 
+ stopifnot(all.equal(ce.3.10, min(l.ida.est.cpdag), tolerance = 0.04))
+ stopifnot(all.equal(ce.3.10, min(o.ida.est.cpdag), tolerance = 0.02))
+ 
+ ## Similarly, when working with data and background knowledge we have to use the estimated PDAG and
+ ## the sample covariance matrix
+ (l.ida.est.pdag <- ida(3,10, cov(dat), pc.fit.pdag, method = "local", type = "pdag"))
+ (o.ida.est.pdag <- ida(3,10, cov(dat), pc.fit.pdag, method = "optimal", type = "pdag"))
+ (g.ida.est.pdag <- ida(3,10, cov(dat), pc.fit.pdag, method = "global", type = "pdag"))
+ ## The unique values of the local and the global method are still identical.
+ stopifnot(all.equal(sort(unique(Rnd7(g.ida.est.pdag))), sort(unique(Rnd7(l.ida.est.pdag)))))
+ ## While not necessarily identical, the values of the optimal method will be similar.
+ stopifnot(all.equal(sort(Rnd7(o.ida.est.pdag)), sort(Rnd7(l.ida.est.pdag)), tolerance = 0.08))
+ ## The true causal effect is contained in both sets, up to a small estimation error
+ stopifnot(all.equal(ce.3.10, min(l.ida.est.pdag), tolerance = 0.04))
+ stopifnot(all.equal(ce.3.10, min(o.ida.est.pdag), tolerance = 0.02))
+ 
+ }
> 
> proc.time()
   user  system elapsed 
   4.43    0.20    4.64