pcalg (version 2.4-3)

checkTriple: Check Consistency of Conditional Independence for a Triple of Nodes

Description

For each subset of nbrsA and nbrsC where a and c are conditionally independent, it is checked if b is in the conditioning set.

Usage

checkTriple(a, b, c, nbrsA, nbrsC, sepsetA, sepsetC, suffStat, indepTest, alpha, version.unf = c(NA, NA), maj.rule = FALSE, verbose = FALSE)

Arguments

a, b, c

(integer) positions in adjacency matrix for nodes $a$, $b$, and $c$, respectively.

nbrsA, nbrsC

(integer) position in adjacency matrix for neighbors of $a$ and $c$, respectively.

sepsetA

vector containing $Sepset(a,c)$.

sepsetC

vector containing $Sepset(c,a)$.

suffStat

a list of sufficient statistics for independent tests; see, e.g., pc.

indepTest

a function for the independence test, see, e.g., pc.

alpha

significance level of test.

version.unf

(integer) vector of length two:

maj.rule

logical indicating that the following majority rule is applied: if b is in less than 50% of the checked sepsets, we say that b is in no sepset. If b is in more than 50% of the checked sepsets, we say that b is in all sepsets. If b is in exactly 50% of the checked sepsets, the triple is considered ‘ambiguous’.

verbose

Logical asking for detailed output of intermediate steps.

Value

Details

This function is used in the conservative versions of structure learning algorithms.

References

D. Colombo and M.H. Maathuis (2014).Order-independent constraint-based causal structure learning. Journal of Machine Learning Research 15 3741-3782.

Examples

##################################################
## Using Gaussian Data
##################################################
## Load predefined data
data(gmG)
n <- nrow    (gmG8$x)
V <- colnames(gmG8$x)


## define independence test (partial correlations), and test level
indepTest <- gaussCItest
alpha <- 0.01
## define sufficient statistics
suffStat <- list(C = cor(gmG8$x), n = n)

## estimate CPDAG
pc.fit <- pc(suffStat, indepTest, alpha=alpha, labels = V, verbose = TRUE)

if (require(Rgraphviz)) {
  ## show estimated CPDAG
  par(mfrow=c(1,2))
  plot(pc.fit, main = "Estimated CPDAG")
  plot(gmG8$g, main = "True DAG")
}

a <- 6
b <- 1
c <- 8
checkTriple(a, b, c,
            nbrsA = c(1,5,7),
            nbrsC = c(1,5),
            sepsetA = pc.fit@sepset[[a]][[c]],
            sepsetC = pc.fit@sepset[[c]][[a]],
            suffStat=suffStat, indepTest=indepTest, alpha=alpha,
            version.unf = c(2,2),
            verbose = TRUE) -> ct
str(ct)
## List of 4
## $ decision: int 2
## $ version : int 1
## $ SepsetA : int [1:2] 1 5
## $ SepsetC : int 1

checkTriple(a, b, c,
            nbrsA = c(1,5,7),
            nbrsC = c(1,5),
            sepsetA = pc.fit@sepset[[a]][[c]],
            sepsetC = pc.fit@sepset[[c]][[a]],
            version.unf = c(1,1),
            suffStat=suffStat, indepTest=indepTest, alpha=alpha) -> c2
stopifnot(identical(ct, c2)) ## in this case,  'version.unf' had no effect