Nothing

```
# test case for the "Lake" example which illustrates the differences between DDGraph and DDGraph*
library(ddgraph)
library(testthat)
# fix the random seed
set.seed(311)
# the real graphs is as follows:
# Trees <- Lake
# Leaves <- Trees
# Fish <- Lake, Season
# People <- Season, Fish
# Lake, Season have no parents
data = matrix(0, ncol=6, nrow=5000)
colnames(data) = c("Fish", "Trees", "Leaves", "Season", "People", "Lake")
data = data.frame(data)
for(i in 1:nrow(data)){
data$Season[i] = sample(c(0,1), 1)
data$Lake[i] = sample(c(0,1), 1)
if(data$Lake[i] == 1){
data$Trees[i] = sample(c(0,1), 1, prob=c(0.2, 0.8))
if(data$Season[i] == 1)
data$Fish[i] = sample(c(0,1), 1, prob=c(0.4, 0.6))
else
data$Fish[i] = sample(c(0,1), 1, prob=c(0.1, 0.9))
} else {
data$Trees[i] = sample(c(0,1), 1, prob=c(0.6, 0.4))
if(data$Season[i] == 1)
data$Fish[i] = sample(c(0,1), 1, prob=c(0.6, 0.4))
else
data$Fish[i] = sample(c(0,1), 1, prob=c(0.1, 0.9))
}
if(data$Season[i] == 1 & data$Fish[i] == 1){
data$People[i] = sample(c(0,1), 1, prob=c(0.1, 0.9))
} else {
data$People[i] = sample(c(0,1), 1, prob=c(0.9, 0.1))
}
if(data$Trees[i] == 1)
data$Leaves[i] = sample(c(0,1), 1, prob=c(0.4, 0.6))
else
data$Leaves[i] = sample(c(0,1), 1, prob=c(0.9, 0.1))
}
dd = data
names(dd)[ncol(dd)] = "class"
d = makeDDDataSet(dd, "Lake")
eg = ncpc(d, alpha=0.05, star=F, verbose=F, test.type="x2")
egs = ncpc(d, alpha=0.05, star=T, verbose=F, test.type="x2")
# only the DDGraph* can correctly identify only Fish and Trees are primary variables
# DDGraph (original) will have a false positive People even when there is infinite data
test_that("Lake example", {
expect_equal(eg$direct, structure(c(1, 2, 5), names=c("Fish", "Trees", "People")))
expect_equal(egs$direct, structure(c(1, 2), names=c("Fish", "Trees")))
})
```

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