pcalg (version 1.0-0)

gSquareBin: Test for (conditional) independence for binary data

Description

G^2 statistic to test for (conditional) independence of X and Y given set S.

Usage

gSquareBin(x, y, S, dm, verbose = FALSE, adaptDF = FALSE)

Arguments

x

Position of node X in adjacency matrix

y

Position of node Y in adjacency matrix

S

Position of set of nodes in adjacency matrix on which is conditioned

dm

Data matrix (rows: samples, columns: variables) with binary entries

verbose

Additional output if TRUE

adaptDF

Lower the degrees of freedom by one for each zero count. The value for the degrees of freedom cannot go below 1.

Value

• The p-value of the test is returned.

Details

The G^2 statistic is used to test for (conditional) independence of X and Y given a set S (cann be NULL). This function is a specialized version of gSquareDis which can deal with an arbitrary amount of levels for discrete variables.

References

R.E. Neapolitan (2004) Learning Bayesian Networks, Prentice Hall Series in Artificial Intelligence, Chapter 10.3.1

See Also

gSquareDis for a (conditional) independence test for discrete variables with more than two levels.

Examples

## Simulate data from a chain of 3 variables: x1 -> x2 -> x3
set.seed(123)
expit <- function(x) { exp(x) / (1 + exp(x)) }
b0 <- 0
b1 <- 1
b2 <- 1
n <- 10000
x1 <- sample(c(0,1),n,replace=TRUE)

p2 <- expit(b0 + b1*x1)
x2 <- rep(NA,length(x1))
for (i in 1:n) {
  x2[i] <- sample(c(0,1),1,prob=c(1-p2[i],p2[i]))
}
p3 <- expit(b0 + b2*x2)
x3 <- rep(NA,length(x2))
for (i in 1:n) {
  x3[i] <- sample(c(0,1),1,prob=c(1-p3[i],p3[i]))
}

dat <- cbind(x1,x2,x3)

## Test marginal and conditional independencies
gSquareBin(3,1,NULL,dat)
gSquareBin(3,1,2,dat)
gSquareBin(1,3,2,dat)