disCItest: G square Test for (Conditional) Independence of Discrete...

In pcalg: Methods for Graphical Models and Causal Inference

G square Test for (Conditional) Independence of Discrete Variables

Description

G^2 test for (conditional) independence of discrete (each with a finite number of “levels”) variables X and Y given the (possibly empty) set of discrete variables S.

disCItest() is a wrapper of gSquareDis(), to be easily used in skeleton, pc and fci.

Usage

gSquareDis(x, y, S, dm, nlev, adaptDF = FALSE, n.min = 10*df, verbose = FALSE)
disCItest (x, y, S, suffStat)

Arguments

x, y	(integer) position of variable X and Y, respectively, in the adjacency matrix.
S	(integer) positions of zero or more conditioning variables in the adjacency matrix.
dm	data matrix (rows: samples, columns: variables) with integer entries; the k levels for a given column must be coded by the integers 0,1,...,k-1. (see example)
nlev	optional vector with numbers of levels for each variable in dm.
adaptDF	logical specifying if the degrees of freedom should be lowered by one for each zero count. The value for the degrees of freedom cannot go below 1.
n.min	the smallest n (number of observations, nrow(dm)) for which the G^2 test is computed; for smaller n, independence is assumed (G^2 := 1) with a warning. The default is 10 m, where m is the degrees of freedom assuming no structural zeros, here, the product of all the number of levels (nlev[x]-1) * (nlev[y]-1) * prod(nlev[S]).
verbose	logical or integer indicating that increased diagnostic output is to be provided.
suffStat	a list with three elements, "dm", "nlev", "adaptDF"; each corresponding to the above arguments of gSquareDis().

Details

The G^2 statistic is used to test for (conditional) independence of X and Y given a set S (can be NULL). If only binary variables are involved, gSquareBin is a specialized (a bit more efficient) alternative to gSquareDis().

Value

The p-value of the test.

Author(s)

Nicoletta Andri and Markus Kalisch ([e-mail]).

References

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

See Also

gSquareBin for a (conditional) independence test for binary variables.

dsepTest, gaussCItest and binCItest for similar functions for a d-separation oracle, a conditional independence test for gaussian variables and a conditional independence test for binary variables, respectively.

Examples

## Simulate data
n <- 100
set.seed(123)
x <- sample(0:2, n, TRUE) ## three levels
y <- sample(0:3, n, TRUE) ## four levels
z <- sample(0:1, n, TRUE) ## two levels
dat <- cbind(x,y,z)

## Analyze data
gSquareDis(1,3, S=2, dat, nlev = c(3,4,2)) # but nlev is optional:
gSquareDis(1,3, S=2, dat, verbose=TRUE, adaptDF=TRUE)
## with too little data, gives a warning (and p-value 1):
gSquareDis(1,3, S=2, dat[1:60,], nlev = c(3,4,2))

suffStat <- list(dm = dat, nlev = c(3,4,2), adaptDF = FALSE)
disCItest(1,3,2,suffStat)

pcalg documentation built on May 29, 2024, 5:24 a.m.