hybridTest: Hybrid test for the Interaction Information.

In teisseyrep/interactionInfo: Statistical tests for Interaction Information

Description

The function performs a hybrid test for the positiveness of Interaction Information I(y1,y2;x1)=MI(y1,y2|x1)-MI(y1,y2), where MI(y1,y2|x1) is conditional mutual information between y1 and y2, given x1 and MI(y1,y2) is mutual information between y1 and y2. The null hypothesis is

H0: x1 is indpependent from (y1,y2).

The alternative hypothesis is

H1: I(y1,y2;x1)>0.

The hybrid test combines a permutation test (see function permTest) and chi squared test (see function chisqTest). If the dependence between y1 and y2 is weak then the chi squared test is used. Otherwise, the permutation test is used.

Usage

hybridTest(y1,y2,x1,nbins=NULL,alpha=0.05,alpha0=0.05,B=1000,method="emp")

Arguments

y1	First variable.
y2	Second variable.
x1	The additional coviariate.
nbins	Number of bins to be used for the discretization. By default the number of bins is set to (N)^(1/3) where N is the number of samples.
alpha0	Significance level of the initial test for dependence between y1 and y2, the default value is 0.05.
alpha	Significance level, the default value is 0.05.
B	Number of permutations, the default value is 1000.
method	The method used to estimate entropy. See function interinformation in R package infotheo for details.

Details

If the variables y1, y2, x1 are not factors, they are discretized using 'discretize' function from R package 'infotheo'. Discretization is needed to calculate Interaction Information. The Interaction Information is computed using function interinformation from R package infotheo.

Value

A list with class "hybridTest" containing the following components:

pv	P-value of permutation test.
intInfo0	Interaction Information computed on original data.
intInfo	Vector of length B, containing values of Interaction Information corresponding to B permuted samples. The value is returned only if the permutation test was used. Otherwise it is NULL.
alpha	Significance level.
alpha0	Significance levelof the initial test.
dec	Logical value. TRUE denotes significantly positive Interaction Information.
B	Number of permutations. The value is returned only if the permutation test was used. Otherwise it is NULL.
df	Degrees of freedom. The value is returned only if the chi squared test was used. Otherwise it is NULL.
type	Type of the test used in the hybrid procedure. The possible values are: "permTest" if the permutation test was used and "chisqTest" if the chi sqaured test was used.

Author(s)

Pawel Teisseyre

References

Pawel Teisseyre, Jan Mielniczuk, Michal J. Dabrowski, Detection of hidden associations and interactions in biomedical data using Interaction Information, manuscript, 2017.

See Also

chisqTest, permTest

Examples

#Example (Positive Interaction Information, no dependence between y1 and y2):
y1=c(rep(0,25),rep(1,25),rep(1,25),rep(0,25))
y2=c(rep(0,25),rep(1,25),rep(0,25),rep(1,25))
x1=c(rep(1,50),rep(0,50))

hybridTest1=hybridTest(y1,y2,x1)
#In this case, chisqTest was used in hybridTest:
print(hybridTest1)


#Example (Positive Interaction Information, dependence between y1 and y2):
y1=c(rep(0,40),rep(1,40),rep(1,10),rep(0,10))
y2=c(rep(0,40),rep(1,40),rep(0,10),rep(1,10))
x1=c(rep(1,80),rep(0,20))

hybridTest1=hybridTest(y1,y2,x1)
#In this case, permTest was used in hybridTest:
print(hybridTest1)

teisseyrep/interactionInfo documentation built on May 31, 2019, 8:32 a.m.