chisqTest: Chi squared test for the Interaction Information.

In teisseyrep/interactionInfo: Statistical tests for Interaction Information

Description

The function performs chi-squared 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.

Usage

chisqTest(y1, y2, x1, nbins=NULL, alpha=0.05,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.
alpha	Significance level, the default value is 0.05.
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 "chisqTest" containing the following components:

pv	P-value of chi squared test.
intInfo0	Interaction Information.
alpha	Significance level.
dec	Logical value. TRUE denotes significantly positive Interaction Information.
df	Degrees of freedom.

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.

Examples

#Example (XOR problem- all variables discrete):
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))

chisqTest1=chisqTest(y1,y2,x1,nbins=NULL,alpha=0.05)
print(chisqTest1)

#Example (XOR problem- x1 continuous):
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(rnorm(50,1,0.5),rnorm(50,0,0.5))

chisqTest2=chisqTest(y1,y2,x1,nbins=NULL,alpha=0.05)
print(chisqTest2)

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