Description Usage Arguments Details Value Author(s) References Examples
The function performs permutation 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.
1 |
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. |
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. |
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.
A list with class "permTest" 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. |
alpha |
Significance level. |
dec |
Logical value. TRUE denotes significantly positive Interaction Information. |
B |
Number of permutations. |
Pawel Teisseyre
Pawel Teisseyre, Jan Mielniczuk, Michal J. Dabrowski, Detection of hidden associations and interactions in biomedical data using Interaction Information, manuscript, 2017.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | #Example (XOR problem):
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))
permTest1=permTest(y1,y2,x1)
# Make histogram for Interaction Information, based on permutation samples.
hist(permTest1$intInfo)
#Example (XOR problem- x1 continuous):
y1=c(rep(0,25),rep(1,25),rep(1,25),rep(0,25))
y2=c(rep(0,25),rep(1,25),rep(0,25),rep(1,25))
x1=c(rnorm(50,1,0.5),rnorm(50,0,0.5))
permTest1=permTest(y1,y2,x1)
# Make histogram for Interaction Information, based on permutation samples.
hist(permTest1$intInfo)
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