shapleyLinearGaussian implements the computation of the Shapley effects in the linear Gaussian framework, using the linear model (without the value at zero) and the covariance matrix of the inputs.

shapleyLinearGaussian is located in package sensitivity. Please install and load package sensitivity before use.

shapleyLinearGaussian(Beta,Sigma,tol=10^(-6))

install.packages("sensitivity", repo="http://cran.r-project.org", dep=T)
library(sensitivity)
library(MASS)
library(igraph)

# First example:

p=5 #dimension
A=matrix(rnorm(p^2),nrow=p,ncol=p)
Sigma=t(A)%*%A
Beta=runif(p)
Shapley=shapleyLinearGaussian(Beta,Sigma)
plot(Shapley)

# Second Example, block-diagonal:

K=5 #number of groups
m=5 # number of variables in each group
p=K*m
Sigma=matrix(0,ncol=p,nrow=p)

for(k in 1:K)
{
A=matrix(rnorm(m^2),nrow=m,ncol=m)
Sigma[(m*(k-1)+1):(m*k),(m*(k-1)+1):(m*k)]=t(A)%*%A
}
# we mix the variables:
samp=sample(1:p,p)
Sigma=Sigma[samp,samp]

Beta=runif(p)
Shapley=shapleyLinearGaussian(Beta,Sigma)
plot(Shapley)

Return Values: shapleyLinearGaussian returns a numeric vector containing all the Shapley effects.

See Also: shapleyPermEx, shapleyPermRand, shapleySubsetMc