Function to estimate the first-order and total support index functions (Fruth et al., 2016).

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

support(model, X, Xnew = NULL, fX = NULL, gradfX = NULL, h = 1e-06, ...)

install.packages("sensitivity", repo="http://cran.r-project.org", dep=T)
library(sensitivity)
# -----------------
# ishigami function
# -----------------
n <- 5000
n.points <- 1000
d <- 3

set.seed(0)
X <- matrix(runif(d*n, min = -pi, max = pi), n, d)
Xnew <- matrix(seq(from = -pi, to = pi, length=n.points), n.points, d)

b <- support(model = ishigami.fun, X, Xnew)

# plot method (x-axis in probability scale), of the normalized support index functions
plot(b, col = c("lightskyblue4", "lightskyblue1", "black"),
xprob = TRUE, p = 'punif', p.arg = list(min = -pi, max = pi), ylim = c(0, 2))

# below : diagonal scatterplots of the gradient,
# on which are based the estimation by smoothing
scatterplot(b, xprob = TRUE)

# now with normal margins
# -----------------------
X <- matrix(rnorm(d*n), n, d)
Xnew <- matrix(rnorm(d*n.points), n.points, d)
b <- support(model = ishigami.fun, X, Xnew)

plot(b, col = c("lightskyblue4", "lightskyblue1", "black"), xprob = FALSE)
scatterplot(b, xprob = FALSE, type = "histogram", bins = 10, cex = 1, cex.lab = 1.5)

Return Values:

Details: The first-order support index of f(X) relative to X_i is the squared conditional expectation of its partial derivative with respect to X_i.

The total support index of f(X) relative to X_i is the conditional expectation of its squared partial derivative with respect to X_i.

These two functions measure the local influence of X_i, in the global space of the other input variables. Up to square transformations, support indices can be viewed as regression curves of partial derivatives df(X)/dX_i with respect to X_i. Estimation is performed by smoothing from the diagonal scatterplots (X_i, df/dX_i) with the function smooth.spline{stats} with the default options.

For the sake of comparison, support index functions may be normalized. The proposed normalization is the sum of the DGSM, equal to the sum of the overall means of total support functions. Normalized support index functions can be plotted with the S3 method plot, as well as the underlying diagonal scatterplots of derivatives (S3 method scatterplot).

See Also: S3 methods plot and scatterplot: plot.support