sobolTIIpf: Pick-freeze Estimation of Total Interaction Indices

Description

sobolTIIpf implements the pick-freeze estimation of total interaction indices as described in Section 3.3 of Fruth et al. (2014). Total interaction indices (TII) are superset indices of pairs of variables, thus give the total influence of each second-order interaction. The pick-freeze estimation enables the strategy to reuse evaluations of Saltelli (2002). The total costs are $(1+N) \times n$ where $N$ is the number of indices to estimate. Via plotFG, the TIIs can be visualized in a so-called FANOVA graph as described in section 2.2 of Muehlenstaedt et al. (2012).

Usage

sobolTIIpf(model = NULL, X1, X2, ...)
## S3 method for class 'sobolTIIpf':
tell(x, y = NULL, \dots)
## S3 method for class 'sobolTIIpf':
print(x, \dots)
## S3 method for class 'sobolTIIpf':
plot(x, ylim = NULL, \dots)
## S3 method for class 'sobolTIIpf':
plotFG(x)

Arguments

model

a function, or a model with a predict method, defining the model to analyze.

the first random sample.

the second random sample.

a list of class "sobolTIIpf" storing the state of the sensitivity study (parameters, data, estimates).

a vector of model responses.

...

any other arguments for model which are passed unchanged each time it is called.

ylim

optional, the y limits of the plot.

Value

sobolTIIpf returns a list of class "sobolTIIpf", containing all the input arguments detailed before, plus the following components:
callthe matched call.
Xa data.frame containing the design of experiments.
ya vector of model responses.
Vthe estimation of the overall variance.
tii.unscaledthe unscaled estimations of the TIIs together.
tii.scaledthe scaled estimations of the TIIs.

References

J. Fruth, O. Roustant, S. Kuhnt, 2014, Total interaction index: A variance-based sensitivity index for second-order interaction screening, J. Stat. Plan. Inference, 147, 212--223. A. Saltelli, 2002, Making best use of model evaluations to compute sensitivity indices, Comput. Phys. Commun., 145, 580-297. T. Muehlenstaedt, O. Roustant, L. Carraro, S. Kuhnt, 2012, Data-driven Kriging models based on FANOVA-decomposition, Stat. Comput., 22 (3), 723--738.

Examples

Run this code

# Test case : the Ishigami function

# The method requires 2 samples
n <- 1000
X1 <- data.frame(matrix(runif(3 * n, -pi, pi), nrow = n))
X2 <- data.frame(matrix(runif(3 * n, -pi, pi), nrow = n))

# sensitivity analysis (the true values are 0, 0.244, 0)
x <- sobolTIIpf(model = ishigami.fun, X1 = X1, X2 = X2)
print(x)

# plot of tiis and FANOVA graph
plot(x)

library(igraph)
plotFG(x)