sobolTIIlo: Liu and Owen Estimation of Total Interaction Indices

Description

sobolTIIlo implements the asymptotically efficient formula of Liu and Owen (2006) for the estimation of total interaction indices as described e.g. in Section 3.4 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 total cost of the method is $(1+N+\choose(N,2)) \times n$ where $N$ is the number of indices to estimate. Asymptotic confidence intervals are provided. Via plotFG (which uses functions of the package igraph), the TIIs can be visualized in a so-called FANOVA graph as described in section 2.2 of Muehlenstaedt et al. (2012).

Usage

sobolTIIlo(model = NULL, X1, X2, conf = 0.95, ...)
## S3 method for class 'sobolTIIlo':
tell(x, y = NULL, \dots)
## S3 method for class 'sobolTIIlo':
print(x, \dots)
## S3 method for class 'sobolTIIlo':
plot(x, ylim = NULL, \dots)
## S3 method for class 'sobolTIIlo':
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.

conf

the confidence level for asymptotic confidence intervals, defaults to 0.95.

a list of class "sobolTIIlo" 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

sobolTIIlo returns a list of class "sobolTIIlo", 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.
tii.scaledthe scaled estimations of the TIIs together with asymptotic confidence intervals.

References

R. Liu, A. B. Owen, 2006, Estimating mean dimensionality of analysis of variance decompositions, JASA, 101 (474), 712--721. 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. 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 of the scaled TIIs are 0, 0.244, 0)
x <- sobolTIIlo(model = ishigami.fun, X1 = X1, X2 = X2)
print(x)

# plot of tiis and FANOVA graph
plot(x)

library(igraph)
plotFG(x)