sobolTIIlo | R Documentation |
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).
sobolTIIlo(model = NULL, X1, X2, conf = 0.95, ...)
## S3 method for class 'sobolTIIlo'
tell(x, y = NULL, ...)
## S3 method for class 'sobolTIIlo'
print(x, ...)
## S3 method for class 'sobolTIIlo'
plot(x, ylim = NULL, ...)
## S3 method for class 'sobolTIIlo'
ggplot(data, mapping = aes(), ylim = NULL, ..., environment
= parent.frame())
## S3 method for class 'sobolTIIlo'
plotFG(x)
model |
a function, or a model with a |
X1 |
the first random sample. |
X2 |
the second random sample. |
conf |
the confidence level for asymptotic confidence intervals, defaults to 0.95. |
x |
a list of class |
data |
a list of class |
y |
a vector of model responses. |
mapping |
Default list of aesthetic mappings to use for plot. If not specified, must be supplied in each layer added to the plot. |
environment |
[Deprecated] Used prior to tidy evaluation. |
... |
any other arguments for |
ylim |
optional, the y limits of the plot. |
sobolTIIlo
returns a list of class "sobolTIIlo"
, containing all
the input arguments detailed before, plus the following components:
call |
the matched call. |
X |
a |
y |
a vector of model responses. |
V |
the estimation of the overall variance. |
tii.unscaled |
the unscaled estimations of the TIIs. |
tii.scaled |
the scaled estimations of the TIIs together with asymptotic confidence intervals. |
Jana Fruth
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.
sobolTIIpf
# 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(ggplot2)
ggplot(x)
library(igraph)
plotFG(x)
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