gsi {multisensi}

Generalised Sensitivity Indices: GSI

Description

The gsi function implements the calculation of Generalised Sensitivity Indices. This method allows to compute a synthetic Sensitivity Index for the dynamic or multivariate models by using factorial designs and the MANOVA decomposition of inertia. It computes also the Sensitivity Indices on principal components

Usage

gsi(formula, model, factors, inertia = 0.95, normalized = TRUE,
    cumul = FALSE, simulonly = FALSE, Name.File = NULL, ...)

Arguments

formula

ANOVA formula like "A+B+C+A:B" OR an integer equal to the maximum interaction order in the sensitivity model

model

output data.frame OR the name of the R-function which calculates the model output. The only argument of this function must be a vector containing the input factors values

factors

input data.frame (the design) if model is a data.frame OR a list of factors levels such as : factor.example <- list(A=c(0,1),B=c(0,1,4))

inertia

cumulated proportion of inertia (a scalar < 1) to be explained by the selected Principal components OR number of PCs to be used (e.g 3)

normalized

logical value. TRUE (default) computes a normalized Principal Component analysis.

cumul

logical value. If TRUE the PCA will be done on the cumulative outputs

simulonly

logical value. If TRUE the program stops after calculating the design and the model outputs

Name.File

optional name of a R script file containing the R-function that calculates the simulation model. e.g "exc.ssc"

...

possible fixed parameters of the model function

Details

If factors is a list of factors, the gsi function generates a complete factorial design. If it is a data.frame, gsi expects that each column is associated with an input factor.

Value

gsi returns a list of class "gsi", containing all the input arguments detailed before, plus the following components:

X

a data.frame containing the experimental design (input samples)

Y

a data.frame containing the output matrix (response)

H

a data.frame containing the principal components

L

a data.frame whose columns contain the basis eigenvectors (the variable loadings)

lambda

the variances of the principal components

inertia

vector of inertia percentages per PCs and global criterion

cor

a data.frame of correlation between PCs and outputs

SI

a data.frame containing the Sensitivity Indices (SI) on PCs and the Generalised SI (GSI)

mSI

a data.frame of first order SI on PCs and first order GSI

tSI

a data.frame containing the total SI on PCs and the total GSI

iSI

a data.frame of interaction SI on PCs and interaction GSI

pred

a data.frame containing the output predicted by the metamodel arising from the PCA and anova decompositions

residuals

a data.frame containing the residuals between actual and predicted outputs

Rsquare

vector of dynamic coefficient of determination

Att

0-1 matrix of association between input factors and factorial terms in the anovas

scale

logical value, see the arguments

normalized

logical value, see the arguments

cumul

logical value, see the arguments

call.info

a list containing informations on the process (reduction, analysis, fct, call)

inputdesign

either the input data.frame or the sensitivity object used

outputs

a list of results on each output variable

...

Note

This function can now be replaced by a call to the multisensi function. It is kept for compatibility with Version 1 of the multisensi package.

References

M. Lamboni, D. Makowski and H. Monod, 2009. Multivariate global sensitivity analysis for dynamic crop models. Field Crops Research, volume 113. pp. 312-320

M. Lamboni, D. Makowski and H. Monod, 2009. Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models. Submitted to Reliability Engineering and System Safety.

See Also

dynsi, multisensi

Examples

# Test case : the Winter Wheat Dynamic Models (WWDM)
#  input factors design
 data(biomasseX)
# input climate variable
 data(Climat)
# output variables (precalculated to speed up the example)
 data(biomasseY)
#
 GSI <- gsi(2, biomasseY, biomasseX, inertia=3, normalized=TRUE, cumul=FALSE,
            climdata=Climat)
 summary(GSI)
 print(GSI)
 plot(x=GSI, beside=FALSE)
 #plot(GSI, nb.plot=4)         # the 'nb.plot' most influent factors
                               # are represented in the plots
 #plot(GSI,nb.comp=2, xmax=1)  # nb.comp = number of principal components
 #plot(GSI,nb.comp=3, graph=1) # graph=1 for first figure; 2 for 2nd one
                               # and 3 for 3rd one; or 1:3 etc.
 #graph.bar(GSI,col=1, beside=F)  # sensitivity bar plot on the first PC
 #graph.bar(GSI,col=2, xmax=1)    #