gsi: Generalised Sensitivity Indices: GSI
In multisensi: Multivariate Sensitivity Analysis

Description Usage Arguments Details Value Note References See Also Examples

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

1 2	gsi(formula, model, factors, inertia = 0.95, normalized = TRUE, cumul = FALSE, simulonly = FALSE, Name.File = NULL, ...)

`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

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.

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

...

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.

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.

dynsi, multisensi

# 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)    #