sivipm: Sensitivity Indices

In sivipm: Sensitivity Indices with Dependent Inputs

Description

Compute total and individual sensitivity indices, significant components and auxiliary results.

Usage

sivipm(Y,  XIndic,
        nc=2,  options= c("fo.isivip", "tsivip", "simca", "lazraq"),
        graph = FALSE, alea = FALSE, fast = FALSE,
        output=NULL)

Arguments

Y	Outputs. A data.frame with as many rows as observations and as many columns as response variables.
XIndic	Object of class polyX which contains the polynomial description and the dataset of inputs.
nc	Required number of components.
options	Options to select what is calculated. A string vector. Valid values are: fo.isivip first order individual sensitivity indices, tsivip total sensitivity indices, simca significant components calculated by the SIMCA software rule. See Details. lazraq significant components calculated by the Lazraq and Cléroux test. See Details.
graph	If TRUE, a graph is drawn when options includes tsivip.
alea	If TRUE, an uniform random variable is included in the analysis when options includes tsivip. Then, the non significant monomials are excluded from the total sensitivity indices calculation.
fast	If TRUE, auxiliary results are calculated from the Miller's formulae more adapted to big datasets.
output	If non NULL, additional results are returned in a component named output. Character vector, which valid values are: isivip to return isivip betaNat to return betaNat and betaNat0 VIP to return VIP and VIPind Q2 to return Q2 and Q2cum PLS to return PLS results: mweights, weights, x.scores, x.loadings, y.scores, y.loadings, cor.tx, cor.ty, expvar, X.hat, Y.hat See "Value". It is advised to first determine the number of significant components, by setting the options simca or lazraq, before asking for additional results.

Details

• When the option simca or lazraq is set, the significant components are computed by the SIMCA software rule, or, by the Lazraq and Cléroux inferential test, at confidence level 0.95, respectively. The option simca is ignored if there are missing values. The option lazraq is ignored if there are missing values and more than one response variables.

• When the option alea is set, the non significant monomials are those for which the individual sensitivity indices is less or equal than the one of the random variable. These non significant monomials are excluded from the total sensitivity indices calculation.

• To analyze big datasets, the option fast is advised.

Value

An object of class sivip, whose slots are:

fo.isivip and fo.isivip.percent	When options includes fo.isivip, values and sorted percentages of the first order individual sensitivity indices.
tsivip and tsivip.percent	When options includes tsivip, values and sorted percentages of the total sensitivity indices for each input variable.
monosignif	When alea is TRUE, and options includes tsivip, logical vector which indicates the significant monomials.
correlalea	When alea is TRUE, and options includes tsivip, the correlation matrix between the random variable and the outputs.
simca.signifcomponents	When options includes simca, the significant components calculated by the S. Wold's rule (SIMCA software rule). Logical matrix with nc rows and as many columns as response variables. Values are TRUE for the components where the test is positive at 95% level, FALSE otherwise.
lazraq.signifcomponents	When options includes simca, the significant components calculated by the Lazraq and Cléroux inferential test. Logical vector of length nc with TRUE for the components where the test is positive at 95% level, FALSE otherwise.
output	When output is not NULL, a list with additional results, whose components depend on output option. isivip Individual sensitivity indices for each monomial. Vector of length equal to the number of monomials. betaNat Natural beta. Matrix with as many rows as monomials and as many columns as response variables. betaNat0 Natural beta0 coefficient. Vector of length equal to the number of response variables. VIP Matrix of nc columns and as many rows as monomials. VIPind Matrix with as many rows as response variables and as many columns as monomials. Q2 Matrix with as many columns as response variables and nc rows. Q2cum Matrix with as many columns as response variables + one column and nc rows. PLS PLS results. The dimension of the components are indicated below in brackets. nmono denotes the number of monomials, ny, the number of response variables and nobs the number of observations. betaCR (beta centered and reduced. Vector ny), mweights (nc X nmono), x.scores (nc X nobs), x.loadings (nc X nmono), y.scores (nc X nobs), y.loadings (nc X ny), weights (nc X nmono), cor.tx (nc X nmono), cor.ty (nc X ny), expvar (4 X nc), x.hat(nobs X nmono), y.hat (nobs X ny).

Note

If the output is multivariate, tsivip are the generalized total sensitivity indices (GTSIVIP) and isivip are the generalized individual sensitivity indices (GISIVIP).

Examples

X <- cornell0[,1:3] # X-inputs
Y <- as.data.frame( cornell0[,8]) # response variable
# Creation of the polynomial:
P <- vect2polyX(X, c("1", "2", "3", "3*3*3"))
# Compute total sensitivity indices:
A <- sivipm(Y, P, options=c("tsivip"))
# See the names of the returned components
getNames(A)
# The main results
summary(A)
# All the results
print(A, all=TRUE)
# Calculation by using the fast algorithm:
B <- sivipm(Y, P, fast = TRUE, options=c("tsivip"))

sivipm documentation built on May 2, 2019, 6:41 a.m.