src {sensitivity}

Standardized Regression Coefficients

Description

src computes the Standardized Regression Coefficients (SRC), or the Standardized Rank Regression Coefficients (SRRC), which are sensitivity indices based on linear or monotonic assumptions in the case of independent factors.

Usage

src(X, y, rank = FALSE, logistic = FALSE, nboot = 0, conf = 0.95)
## S3 method for class 'src'
print(x, ...)
## S3 method for class 'src'
plot(x, ylim = c(-1,1), ...)
## S3 method for class 'src'
ggplot(data,  mapping = aes(), ylim = c(-1, 1), ..., environment
                 = parent.frame())

Arguments

X

a data frame (or object coercible by as.data.frame) containing the design of experiments (model input variables).

y

a vector containing the responses corresponding to the design of experiments (model output variables).

rank

logical. If TRUE, the analysis is done on the ranks.

logistic

logical. If TRUE, the analysis is done via a logistic regression (binomial GLM).

nboot

the number of bootstrap replicates.

conf

the confidence level of the bootstrap confidence intervals.

x

the object returned by src.

data

the object returned by src.

ylim

the y-coordinate limits of the plot.

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.

...

arguments to be passed to methods, such as graphical parameters (see par).

Details

Logistic regression model (logistic = TRUE) and rank-based indices (rank = TRUE) are incompatible.

Value

src returns a list of class "src", containing the following components:

call

the matched call.

SRC

a data frame containing the estimations of the SRC indices, bias and confidence intervals (if rank = FALSE).

SRRC

a data frame containing the estimations of the SRRC indices, bias and confidence intervals (if rank = TRUE).

Author(s)

Gilles Pujol and Bertrand Iooss

References

L. Clouvel, B. Iooss, V. Chabridon, M. Il Idrissi and F. Robin, 2023, A review on variance-based importance measures in the linear regression context, Preprint https://hal.science/hal-04102053

B. Iooss, V. Chabridon and V. Thouvenot, Variance-based importance measures for machine learning model interpretability, Congres lambda-mu23, Saclay, France, 10-13 octobre 2022 https://hal.science/hal-03741384

A. Saltelli, K. Chan and E. M. Scott eds, 2000, Sensitivity Analysis, Wiley.

See Also

pcc, lmg, pmvd

Examples

# a 100-sample with X1 ~ U(0.5, 1.5)
#                   X2 ~ U(1.5, 4.5)
#                   X3 ~ U(4.5, 13.5)

library(boot)
n <- 100
X <- data.frame(X1 = runif(n, 0.5, 1.5),
                X2 = runif(n, 1.5, 4.5),
                X3 = runif(n, 4.5, 13.5))

# linear model : Y = X1 + X2 + X3

y <- with(X, X1 + X2 + X3)

# sensitivity analysis

x <- src(X, y, nboot = 100)
print(x)
plot(x)

library(ggplot2)
ggplot(x)