sensitivity (version 1.31.0)

pcc: Partial Correlation Coefficients

Description

pcc computes the Partial Correlation Coefficients (PCC), Semi-Partial Correlation Coefficients (SPCC), Partial Rank Correlation Coefficients (PRCC) or Semi-Partial Rank Correlation Coefficients (SPRCC), which are variance-based measures based on linear (resp. monotonic) assumptions, in the case of (linearly) correlated factors.

Usage

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

Value

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

call

the matched call.

PCC

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

PRCC

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

SPCC

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

SPRCC

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

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.

semi

logical. If TRUE, semi-PCC are computed.

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 pcc.

data

the object returned by pcc.

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).

Author

Gilles Pujol and Bertrand Iooss

Details

This function cannot be used with categorical inputs.

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

References

L. Clouvel, B. Iooss, V. Chabridon, M. Il Idrissi and F. Robin, 2023, An overview of variance-based importance measures in the linear regression context: comparative analyses and numerical tests, Socio-Environmental Systems Modelling, vol. 7, 18681, 2025, doi:10.18174/sesmo.1868. 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

J.W. Johnson and J.M. LeBreton, 2004, History and use of relative importance indices in organizational research, Organizational Research Methods, 7:238-257.

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

See Also

src, lmg, pmvd

Examples

# \donttest{
# 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 = X1^2 + X2 + X3
y <- with(X, X1^2 + X2 + X3)

# sensitivity analysis
x <- pcc(X, y, nboot = 100)
print(x)
plot(x)

library(ggplot2)
ggplot(x)
ggplot(x, ylim = c(-1.5,1.5))

x <- pcc(X, y, semi = TRUE, nboot = 100)
print(x)
plot(x)
# }