pcc: Partial Correlation Coefficients

In sensitivity: Global Sensitivity Analysis of Model Outputs

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 class 'pcc'
print(x, ...)
## S3 method for class 'pcc'
plot(x, ylim = c(-1,1), ...)
## S3 method for class 'pcc'
ggplot(data, mapping = aes(), ..., environment
                 = parent.frame(), ylim = c(-1,1))

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).

Details

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

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).

Author(s)

Gilles Pujol and Bertrand Iooss

References

L. Clouvel, V. Chabridon, B. Iooss, M. Il Idrissi and F. Robin, 2023, Variance-based importance measures in the linear regression context: Review, new insights and applications, 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

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

# 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)

sensitivity documentation built on Aug. 31, 2023, 5:10 p.m.