pcaiv {ade4}R Documentation

Principal component analysis with respect to instrumental variables

Description

performs a principal component analysis with respect to instrumental variables.

Usage

pcaiv(dudi, df, scannf = TRUE, nf = 2)
plot.pcaiv (x, xax = 1, yax = 2, ...) 
print.pcaiv (x, ...) 

Arguments

dudi a duality diagram, object of class dudi
df a data frame with the same rows
scannf a logical value indicating whether the eigenvalues bar plot should be displayed
nf if scannf FALSE, an integer indicating the number of kept axes
x an object of class pcaiv
xax the column number for the x-axis
yax the column number for the y-axis
... further arguments passed to or from other methods

Value

returns an object of class pcaiv, sub-class of class dudi

rank an integer indicating the rank of the studied matrix
nf an integer indicating the number of kept axes
eig a vector with the all eigenvalues
lw a numeric vector with the row weigths (from dudi)
cw a numeric vector with the column weigths (from dudi)
Y a data frame with the dependant variables
X a data frame with the explanatory variables
tab a data frame with the modified array (projected variables)
c1 a data frame with the Pseudo Principal Axes (PPA)
as a data frame with the Principal axes of dudi$tab on PPA
ls a data frame with the projections of lines of dudi$tab on PPA
li a data frame dudi$ls with the predicted values by X
fa a data frame with the loadings (Constraint Principal Components as linear combinations of X
l1 data frame with the Constraint Principal Components (CPC)
co a data frame with the inner products between the CPC and Y
cor a data frame with the correlations between the CPC and X

Author(s)

Daniel Chessel chessel@biomserv.univ-lyon1.fr
Anne B Dufour dufour@biomserv.univ-lyon1.fr

References

Rao, C. R. (1964) The use and interpretation of principal component analysis in applied research. Sankhya, A 26, 329–359.

Obadia, J. (1978) L'analyse en composantes explicatives. Revue de Statistique Appliquée, 24, 5–28.

Lebreton, J. D., Sabatier, R., Banco G. and Bacou A. M. (1991) Principal component and correspondence analyses with respect to instrumental variables : an overview of their role in studies of structure-activity and species- environment relationships. In J. Devillers and W. Karcher, editors. Applied Multivariate Analysis in SAR and Environmental Studies, Kluwer Academic Publishers, 85–114.

Examples

data(rhone)
pca1 <- dudi.pca(rhone$tab, scan = FALSE, nf = 3)
iv1 <- pcaiv(pca1, rhone$disch, scan = FALSE)
iv1
# iner inercum inerC inercumC ratio R2    lambda
# 6.27 6.27    5.52  5.52     0.879 0.671 3.7   
# 4.14 10.4    4.74  10.3     0.984 0.747 3.54  
plot(iv1)

[Package ade4 version 1.4-0 Index]