pcaiv: Principal component analysis with respect to instrumental...

In ade4: Analysis of Ecological Data : Exploratory and Euclidean Methods in Environmental Sciences

Description

performs a principal component analysis with respect to instrumental variables.

Usage

pcaiv(dudi, df, scannf = TRUE, nf = 2)
## S3 method for class 'pcaiv'
plot(x, xax = 1, yax = 2, ...) 
## S3 method for class 'pcaiv'
print(x, ...)
## S3 method for class 'pcaiv'
summary(object, ...) 

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, object	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

tab	a data frame with the modified array (projected variables)
cw	a numeric vector with the column weigths (from dudi)
lw	a numeric vector with the row weigths (from dudi)
eig	a vector with the all eigenvalues
rank	an integer indicating the rank of the studied matrix
nf	an integer indicating the number of kept axes
c1	a data frame with the Pseudo Principal Axes (PPA)
li	a data frame dudi$ls with the predicted values by X
co	a data frame with the inner products between the CPC and Y
l1	data frame with the Constraint Principal Components (CPC)
call	the matched call
X	a data frame with the explanatory variables
Y	a data frame with the dependant variables
ls	a data frame with the projections of lines of dudi$tab on PPA
param	a table containing information about contributions of the analyses : absolute (1) and cumulative (2) contributions of the decomposition of inertia of the dudi object, absolute (3) and cumulative (4) variances of the projections, the ration (5) between the cumulative variances of the projections (4) and the cumulative contributions (2), the square coefficient of correlation (6) and the eigenvalues of the pcaiv (7)
as	a data frame with the Principal axes of dudi$tab on PPA
fa	a data frame with the loadings (Constraint Principal Components as linear combinations of X
cor	a data frame with the correlations between the CPC and X

Author(s)

Daniel Chessel
Anne B Dufour [e-mail]
Stephane Dray [e-mail]

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 Appliquee, 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)
summary(iv1)
plot(iv1)

Example output

Principal component analysis with instrumental variables

Class: pcaiv dudi
Call: pcaiv(dudi = pca1, df = rhone$disch, scannf = FALSE)

Total inertia: 7.543

Eigenvalues:
    Ax1     Ax2     Ax3 
 3.7031  3.5381  0.3015 

Projected inertia (%):
    Ax1     Ax2     Ax3 
 49.095  46.907   3.998 

Cumulative projected inertia (%):
    Ax1   Ax1:2   Ax1:3 
   49.1    96.0   100.0 

Total unconstrained inertia (pca1): 15

Inertia of pca1 explained by rhone$disch (%): 50.28

Decomposition per axis:
  iner inercum inerC inercumC ratio    R2 lambda
1 6.27    6.27  5.52     5.52 0.879 0.671   3.70
2 4.14   10.42  4.74    10.25 0.984 0.747   3.54

ade4 documentation built on May 2, 2019, 5:50 p.m.