ade4 (version 1.4-16)

pcaiv: 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)
## S3 method for class 'pcaiv':
plot(x, xax = 1, yax = 2, \dots) 
## S3 method for class 'pcaiv':
print(x, \dots)

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
• 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

encoding

latin1

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)
iv1$param
# 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)