ade4 (version 1.01)

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)
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

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 Appliqu�e, 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)