ade4 (version 1.7-22)

pcaivortho: Principal Component Analysis with respect to orthogonal instrumental variables

Description

performs a Principal Component Analysis with respect to orthogonal instrumental variables.

Usage

pcaivortho(dudi, df, scannf = TRUE, nf = 2)
# S3 method for pcaivortho
summary(object, ...)

Value

an object of class 'pcaivortho' 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 axis of dudi$tab on PAP

ls

a data frame with the projection of lines of dudi$tab on PPA

li

a data frame dudi$ls with the predicted values by X

l1

a data frame with the Constraint Principal Components (CPC)

co

a data frame with the inner product between the CPC and Y

param

a data frame containing a summary

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

object

an object of class pcaiv

...

further arguments passed to or from other methods

Author

Daniel Chessel
Anne-Béatrice Dufour
Stéphane Dray

References

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

Sabatier, R., Lebreton J. D. and Chessel D. (1989) Principal component analysis with instrumental variables as a tool for modelling composition data. In R. Coppi and S. Bolasco, editors. Multiway data analysis, Elsevier Science Publishers B.V., North-Holland, 341--352

Examples

if (FALSE) {
data(avimedi)
cla <- avimedi$plan$reg:avimedi$plan$str
# simple ordination
coa1 <- dudi.coa(avimedi$fau, scan = FALSE, nf = 3)
# within region
w1 <- wca(coa1, avimedi$plan$reg, scan = FALSE)
# no region the same result
pcaivnonA <- pcaivortho(coa1, avimedi$plan$reg, scan = FALSE)
summary(pcaivnonA)
# region + strate
interAplusB <- pcaiv(coa1, avimedi$plan, scan = FALSE)

if(adegraphicsLoaded()) {
  g1 <- s.class(coa1$li, cla, psub.text = "Sans contrainte", plot = FALSE)
  g21 <- s.match(w1$li, w1$ls, plab.cex = 0, psub.text = "Intra Région", plot = FALSE)
  g22 <- s.class(w1$li, cla, plot = FALSE)
  g2 <- superpose(g21, g22)
  g31 <- s.match(pcaivnonA$li, pcaivnonA$ls, plab.cex = 0, psub.tex = "Contrainte Non A", 
    plot = FALSE)
  g32 <- s.class(pcaivnonA$li, cla, plot = FALSE)
  g3 <- superpose(g31, g32)
  g41 <- s.match(interAplusB$li, interAplusB$ls, plab.cex = 0, psub.text = "Contrainte A + B", 
    plot = FALSE)
  g42 <- s.class(interAplusB$li, cla, plot = FALSE)
  g4 <- superpose(g41, g42)
  G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))

} else {
  par(mfrow = c(2, 2))
  s.class(coa1$li, cla, sub = "Sans contrainte")
  s.match(w1$li, w1$ls, clab = 0, sub = "Intra Région")
  s.class(w1$li, cla, add.plot = TRUE)
  s.match(pcaivnonA$li, pcaivnonA$ls, clab = 0, sub = "Contrainte Non A")
  s.class(pcaivnonA$li, cla, add.plot = TRUE)
  s.match(interAplusB$li, interAplusB$ls, clab = 0, sub = "Contrainte A + B")
  s.class(interAplusB$li, cla, add.plot = TRUE)
  par(mfrow = c(1,1))
}}