ade4 (version 1.5-2)

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 class 'pcaivortho':
summary(object, \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

object

an object of class pcaiv

...

further arguments passed to or from other methods

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

encoding

latin1

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

par(mfrow = c(2,2))
data(avimedi)
cla <- avimedi$plan$reg:avimedi$plan$str

# simple ordination
coa1 <- dudi.coa(avimedi$fau, scan = FALSE, nf = 3)
s.class(coa1$li, cla, sub = "Sans contrainte")

# within region
w1 <- within(coa1, avimedi$plan$reg, scan = FALSE)
s.match(w1$li, w1$ls, clab = 0, sub = "Intra R�gion")
s.class(w1$li, cla, add.plot = TRUE)

# no region the same result
pcaivnonA <- pcaivortho(coa1, avimedi$plan$reg, scan = FALSE)
summary(pcaivnonA)

s.match(pcaivnonA$li, pcaivnonA$ls, clab = 0, 
    sub = "Contrainte Non A")
s.class(pcaivnonA$li, cla, add.plot = TRUE)

# region + strate
interAplusB <- pcaiv(coa1, avimedi$plan, scan = FALSE)
s.match(interAplusB$li, interAplusB$ls, clab = 0, 
    sub = "Contrainte A + B")
s.class(interAplusB$li, cla, add.plot = TRUE)

par(mfrow = c(1,1))