ade4 (version 1.01)

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)

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

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

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)
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))