pcaivortho {ade4}R Documentation

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

Author(s)

Daniel Chessel
Anne B Dufour dufour@biomserv.univ-lyon1.fr

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

## Not run: 
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 Région")
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))
## End(Not run)

Worked out examples


> library(ade4)
> ### Encoding: UTF-8
> 
> ### Name: pcaivortho
> ### Title: Principal Component Analysis with respect to orthogonal
> ###   instrumental variables
> ### Aliases: pcaivortho
> ### Keywords: multivariate
> 
> ### ** 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 Région")
> 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))
> 
> 
> 
> 

[Package ade4 Index]