R help - Jul 2015 - Addition to: PCAgrid scores cannot be predicted correctly

I played around with the function a bit more and could actually narrow 
down the problem some more. The problem seems to lie in the scale-option 
of PCAgrid. So, for the example below, this code line produces a 
princomp object with which the scores of Dat can be predicted correctly:

rPCA<-PCAgrid(Dat, k=4, center=median, method="qn")

However, when using this code line the predicted scores of Dat are wrong:

rPCA<-PCAgrid(Dat, k=4, center=median, method="qn", scale=mad)

Since rPCA$scale is present in both cases (but naturally 1 for the first 
example) this seems to point into the direction that the scaling factors 
returned by PCAgrid might be wrong!?

Thanks a lot for your help.



On 07.07.2015 12:00, r-help-request at r-project.org wrote:
Message: 25
Date: Mon, 06 Jul 2015 17:52:38 +0200
From: Manuel Weinkauf <Manuel.Weinkauf at gmx.de>
To: R-help at r-project.org
Subject: [R] PCAgrid scores cannot be predicted correctly
Message-ID: <559AA446.2050401 at gmx.de>
Content-Type: text/plain; charset=utf-8; format=flowed

I have been running into a problem with the PCAgrid() function of the
R-package pcaPP. When trying to predict the scores of new data using the
resulting PCA, the predicted score values are wrong. This is true for
both, using the predict() function and for calculating the scores
manually after scaling the data.

The example below illustrates that: In princomp(), when I either use
predict() or the manual calculation of the scores of the data originally
used for the PCA, the predicted points coincide exactly with the PCA
scores (as it should be, as they are using the same raw data). However,
when doing this with the princomp-object calculated with the pcaPP
package, the predicted values are nowhere close to where they should be.
Note that the results of predict() exactly match the results calculated
manually, so it is not that predict() could not handle this object
correctly.

Can anybody explain this weird behaviour to me? Thanks a lot.


##EXAMPLE##
library(pcaPP)

#Create data
t1<-rnorm(10, 10, 1)
t2<-rnorm(10, 8, 2)
t3<-rnorm(10, 60, 4)
t4<-rnorm(10, 1, 0.05)
Dat<-matrix(c(t1, t2, t3 , t4), ncol=4)
colnames(Dat)<-paste("Var", 1:4, sep=".")

win.graph(20, 10, 10)
layout(matrix(c(1, 2), 1, 2))
#Normal PCA
PCA<-princomp(Dat)
PCA.pred<-predict(PCA, Dat)
Dat.Scale<-scale(Dat, center=PCA$center, scale=PCA$scale)
Load<-PCA$loadings
PCA.man<-matrix(NA, nrow(PCA$scores), 2)
for (i in 1:nrow(PCA.man)) {
PCA.man[i,1]<-Dat.Scale[i,1]*Load[1,1]+Dat.Scale[i,2]*Load[2,1]+Dat.Scale[i,3]*Load[3,1]+Dat.Scale[i,4]*Load[4,1]
PCA.man[i,2]<-Dat.Scale[i,1]*Load[1,2]+Dat.Scale[i,2]*Load[2,2]+Dat.Scale[i,3]*Load[3,2]+Dat.Scale[i,4]*Load[4,2]
}
plot(PCA$scores[,1:2], pch=1, cex=2, main="Normal PCA")
points(PCA.pred, pch=16)
points(PCA.man, pch=0, col="red", cex=3)
legend("topleft", pch=c(1, 16, 0), col=c("black",
"black", "red"),
legend=c("Ordination", "Prediction", "Manual
prediction"))

#robust PCA
rPCA<-PCAgrid(Dat, k=4, center=median, method="qn", scale=mad)
rPCA.pred<-predict(rPCA, Dat)
Dat.Scale<-scale(Dat, center=rPCA$center, scale=rPCA$scale)
Load<-rPCA$loadings
rPCA.man<-matrix(NA, nrow(rPCA$scores), 2)
for (i in 1:nrow(rPCA.man)) {
rPCA.man[i,1]<-Dat.Scale[i,1]*Load[1,1]+Dat.Scale[i,2]*Load[2,1]+Dat.Scale[i,3]*Load[3,1]+Dat.Scale[i,4]*Load[4,1]
rPCA.man[i,2]<-Dat.Scale[i,1]*Load[1,2]+Dat.Scale[i,2]*Load[2,2]+Dat.Scale[i,3]*Load[3,2]+Dat.Scale[i,4]*Load[4,2]
}
plot(rPCA$scores[,1:2], pch=1, cex=2, main="Robust PCA")
points(rPCA.pred, pch=16)
points(rPCA.man, pch=0, col="red", cex=3)
legend("topleft", pch=c(1, 16, 0), col=c("black",
"black", "red"),
legend=c("Ordination", "Prediction", "Manual
prediction"))

-- 
Dr Manuel Weinkauf
MARUM Bremen
Room MARUM II?2050
Leobener Stra?e
28359 Bremen
Germany
e-mail: mweinkauf at marum.de
phone: +49 421 218 659 75