'Is calculated factor scores in robCompositions R package, correct?
Please have a look at the factor scores returned from robCompositions package in this example:
data(expenditures)
x <- expenditures
res.rob <- pfa(x, factors=1, score="regression")
according to pfa help, since the covariance is not specified,
the covariance is estimated from isometric log-ratio transformed data internally, but the data used for factor analysis are back-transformed to the "clr" space.
So the clr transformed data obtain as follows:
# ilr transformation
ilr <- function(x){
x.ilr=matrix(NA,nrow=nrow(x),ncol=ncol(x)-1)
for (i in 1:ncol(x.ilr)){
x.ilr[,i]=sqrt((i)/(i+1))*
log(((apply(as.matrix(x[,1:i]), 1, prod))^(1/i))/(x[,i+1]))
}
return(x.ilr)
}
#construct orthonormal basis:
#(matrix with ncol(x) rows and ncol(x)-1 columns)
V=matrix(0,nrow=ncol(x),ncol=ncol(x)-1)
for (i in 1:ncol(V)){
V[1:i,i] <- 1/i
V[i+1,i] <- (-1)
V[,i] <- V[,i]*sqrt(i/(i+1))
}
z=ilr(x) #ilr transformed data
y=z%*%t(V) #clr transformed data
now the factor scores using regression method might be calculated as follows:
loa<-c(0.970,0.830,0.986,0.876,0.977) #res.rob object
facscores<- y%*%loa
head(facscores)
-0.009485110
0.009680645
0.008426665
-0.015401000
-0.003610644
-0.004584145
but calling res.rob$scores returns us
head(res.rob$scores)
Factor1 -755.2681 705.5309 4196.5652 -778.6955 -628.2141 -663.4534
So please check am I wrong or there is probably a bug in the pfa command? Yours, Hamid
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