R help - Nov 2010 - pca analysis: extract rotated scores?

Dear all
I'm unable to find an example of extracting the rotated scores of a
principal components analysis. I can do this easily for the un-rotated
version.

data(mtcars)
.PC <- princomp(~am+carb+cyl+disp+drat+gear+hp+mpg, cor=TRUE, data=mtcars)
unclass(loadings(.PC))  # component loadings
summary(.PC) # proportions of variance
mtcars$PC1 <- .PC$scores[,1] # extract un-rotated scores of 1st
principal component
mtcars$PC2 <- .PC$scores[,2] # extract un-rotated scores of 2nd
principal component
head(mtcars[, c('PC1', 'PC2')])

However, I no longer understand how to do so if I want to use
?principal in 'psych' and any of the GPArotation methods. For example,
require(psych)
r <-
cor(mtcars[,c("am","carb","cyl","disp","drat","gear","hp","mpg")])
pca <- principal(r, nfactors = 8, residuals = T, rotate="none") #
or
'varimax' or any other GPArotation supported rotation
pca

I've turned the 'pca' object and ?principal help page upside down
and
I still cannot find anything that would resemble a 'scores' value.
I'm
pretty sure it's one matrix computation away, but I cannot find which
one.

Ideas? Thank you
Liviu



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Take 2 on this. Below I'm pasting the code to perform PCA in R
(without any rotation), manually; using ?princomp; and using
?principal. I also point out some differences in teh output and
terminology of the two functions. In short, I found how to compute the
scores of principal components when no rotation is used.

However, I'm still confused on how to compute the scores when
rotations (such as 'varimax' or other methods in GPArotation) are
applied. Any ideas on how to obtain (non-scale'd) scores of the
rotated principal components? Thank you
Liviu


###
require(psych)
data(mtcars)
rawd <-
mtcars[,c("am","carb","cyl","disp","drat","gear","hp","mpg")]

## compute acp
.PC <- princomp(~am+carb+cyl+disp+drat+gear+hp+mpg, cor=TRUE, data=mtcars)
pca <- principal(rawd, nfactors = 8, residuals = T, rotate="none",
scores=T)

## eigenvectors of the correlation matrix of raw data
eigens <- eigen(cor(rawd))
eigens$vectors
unclass(loadings(.PC))  # component 'loadings' in ?princomp parlance
#not sure if ?principal outputs this

## correlation matrix between raw data and unrotated component scores
## 'loadings' in ?principal parlance and 'component matrix' in
SPSS
eigens$vectors %*% diag(sqrt(eigens$values))
cor(cbind(rawd, .PC$scores))
unclass(pca$loadings)

## extract un-rotated scores of principal components
head(scale(rawd) %*% eigens$vectors) # app, but very similar results
head(.PC$scores)
head(pca$scores) # scale'd, and obtained via regression on scale'd data
head(factor.scores(scale(rawd),
    unclass(pca$loadings))) # same scores as from ?principal
#for differeneces between ?princomp and ?principal scores
#see last paragraph of Details in ?principal



On Tue, Nov 30, 2010 at 10:22 AM, Liviu Andronic <landronimirc at
gmail.com> wrote:
> Dear all
> I'm unable to find an example of extracting the rotated scores of a
> principal components analysis. I can do this easily for the un-rotated
> version.
>
> data(mtcars)
> .PC <- princomp(~am+carb+cyl+disp+drat+gear+hp+mpg, cor=TRUE,
data=mtcars)
> unclass(loadings(.PC)) ?# component loadings
> summary(.PC) # proportions of variance
> mtcars$PC1 <- .PC$scores[,1] # extract un-rotated scores of 1st
> principal component
> mtcars$PC2 <- .PC$scores[,2] # extract un-rotated scores of 2nd
> principal component
> head(mtcars[, c('PC1', 'PC2')])
>
> However, I no longer understand how to do so if I want to use
> ?principal in 'psych' and any of the GPArotation methods. For
example,
> require(psych)
> r <-
cor(mtcars[,c("am","carb","cyl","disp","drat","gear","hp","mpg")])
> pca <- principal(r, nfactors = 8, residuals = T,
rotate="none") # or
> 'varimax' or any other GPArotation supported rotation
> pca
>
> I've turned the 'pca' object and ?principal help page upside
down and
> I still cannot find anything that would resemble a 'scores' value.
I'm
> pretty sure it's one matrix computation away, but I cannot find which
> one.
>
> Ideas? Thank you
> Liviu
>
>
>
> --
> Do you know how to read?
> http://www.alienetworks.com/srtest.cfm
> http://goodies.xfce.org/projects/applications/xfce4-dict#speed-reader
> Do you know how to write?
> http://garbl.home.comcast.net/~garbl/stylemanual/e.htm#e-mail
>


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Do you know how to read?
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Hi,

I am also doing PCA.
Is the following right for extracting the scores?

library(psych)
pca<-principal(data,nfactors=,rotate="varimax",scores=T)
pca$loadings
pca$score

Best regards,
He

On Tue, Nov 30, 2010 at 10:22 AM, Liviu Andronic <landronimirc at
gmail.com> wrote:
> Dear all
> I'm unable to find an example of extracting the rotated scores of a
> principal components analysis. I can do this easily for the un-rotated
> version.
>
> data(mtcars)
> .PC <- princomp(~am+carb+cyl+disp+drat+gear+hp+mpg, cor=TRUE,
data=mtcars)
> unclass(loadings(.PC)) ?# component loadings
> summary(.PC) # proportions of variance
> mtcars$PC1 <- .PC$scores[,1] # extract un-rotated scores of 1st
> principal component
> mtcars$PC2 <- .PC$scores[,2] # extract un-rotated scores of 2nd
> principal component
> head(mtcars[, c('PC1', 'PC2')])
>
> However, I no longer understand how to do so if I want to use
> ?principal in 'psych' and any of the GPArotation methods. For
example,
> require(psych)
> r <-
cor(mtcars[,c("am","carb","cyl","disp","drat","gear","hp","mpg")])
> pca <- principal(r, nfactors = 8, residuals = T,
rotate="none") # or
> 'varimax' or any other GPArotation supported rotation
> pca
>
> I've turned the 'pca' object and ?principal help page upside
down and
> I still cannot find anything that would resemble a 'scores' value.
I'm
> pretty sure it's one matrix computation away, but I cannot find which
> one.
>
> Ideas? Thank you
> Liviu
>
>
>
> --
> Do you know how to read?
> http://www.alienetworks.com/srtest.cfm
> http://goodies.xfce.org/projects/applications/xfce4-dict#speed-reader
> Do you know how to write?
> http://garbl.home.comcast.net/~garbl/stylemanual/e.htm#e-mail
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

Hi He Zhang,
>> Is the following right for extracting the scores?
>> ...
>> pca$loadings 
>> pca$score
Yes.

But you should be aware that the function principal() in package psych is
standardizing your data internally, which you might not want. That is, the
analysis is being based on the correlation matrix rather than on the
covariance matrix. The two analyses (and the "default" biplots that
issue
from them) have somewhat different properties. You should know about these.

Regards, Mark.
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