These calculations are all performed on:
Version 3.4 Release 1 for Sun SPARC
The model is
x = L f + e
where x is the standardised p dimensional data vector
f an unobserved k dimensional vector of common factors
e a p dimensional vector of factors one unique to each component of x.
L is a pxk matrix of loadings.
As a first step the components of f are uncorrelated with unit variance,
and the components of e are uncorrelated.
Using the standard data set 'testscores' the analysis goes like this:
[The 'scale' function makes no difference, but guarantees to the reader
that x is standardised]
> testscores.no.rot <- factanal(scale(testscores) ,rotation='none', factors=2)
> summary(testscores.no.rot)
[useful stuff with which I have no problem]
My problems lies with the properties of f. I believe these are the
'scores' component of the factanal, but
> var(testscores.no.rot$scores)
Factor1 Factor2
Factor1 0.99703074 -0.00790189
Factor2 -0.00790189 0.52859672
>
But should not f1, f2 have unit variance?
[var(f1) may see close enough, but other less highly correlated data sets
give all var(fi)<<1]
Just what do the 'scores' really represent?
Greg Arnold
Statistics, Social Science Building
Institute of Information Science and Technology
Massey University
P B 11 222
Palmerston Nth
New Zealand
g.arnold@massey.ac.nz
Phone +64 6 350 4254
Fax +64 6 350 2261
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