🚀 go-pugleaf

Rod Custer posed a question on METHODS-L.
>> I have some questions about factor scores which are generated
>> as a part of factor analysis.  Kerlinger gives a formula for
>> calculating them based on sums of individual's item scores multiplied
>> by factor loadings.  He also indicates that this is not the best way
>> of doing the calculation.  Anyone have any suggestions?

I don't think I'm qualified to answer Rod Custer's questions about factor
scores, I seem to remember that the issues seemed daunting!
However, he also asks:
>> Finally, again in lay terms, what are the essential differences between
>> the principal component, common factor, and other methods of doing
>> factor analysis?  How does one choose?  Any good references?

As I understand it the basic issue is that doesn't impute any "unique factors"
(and image component analysis is similar); I believe all the other factor
analytic methods assume common and unique factors.  However, I believe that
only rare datasets give markedly different results which means that the
computational efficiency (and determinacy?) of PCA makes it a winner for me.
The best review I know is that of:
     Velicer, Wayne F; Jackson, Douglas N. (1990)
     "Component analysis versus common factor analysis:
      some issues in selecting an appropriate procedure"
     Multivariate behavioral research 25(1):1-28
which is followed by commentary from various authors and response by
V&J pp.97-114.  Brilliant and convincing stuff.

That all applies to pure exploratory forms of factor analysis.  Multiple
groups factor analysis takes one into sort of confirmatory analysis and is
computationally simple but the winner at present for confirmatory work has
to be the maximum likelihood, GLS and other methods of factor analysis.  I
think there is an argument that confirmatory PCA methods could be developed
in theory but I'm not aware that they exist at present (though you can get
LISREL, EQS, AMOS etc. to estimate what amount to PCA models by setting
uniquenesses to zero; perhaps a better mathematician than I could tell us
more about what you're getting if you use that in combination with a
confirmatory pattern of loadings fixed to zero: are you getting a maximum
likelihood confirmatory components analysis?  sounds a bit of a bizarre
hybrid to me but I guess it's possible.
Hm, that's intrigued me so much I'll cross post this to STAT-L in hope of
enlightenment!

Chris Evans