Your response was really useful - thanks Jeremy. I "finally" know the
answer and it seems I was on the right track. In reporting factor
analysis results for publication in a journal then, I am reporting the
rotated eigenvalues for the varimax FAs, but for the oblique ones shall
i report the unrotated eigenvalues or not report any?
Glad to hear someone read my article, and liked it :-)
Kathryn
>>> "Jeremy Miles" <[log in to unmask]> 06/08/07 3:49 PM >>>
It's a bit analogous with multiple regression. When you have a
multiple regression with uncorrelated predictors, you can take the
standardized beta, and square, it, and that is the proportion of
variance that each predictor explains in the outcome variable. You
can sum those proportions of variance, and you'll get R^2.
When your predictors are correlated, you can't do that. They don't sum
to R^2. You can enter them hierarchically, and get the unique
variance accounted for by each predictor, but that's the unique
variance, and they won't sum to R^2, because some variance is shared
between predictors, you don't know which one it 'belongs' to.
Same thing with factors, except the outcome is now the
variance/covariance matrix, and the predictors are the factors. When
you do an orthogonal rotation, the factors are uncorrelated. That
means you can uniquely identify how much (co)variance is associated
with each factor - that's like its variance accounted for, and is the
eigenvalue. When the factors are correlated, that doesn't work any
more, because they share some variance, and although you can know the
total of the eigenvalues, you don't know which factor it belongs to,
because that total variance is shared.
Jeremy
P.S. Nice piece in The Psychologist.
On 08/06/07, Kathryn Jane Gardner <[log in to unmask]> wrote:
> Hi all,
>
> Is there a reason why oblique (i.e., correlated) factor analysis such
> as direct oblim doesn't produce rotated eigenvalues? Is there a way I
> can get SPSS to produce them or are they not appropriate for oblique
> rotations?
>
> When components are correlated like in oblim, sums of squared loadings
> isn't computed to get a total variance and the rotated eigenvalues
> output usually comes off with this part of the output (in orthogonal
> varimax rotation). Perhaps I am missing something (occupational hazard
> of fixating my eyes on a PC until midnight) but I can't find the
answer
> in any textbook and no-one else seems to know the answer.
>
> Hopefully someone can shed some light as I need to find the answer out
> for this by next week!
>
> Many thanks
> Kathryn
>
--
Jeremy Miles
Learning statistics blog: www.jeremymiles.co.uk/learningstats
Psychology Research Methods Wiki: www.researchmethodsinpsychology.com
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