Steven A Harvey
> I am working with v 6.0 & have two questions. I could not
> find answers
> in the reference manuals or on the Stata website:
>
> 1. When performing factor analysis, Stata produces a table
> labeled "eigenvectors." This looks to me like what I know
> as factor
> loadings. Is this correct or is there a different interpretation?
Terminology is a real problem here. Depending on tribal
customs and attitudes, some see factor analysis
as a superset of principal components analysis
and some see the two as disjoint.
I'll reply in terms of principal components
analysis.
In Stata 6, the two are both obtainable from
-factor-.
Whatever you mean, I hope this may help, as
I think that despite differences between PCA
and (other kinds of) factor analysis, the
answer here would have the same flavour.
As I understand it, with PCA the loadings are the
correlations between the new components ("factors"
wide sense) and the original variables. These
are not contained in the eigenvectors, which are
-- the eigenvectors. That is, each PC is
a linear function of the existing variables,
and the eigenvectors contain the coefficients
of those functions.
If you want the correlations,
you need to calculate them directly.
Let's illustrate with some "size" variables
from the auto data.
. factor headroom trunk length turn displacement, pc
(obs=74)
(principal components; 5 components retained)
Component Eigenvalue Difference Proportion Cumulative
------------------------------------------------------------------
1 3.62292 2.87719 0.7246 0.7246
2 0.74573 0.43899 0.1491 0.8737
3 0.30674 0.08654 0.0613 0.9351
4 0.22020 0.11578 0.0440 0.9791
5 0.10442 . 0.0209 1.0000
Eigenvectors
Variable | 1 2 3 4 5
-------------+------------------------------------------------------
headroom | 0.36700 0.75326 0.52068 0.15988 -0.03536
trunk | 0.44225 0.36252 -0.77027 -0.16372 0.22995
length | 0.49374 -0.23421 -0.09274 0.08915 -0.82753
turn | 0.46041 -0.39324 0.07413 0.65353 0.44810
displacement | 0.46257 -0.30281 0.34853 -0.71595 0.24550
. score pc1-pc5
(based on unrotated principal components)
Scoring Coefficients
Variable | 1 2 3 4 5
-------------+------------------------------------------------------
headroom | 0.36700 0.75326 0.52068 0.15988 -0.03536
trunk | 0.44225 0.36252 -0.77027 -0.16372 0.22995
length | 0.49374 -0.23421 -0.09274 0.08915 -0.82753
turn | 0.46041 -0.39324 0.07413 0.65353 0.44810
displacement | 0.46257 -0.30281 0.34853 -0.71595 0.24550
You could use -correlate- but for this purpose I prefer -cpcorr-
from SSC:
. cpcorr headroom trunk length turn displacement \ pc1-pc5
(obs=74)
pc1 pc2 pc3 pc4 pc5
headroom 0.6985 0.6505 0.2884 0.0750 -0.0114
trunk 0.8418 0.3131 -0.4266 -0.0768 0.0743
length 0.9398 -0.2023 -0.0514 0.0418 -0.2674
turn 0.8763 -0.3396 0.0411 0.3067 0.1448
displacement 0.8805 -0.2615 0.1930 -0.3360 0.0793
It is common, but in essence accidental, that the magnitudes
of the eigenvector elements are such that they look as if
they might be correlations.
> 2. I have been told that in running the alpha command (Cronbach's
> alpha for measuring inter-item correlation) with a list of
> dichotomous
> variables that Stata recognizes that it is processing
> binary variables
> and automatically substitutes the KR20 formula for
> Cronbach's alpha.
> Is this true? If so, is there a reference I can cite to
> that effect?
> (A colleage claims that if I want KR20 values instead of Cronbach's
> alpha, my only option is to calculate them by hand.)
I'd trust the manual over hearsay here. [R] alpha p.20
(v.6 documentation) seems pertinent.
Nick
[email protected]
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