Factor analysis: second dimension

[Bob Schacht-3]

I am performing a series of Principal Components Analysis for Likert rating
scales, so CATPCA seems to be preferred.
For one of my sets of 11 items, I ask CATPCA for 3 Dimensions, so it gives
me three, of course. Cronbach's Alpha is .936 for the first, accounting for
61% of the variance, .548 on the second, accounting for 18%, and -.301
(yes, minus .301) on the third, accounting for 7% of the variance.
Six of the items loaded highest on Dimension 1. Four loaded highest on
Dimension 2, and one loaded highest on Dimension 3.

I also tried a straightforward conventional PCA on the same data. First
component had an eigenvalue of 6.9, with 62% of variance, second component
had an eigenvalue of .881 with 8% of variance. Only one dimension was
extracted-- because the second eigenvalue was less than one?

So, only one component could be extracted because the second eigenvalue was
less than one? Is that why the varimax solution could not be rotated?

Just for fun, I ran the CATPCA again, for the four items that loaded
highest on Dimension 2  and got Cronbach's Alpha of .857 for the new
dimension 1, with all 4 items loading highest on Dimension 1. However, the
item loading highest on this dimension is different than the item that
loaded highest on Dimension 2 of the preceding analysis.

I'm doing this for data reduction. So for this set of variables, do I say
that I only need the one item that loads highest on Dimension 1 of the
first dimension of the original CATPCA, and can disregard other possible
dimensions because Cronbach's Alpha is < .700 and the eigenvalue for the
second dimension was less than 1?

Thanks,
Bob

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[Kooij, A.J. van der]

CATPCA solutions are not nested: if you run CATPCA with a different
number of dimensions (=components) the result will not be equal. So, I
would also look at CATPCA results for 2 dimensions and for 1 dimension
(if 3 dimensions are requested, CATPCA finds transformations that are
optimal for 3 dimensions; if 2 dimensions are requested, the
transformations are optimized for 2 dimensions).
Cronbach's Alpha is a function of the eigenvalue. Alpha is negative for
eigenvalues less than 1.
Eigenvalues less than one is one criterion to decide not to include a
dimension. This is the default in SPSS conventional PCA (you can click
the Extraction button in Factor window to choose the number of
components).
For only one component there is no point in rotating: rotation is used
to obtain a clear structure, that is, to more easily identify which
variables load on which components. With only one component this is
already clear.

Regards,
Anita van der Kooij
Data Theory Group
Leiden University


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Bob Schacht
Sent: 14 May 2009 02:52
To: [hidden email]
Subject: Factor analysis: second dimension

I am performing a series of Principal Components Analysis for Likert
rating scales, so CATPCA seems to be preferred.
For one of my sets of 11 items, I ask CATPCA for 3 Dimensions, so it
gives me three, of course. Cronbach's Alpha is .936 for the first,
accounting for 61% of the variance, .548 on the second, accounting for
18%, and -.301 (yes, minus .301) on the third, accounting for 7% of the
variance.
Six of the items loaded highest on Dimension 1. Four loaded highest on
Dimension 2, and one loaded highest on Dimension 3.

I also tried a straightforward conventional PCA on the same data. First
component had an eigenvalue of 6.9, with 62% of variance, second
component had an eigenvalue of .881 with 8% of variance. Only one
dimension was
extracted-- because the second eigenvalue was less than one?

So, only one component could be extracted because the second eigenvalue
was less than one? Is that why the varimax solution could not be
rotated?

Just for fun, I ran the CATPCA again, for the four items that loaded
highest on Dimension 2  and got Cronbach's Alpha of .857 for the new
dimension 1, with all 4 items loading highest on Dimension 1. However,
the item loading highest on this dimension is different than the item
that loaded highest on Dimension 2 of the preceding analysis.

I'm doing this for data reduction. So for this set of variables, do I
say that I only need the one item that loads highest on Dimension 1 of
the first dimension of the original CATPCA, and can disregard other
possible dimensions because Cronbach's Alpha is < .700 and the
eigenvalue for the second dimension was less than 1?

Thanks,
Bob

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For a list of commands to manage subscriptions, send the command
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