Date: Mon, 26 Jan 2009 18:57:17 +0100
Reply-To: "Kooij, A.J. van der" <KOOIJ@fsw.leidenuniv.nl>
Sender: "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From: "Kooij, A.J. van der" <KOOIJ@fsw.leidenuniv.nl>
Subject: Re: CATPCA Categories vs. conventional factor analysis
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>The Iteration history accounts for only 11 (%?) of the variance.
Is 11 in the Total VAF column of the Iteration history table?
This is the total eigenvalue then. The total percentage VAF then would be 11 divided by number of variables times 100, is 84%.
(the % VAF is given in the Model Summary table, that is, if there are no variables with missings for which Missing option is Exclude values; see below).
But if with conventional PCA you obtained about 30% VAF for 3 components, I don't think it is likely you obtained 84% VAF with CATPCA for 3 components. Treating likert items ordinal results in higher VAF then when treating the items numerical
(or equal; but lower is not possible), but usually the increase in VAF is not that big.
How many components (= dimensions in CATPCA terminology) did you specify for the CATPCA analysis?
If you want rotated CATPCA results, you can use the Save option to save the transformed variables and use them in conventional PCA.
The results of conventional PCA on the transformed variables are equal to the CATPCA results, but not if there are missings and missing option is Exclude values, which is the default; this is passive treatment of missings (cases with missing values are not excluded, missings are not imputed. Missing cells in the datamatrix are ignored in the computations, which is possible because CATPCA does not compute the solution from the correlation matrix but from the data itself). With the Exclue values Missing option, the transformed variables will have missings where the original variables have missings. With SPSS conventional PCA, the passive missing option is not available, thus the results will not be the same. So, if there are missings and you want to perform conventional PCA on the transformed variables, choose missing option Listwise deletion or Imputation in CATPCA.
With Missing option passive (Exclude values), there is no % VAFcolumn in the Model Summary table, because computing % VAF then is not possible. Also, with this missing option
loadings are not correlations of the transformed variables with the component (object) scores (it is possible to have loadings with absolute value > 1).
Regards,
Anita van der Kooij
Data Theory Group
Leiden University
________________________________
From: SPSSX(r) Discussion on behalf of Bob Schacht
Sent: Sat 24-Jan-09 01:46
To: SPSSX-L@LISTSERV.UGA.EDU
Subject: CATPCA Categories vs. conventional factor analysis
I am analyzing results from a pilot questionnaire, specifically a group of
13 questions, with 70 responses.
The data consists of Likert scale responses on a 5-point scale.
Conventional PCA with varimax rotation produces 3 components, each
explaining more than 10% of the variance. The rotated component matrix
sorts out the original questions nicely into 3 groups with approximately
the same number of questions. From these, I can easily chose one question
from each of the three groups, and add a fourth (question with the largest
standard deviation of responses, indicating the widest variability in response.
CATPCA, however, does not provide a rotated component matrix. The Iteration
history accounts for only 11 (%?) of the variance.
The three questions with the top 3 loadings on the first dimension are the
same 3 that loaded most highly on the conventional PCA, but none of the
questions loaded more highly on the second dimension than the first, so it
is not so clear how to define the second dimension.
I am just learning how to interpret CATPCA output, and some of the
terminology is unfamiliar to me.
My objective here is data reduction: With the conventional PCA, I can
see how to reduce the original set of 13 questions down to 4 questions
that seem to cover all the bases. But I'm not seeing how to do that with
the CATPCA results, which ought to be more appropriate, given the
measurement level.
What do you suggest?
Thanks in advance,
Bob Schacht
Robert M. Schacht, Ph.D. <schacht@hawaii.edu>
Pacific Basin Rehabilitation Research & Training Center
1268 Young Street, Suite #204
Research Center, University of Hawaii
Honolulu, HI 96814
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