My experience and that of other’s (eg. Preacher and MacCallum) is that most factors in behavioral sciences and many in biomedical sciences are in fact correlated. And in that case, allowing the factors to be correlated gives a cleaner solution. When factors are truly correlated, forcing them to be uncorrelated is what gives crossloadings.
Paul
Dr. Paul R. Swank,
Children's Learning Institute
Professor, Department of Pediatrics, Medical School
Adjunct Professor, School of Public Health
University of Texas Health Science Center-Houston
From: Rich Ulrich [mailto:[hidden email]]
Sent: Friday, November 18, 2011 11:55 AM
To: Swank, Paul R; SPSS list
Subject: RE: EFA to CFA( was Re: )
[see below]
From: [hidden email]
To: [hidden email]; [hidden email]
Date: Fri, 18 Nov 2011 11:11:14 -0600
Subject: RE: EFA to CFA( was Re: )
How can you justify forcing factors to be uncorrelated if in fact they are correlated?
[snip previous; my recommendation of Varimax over Promax.]
- thanks for asking -
It works.
In more detail: It works a lot better than the alternatives.
Explanation: Since we are intending to compute factors from
items using equal weights, we will end up with factors that are
correlated, just as expected. And they will have just about as
much correlation as we expected, judging from my own experience.
If we start with an oblique rotation, we pile correlation (from selecting
items) on top of allowed-correlation (oblique solution). That is,
we are faced with factors that have a lot of double-loaded items.
Either we end up suffering from too much induced correlation from
using non-exclusive scale definitions; or else we drop entirely (as our
OP did) many items which are central to our universe of items.
The situation is different if we were preserving and using the
theoretical factors, but there are good reasons (interpretation,
generalizability) that that practice is rare.
If we look at the geometrical representation in plots, we will see
that a varimax solution does a pretty decent job of describing
factors as correlated as, say, 0.60. And varimax does a much
better job that any oblique solution in separating out the variables
into non-overlapping sets.
By the way, Promax is what I did most of my experimenting with,
after it seemed superior (to several other oblique rotations)
for the sort of scaled data I've regularly reduced to factors.
--
Rich Ulrich
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