Re: Presenting unorthodox factor analysis findings
- From: hrubin@xxxxxxxxxxxxxxxxxxxx (Herman Rubin)
- Date: 12 Jan 2008 17:47:43 -0500
In article <be4e7c90-ac01-42e9-8500-dc5499b27c28@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
shysong <shysong@xxxxxxxxx> wrote:
Hi everyone,
I have a somewhat unorthodox set of findings and I'm trying to figure
out what the best way of presenting them would be in a paper or
abstract. I have a set of 12 measures that were collected over 7 time
points on approximately 133 subjects. I ran an exploratory factor
analysis with the measures at each of the time points, to see what the
factor structure was and whether the factor structure was stable over
the 7 time points.
The bad news is that the factor structure was not stable over time;
some time points showed a four factor structure whereas others showed
a five factor structure. And the measures that fell into the each
factor tended to vary somewhat. The interesting finding, however, was
that there were small clusters of variables that always seemed to
appear together, regardless of what factor they were in. So for
example, measures 1 and 2 always appeared together, almost always as
a single factor, though sometimes they were factor 3 and sometimes
they were factor 4; measures 6,8,9, and 10 appeared together in 1/2 of
the time points, always as factor 1 (factor 1 was always composed of
four measures).
This is the finding that I would like to present, because the sets of
variables that cluster together consistently are of interest. But of
course, this is not the usual kind of thing you report from a factor
analysis. So the question is, what would an appropriate table in the
results section contain? Maybe a graph with correlations over time?
Any ideas would be appreciated on how to credibly present and report
the piece of the analysis I'm interested in.
Many thanks,
Sylvia Hysong
There are ways to use factor analysis to do what you are
after, but not by using a separate factor analysis at
each point as you are doing. Understanding the factor
analysis model might make this clear. The model is
x_it = sum load_ij*f_jt + u_it
where x_it is the score of individual t on the i-th measure,
f_jt is the factor score, and u_it is the individual component.
The factor structure is the loadings load_ij.
The usual procedure assumes that the f_j have a certain
covariance matrix, and usually correlations are used.
Both of these obscure the picture. One should use
covariances rather than correlations, and not assume that
the covariances of the factors are constant; the latter
might be part of your assumptions, however, and this can
be tested.
I doubt that there is an existing package procedure to do
what you want, although there should be no real problem for
someone who understands mathematical statistics and can
"speak" matrix to produce one, with programming
assistance. The results of my abstracts in 1956 go over
with little problem, and also the properties of tests of
overall goodness of fit go over, again if no assumptions
are made about the distributions of the factors. The
structure tests are almost independent of them.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.
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- Presenting unorthodox factor analysis findings
- From: shysong
- Presenting unorthodox factor analysis findings
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