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Bob,
=0D
I have been simulting extreme types of
variables to make my point concerning
the mathematics of grid analysis.
Simulations keep us close to the =
mathematical logic. This is necessary
because of the danger of jumping to
psychological conclusions from fishing
trips on real data. For too long, people =
have used factor analysis and other grid
measures without tracing the logic of
the measure from the basic math
assumptions, to simulated examples,
to experimental elaboration, to clinical
assessment. This is how Landfield's
ordination measure managed to be =
used in so many dissertations and
other publications. Grid analysis has
become something of an art of tea
leaf reading, somewhat akin to the
use of Rorschach cards in the hands
of the less than brilliant. Have no
doubt about it- grids have been the
most prolific source of research in
PCP. Unfortunately, because the =
assumptions of the grid methods
were not adequately developed, =
what was a respected domain of =
inquiry in the 1960's and 70's has =
degenerated in both content and
repute. By not learning from our
mistakes and carrying on the =
tradition of systematic inquiry, we
lost the ball. It is possible but
unlikely that it will be recovered
on a rainy day.
=0D
Thank you for the Brunswick reference
=2E I literally live in a house in the woods, =
without the income to travel to a =
university library. I do not have access
to a good library locally. Perhaps we
could do a trade. Send me a copy of
the Brunswick article and I will analyze
your grid data for you. If the results of =
the corresponding regressions analysis
are meaningful, I'll add my two cents
further in the write up, for junior
authorship. I'll need the data in ascii
format on a 3 1/2" diskette. =
=0D
I would like to suggest that those of us
interested in grids find a way to all get
access to the GAUSS matrix algebra
package. It is not that expensive and
it would allow us to pass programs back
and forth for any type of grid analysis we
can imagine. This would greatly =
excellerate the growth of our grid analysis
knowledge, not to mention being of
significant use clinically.
=0D
Concering principal components analysis
and cluster analysis. Many cluster
analysis programs are based on linkage
measures that are more akin to
Euclidean distances than to correlations.
You might consider also finding the
components of the Euclidan distances.
Nunnally discusses this in his Psychometric
Theory text under Raw score factor analysis.
The raw score factor analysis is available
in Circumgrids. You can perform the PCA
on the correlations and/or Euclidean
distance cross products matrix in =
Circumgrids.
=0D
Concerning averaging correlations. =
Correlations are not linear in addition.
The squares of correlations are. This is
why the inter construct correlations were
squared before they were added to get
the intensity measure in the Bannister
-Fransella Grid test. I suggest you first
square the correlations (retaining signs) ,
then average, then find the square root of =
the average correlations (retaining signs)
and then factor these roots (correlations).
I may be wrong about this. I am predicating
my argument on the rationale of coefficients
of determination. I would at least try it both
ways. You might try using the fundamental
factor equation to decompose your loadings
back into correlations and compare these
correlations with your original correlations
and those obtained by not averaging.
=0D
Regarding the authorship of corresponding
regressions. I created corresponding
regressions. The articles in the Journal
of Mind and Behavior introduced them.
As far as I know, nothing else has ever
been created that will do the same job.
Rue Cromwell recently directed our attention
to HICLASS cluster analysis as potentially
a way of doing the job using dichotomous
data. I am unfamiliar with the method. It may
or may not do the same thing- as far as
dichotomous data. I'll try to get at the
literature. Corresponding regressions does
work when the IVs are dichotomous but =
the Dvs can not be dichotomous.There would
be no extreme versus midrange to polarize
correlations across. Logically, the DV
should not be dichotomous either. Adding
dichotomies creates 3 possible outcomes:
0, 1 2.Dropping the middle value through
dichotomization is degrading of the
information in the DV. =
=0D
Send me the data in ascii format and
I will analyze it. Try to get GAUSS.
The fun might be just beginning. =
=0D
Regards,
=0D
Bill
=0D
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