Re: PCA analysis of rep grids

Tony Downing (
Mon, 3 Mar 1997 09:47:52 +0000

Very many thanks to Brian Gaines for clarifying so well and so promptly
several of the points that I raised in my message about PCA in rep grid
analysis in general, and in the RepGrid 2 package in particular.

I obviously have to apologise for not having mastered the package well
enough to have spotted how to get it to plot principal components other
than the first two! I still think it would be nice if it gave scree plots
but I do now see how, in the PrinCom dialogue screen, to get it to give the
necessary eigenvalues numerically, and I can thus see that it is an even
package better than I had thought it was.

I am puzzled to learn from Brian Gaines's message that RepGrid2 does not,
after all, rotate factors. On the one grid which I analysed using the PCA
command in Minitab and for which I then plotted the projections of the
construct axes manually, the pattern of axes that I got was the same as we
had got from the RepGrid2 PrinCom output for the same grid - except that
the whole plot definitely was swung round a bit in relation to PrinCom's
orthogonal axes for Components 1 and 2. (Of course, for most of the
purposes for which rep grids are used in PCP, it makes no difference
whether axes are rotated or not, but I can see some circumstances, in
research, where a single factor seems to run strongly through the
constructs in a grid, when rotation and use of a rotated factor score could
be useful.)

I do take the point about the both PCA and hierarchical cluster analysis of
grids being, at one level at least, purely descriptive. In this spirit,
perhaps the best thing about the displays provided by RepGrid2 is the
rearranged grid, against which any tendencies to patterns, as summarised by
clusters or principal components, can be checked directly, in a way that
make the exceptions to such patterns, as well as the patterns themselves,
very clear in the most direct way possible.

Brian's message has helped me to see more clearly the issue about the scale
with which elements are plotted in the construct space. I see that I was
muddled in being tempted to read any meaning into the distances, on any 2-D
plot, between the ends of construct axes and the plotted position of any
given element. I don't think I am by any means the only person to make that
mistake, but I clearly was mistaken. Thanks vor a very helpful reply.

Tony Downing

Dept. of Psychology, University of Newcastle upon Tyne,
Ridley Building, Claremont Place, Newcastle upon Tyne, NE1 7RU, England.
Telephone: +44 (0)191 222 6184, Mobile: +44 (0)468427481
Fax: +44 (0)191 222 5622