# Re: Slater's PCA

Arne Raeithel (raeithel@rzdspc1.informatik.uni-hamburg.de)
Thu, 12 May 1994 12:00:36 +0200 (MET DST)

Eva and you-all:

Patrick Slater was the pioneer of using the well known Principal Components
Analysis (PCA) -- in psychology also known as Factor Analysis, with some
15 or 20 variants -- for Repertory Grids on big mainframe computers in
for extracting factors from a Grid. Kelly seems to have been a quite good

Well. Slater was not very lucky in getting lectureship or tenure, but he
succeeded in building up a computing service for UK researchers and
practitioners in those days where you gave a pack of real cards (no Hypers)
to professionals working behind glass panes in a hall packed with
equipment. Hours or minutes later, depending on other customers, you
would get a thick pad of "no-end-paper" (German: Endlospapier) full of
error messages....

Slater's innovation was to do a *dual* PCA, namely one regarding the
rows of the Grids (i.e. the constructs) as primary data vectors and
thereby getting element *images* (also vectors, may be plotted on the
plane or in 3D-space), and another one that regards the columns of
the Grid (i.e. the elements) as primary, and that yields construct images.

Slater was bold enough to plot both image vector set in the SAME PLANE
OR SPACE. In this way we get *angular distances* between elements and
constructs (i.e. measures akin to the well-known correlation coefficient
of Pearson).

In substantive terms, this means that a construct having a small angle
with an element (in the plot) is a *prototypical construct* for that
element, and, at the same time: that this element is prototypical for
the respective *pole* of the construct.

This trick of plotting both image vector sets in one space was invented
in parallel by many researchers over the world (the French "correspondence
analysis" is another example; Feixas uses it in the programs offered
by his group in Barcelona).

GridStack does a "raw value PCA" -- to be more exact. Grid data must
be "naturally centered" around zero (e.g. a seven point scale would
use the values: -3, -2, -1, 0, 1, 2, 3); optionally a scale using the
natural numbers (1, 2, 3, 4, 5, 6, 7) is transformed into the prescribed
scale.

Slater's standard transformation was to get deviation scores for the
construct (arithmetical centering of rows; after the transformation
all scores of a row sum to zero). My considered and strong opinion
is that this should not be allowed, because our informants use the
midpoint consciously: as the dividing line between emergent pole
and contrast pole, or as the neutral "white noise" midway between
an element and its antipode.

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We have an holiday here. It is sunny.

Best wishes: Arne.

p.s. for Geoff: I'm sorry. I have GridStack only for the Mac. There
are some rumours that a generic application like HyperCard has
been implemented on Intel-Machines, too (MS-DOS?, surely Windows).
One that I heard of is "MetaCard".
There are several sources for Slater's INGRID for PC's.
Maybe some of those who are nearer, and are reading this,
will soon comment?
Electronic discussion lists like ours have a notoriously bad
memory. David Nightingale could surely look up some older
messages giving the information that Geoff wants to have...
```