I was interested in your recent 'ramblings' for several reasons:
1. The Horn procedure of parallel analysis of random data to determine the
number of factors is alive and well in factor analysis (see Educational &
Psychological Measurement from 1993 on for example). It has also been used
in multidimensional scaling for similar purposes. It is very easy to do in
modern statistical packages such as SPSS. Patrick Slater built this into a
program called GRANNY, but it did not seem to attract much attention and I
put a similar thing into a version of G-pack where it similarly failed to
arouse enthusiasm. I suspect this is because the number of factors problem
is not seen as particularly important for grids. We extract one factor if
we are interested in 'PVAFF' as a measure of grid complexity, two factors
if we want to draw a picture, or three factors if we have been brought up
on INGRID or Osgood's semantic differential. Since three variables are
needed to define a factor, we are never going to have many factors with
ordinary grids, anyway.
2. But you do raise an interesting question: how do we know if a grid is
simply random data? Neither principal components or cluster analysis will
detect this. My feeling is that we would need to look at simpler
statistics. Or perhaps we don't really want to know the answer.
3. I have forwarded your comments about the impact of factor rotation to
Terry Keen as I am sure he will be pleased to see his work lives on. The
impact of transformations on grid representations is an issue which seems
to get neglected (another question perhaps that we don't want to look too
closely at) but I think it is difficult to say whether prior
transformations (as I talked about in Seattle) or rotational
transformations, such as Terry talks about, are the more important.
Rotational transformations are difficult to apply in INGRID type analyses
(I have given up on this for the moment in GRIDSTAT) - but since we usually
only use this type of analysis to produce a two-dimensional picture, it
doesn't really matter much, since orthogonal rotations won't change the
relationships between the points.
Richard
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%