I was especially interested in the issue of "noise" raised by
Travis as my understanding is that grids with different
constructs(but common elements)can be analysed using MDS if they
are transformed into proximities. Often data for MDS is collected
by asking subjects to rate how (dis)similar phenomena(eg
elements) are without reference to any labels (eg construct
poles). I had considered the approach adopted as analogous
to the (dis)similarity approach, with the ratings indicating
(dis)similarity.
Also of interest was Travis' comment regarding the possible
significance of a 3rd dimension. This is an interesting
proposition and upon reflection suggests to me,
1)the 2 dimensional model is a reasonable representation for the
majority of participants in the research,
2)while the addition of a 3rd dimension adds little to explained
variance, it is of significance to several participants...
perhaps this may well be the difference between statistical
significance and personal meaning. Certainly a 3rd dimension can
be interpreted and allows for greater case discrimination (among
a cluster of cases with several similar features).
My previous reservations re a 3rd dimension were, a) minimal
change in RSQ and 2), the relocation of a case in the
3dimensional plot, somewhat inconsistent with the dimensional
interpretation. Given the process of fitting a model to
subjective data is a less exact process than scaling physical
phenomena, perhaps it is too much to expect an exact fit in such
circumstances ?
A final comment re individual MDS: I have not undertaken this
though have considered calculation of the plots from the subject
weights... I believe this can be done. I have carried out
individual cluster and factor analyses, though the sheer number
of these is difficult to integrate. I also tried to analyse the 4
scales using MDU though didn't find the 40 plots too illuminating
(perhaps because when entered into regression the supplied
constructs don't predict much of the variation in the release
construct).
Any further comments are welcomed and thanks again,
Bob Green