Mike,
This is exactly the kind of problem MDS was designed to handle. If you use
a two-way approach-- preferably a nonmetric MDS procedure such as Kruskal's
KYST (most recent version is called KYST-2A)-- you need simply use the
(symmetric) co-ocurrence data as input, calling the data "similarities"
(which, in KYST, tells the program that the data are related to distances
via a non-increasing monotonic transformation), indicate the dimensionality
in which you want a solution, or try a number if you're not sure, using
standard criteria based on values of STRESS. (I'd strongly suggest use of
STRESS-1, the default option in KYST) and interpretability to determine (or
at least "guesstimate") the correct dimensionality.
Since you have 3 replications, you could, if desired, do a "three-way"
individual differences analysis such as INDSCAL (or, better yet, SINDSCAL),
in case you suspect there might be some systematic changes in perceptual
structure of the items occurring over trials.
Heiser and Busing have devised an MDS procedure called ProxScal that
combines important features of KYST and INDSCAL, doing either 2-way or
3-way MDS analyses either metrically or nonmetrically. When
done nonmetrically it optimizes an objective function equivalent to STRESS,
and is, to my knowledge, the only three-way MDS program optimizing
STRESS. It's available on SPSS Categories.
Best regards,
Doug Carroll
At 05:53 PM 12/9/2005 -0800, Michael Healy wrote:
Hi Friends, I am looking for advice and recomendations about a data set that
i'd like to analyze where I will measure association by frequencies of
co-occurence.
Let me explain in more detail. In my experiment participants were shown an
object and asked to choose words that described the item from a list of 50
words. Responses were either 'yes' or no response was given. This
procedure was repeated up to 3 times.
I now want to group the word-associates by target item, I have a rough idea
of what I want, but I'm open to suggestions from people who know more about
this than I do. My plan is to find some method for finding the strength or
description of association between items by examining counts of numbers of
times items co-occured and produce a 'topographical map' where more
frequently listed items are closer together--by analogy, something like an
MDS model where we have a similarity matrix representing how often items are
co-occuring (or is that the answer?)
Anyway, looking forward to your input and suggestions, I think this is an
interesting although maybe standard problem.
Mike Healy
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