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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