Dear List:
I have a question regarding an MDS procedure that I am accustomed to
using. I have searched around the archives a bit and the help doc and
still need a little assistance. The package isoMDS is what I need to
perform the non-metric scaling, but I am working with similarity
matrices, not dissimilarities. The question may end up being resolved
simply.
Here is a bit of substantive background. I am working on a technique
where individuals organize items based on how similar they perceive the
items to be. For example, assume there are 10 items. Person 1 might
group items 1,2,3,4,5 in group 1 and the others in group 2. I then turn
this grouping into a binomial similarity matrix. The following is a
sample matrix for Person 1 based on this hypothetical grouping. The off
diagonals are the similar items with the 1's representing similarities.
a b c d e f g h i j
a 1 1 1 1 1 0 0 0 0 0
b 1 1 1 1 1 0 0 0 0 0
c 1 1 1 1 1 0 0 0 0 0
d 1 1 1 1 1 0 0 0 0 0
e 1 1 1 1 1 0 0 0 0 0
f 0 0 0 0 0 1 1 1 1 1
g 0 0 0 0 0 1 1 1 1 1
h 0 0 0 0 0 1 1 1 1 1
i 0 0 0 0 0 1 1 1 1 1
j 0 0 0 0 0 1 1 1 1 1
Each of these individual matrices are summed over individuals. So, in
this summed matrix diagonal elements represent the total number of
participants and the off-diagonals represent the number of times an item
was viewed as being similar by members of the group (obviously the
matrix is symmetric below the diagonal). So, a "4" in row 'a' column 'c'
means that these items were viewed as being similar by 4 people. A
sample total matrix is at the bottom of this email describing the
perceived similarities of 10 items across 4 individuals.
It is this total matrix that I end up working with in the MDS. I have
previously worked in systat where I run the MDS and specify the matrix
as a similarity matrix. I then take the resulting data from the MDS and
perform a k-means cluster analysis to identify which items belong to a
particular cluster, centroids, etc.
So, here are my questions.
1) Can isoMDS work only with dissimilarities? Or, is there a way
that it can perform the analysis on the similarity matrix as I have
described it?
2) If I cannot perform the analysis on the similarity matrix, how
can I turn this matrix into a dissimilarity matrix necessary? I am less
familiar with this matrix and how it would be constructed?
Thanks for any help offered,
Harold
a b c d e f g h i j
a 4 2 4 3 3 2 0 0 0 0
b 2 4 2 3 1 0 2 2 2 2
c 4 2 4 3 3 2 0 0 0 0
d 3 3 3 4 2 1 1 1 1 1
e 3 1 3 2 4 3 1 1 1 1
f 2 0 2 1 3 4 2 2 2 2
g 0 2 0 1 1 2 4 4 4 4
h 0 2 0 1 1 2 4 4 4 4
i 0 2 0 1 1 2 4 4 4 4
j 0 2 0 1 1 2 4 4 4 4
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