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Hi,
 
Last week I posted questions on the Socnet list and got the responses below. I have also appended the email addresses of those who responded with their responses.
 
Regards.
 
MY QUERY BELOW:
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Hello again everyone,
 
A colleague of mine has overwhelmed me with some 500 matrices.Each matrix is a 15X15 cognitive map. The expected hypothesis use QAP and are not so strongly supported.
 
Therefore, we are exploring how to cluster these 500 matrices into groups of matrices depending on certain characteristic of each matrix such as centralities of nodes, etc. The end result could be a few clusters where matrices in these clusters are similar in certain respects.
 
With this clustering, we plan to add dummy variables for these matrices in a QAP regression and hope to get more significance.
 
1. Is this a statistically valid thing to do?
2. Which software package facilitates clustering of matrices (unlike clustering nodes in a single matrix) ?
3. Running a QAP correlation on a hundred pairs of matrices is troublesome if I use the user interface in UCINET. Is there a way one can write a simple small program to automate this once the matrices are stored in certain known files? (e.g., like a SAS procedure)
 
 
Thank you.
 
Regards.
Nilesh Saraf 
 
 
RESPONSES :
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Kathleen Carley and I have recently done some work on this problem. The paper in question is currently under review, but you can find a draft at http://legba.hss.cmu.edu/~eagle/distribution/multiv.1.0.pdf This paper provides a general approach to distance methods (e.g.,  cluster analysis, MDS) and covariance analysis (e.g., PCA, CCA, network regression) for graph sets under arbitrary labeling conditions. I have S routines which will implement these analyses, some of which are in my network S toolkit. (The rest will be added eventually, but aren't currently in a user-friendly form; OTOH, the structdist and gscor/gscov routines are all you really need, and these are in the current release.)

Hope that helps,

- Carter T Butts [[log in to unmask]]

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Hi Nilesh -
 My advice would be to cluster a structural summary of the matrix, and the best one that comes to mind would be the triad census.  That is, you could:
                a) Calculate the triad census for each matrix, which results in a 16 element frequency distribution for each matrix
                b) you would then have a dataset with 500 observations and 16 variables
                c) run that through a cluster analysis program to get your clusters.

If it were me, I'd do it all in SAS.  I have programs for getting the triad census, and then use the SAS PROC CLUSTER to do the clustering.  It is also fairly easy to write a QAP routine in SAS (I've one for regression and logistic regression).

Let me know if you need any of these programs.

Best of luck,
Jim Moody [[log in to unmask]]
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Nilesh,
 
1. In UCINET, you can JOIN all the matrices together into a single file containing 500 2-way matrices: in effect a 15x15x500 matrix. Then you can run SIMILARITIES on that file, specifying MATRICES as the dimension to correlate (at least in fairly recent versions of ucinet). The result is a 500 by 500 matrix of similarity coefficients. You can then submit this correlation matrix to any clustering routine.
 
2. In SPSS or SAS, it is not difficult to cluster your 500 matrices. Just string out each one as a row of 225 numbers (call these variables). So you have a new matrix that is 500 rows by 225 columns. Then submit to clustering routine (specifying cases as the dimension to cluster).
 
3. I'm not sure what you are trying to do so is difficult to comment on the larger issues. But I think you flirt with the Dark Side whenever you manipulate the data expressly to "get more significance".
 
Steve Borgatti [[log in to unmask]]
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3. Running a QAP correlation on a hundred pairs of matrices is troublesome if I use the user interface in UCINET. Is there a way one can write a simple small program to automate this once the matrices are stored in certain known files? (e.g., like a SAS procedure)

If you use Stata, you might want to check out a small progam called, conveniently, qap at: http://ideas.uqam.ca/ideas/data/bocasug01.html

Gindo Tampubolon [[log in to unmask]]

University of Manchester

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Hello Saraf,

please contact Stephen Borgatti about QAP-procedure and the application of it. The tests are somewhat questionable as he said at the last Sunbelt Conference in Budapest.

Gerhard Wuehrer [[log in to unmask]]

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it is not statistically valid.
Stanley Wasserman [[log in to unmask]]
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