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I have a question on elementwise correlations between the entries in each
of two matrices.

My data: I have complete network data for two cities at three points in
time.  Data are from board interlocks.

I have decomposed these six networks in two relational networks.  One
relation I am defining as economic and the other as civic.  I want to
measure the overlap between the two networks at any given moment in time (I
am not trying to compare across time so the actors in both networks are
identical).

Specifically, I am asking, at the level of ego, to what degree are actors
connected along one relation also connected on the other?  And, for the
network as a whole, to what degree does one network overlap with the other?

I am calling the concept I am trying to measure 'multiplex
independence.'  The idea is that a person's network is perfectly 'multiplex
independent' if their ties on one relational dimension (civic) do not
overlap with any of their ties on another relational dimension
(economic).  Similarly, a complete network is 'multiplex independent' if
actors' ties on one relation do not overlap at all with those same actors
ties on another dimension.

I have looked at the QAP proceedure.  That gets me partially there since it
tells me whether the overall structures of the networks are similar with
some statistical confidence.  But, it doesn't tell me much about the degree
to which specific ties in the each of the two networks do or do not overlap.

I have also looked at Burt's measure of structural holes which is
related.  However, its not clear to me how it plays out in multi-relational
space (I don't think that's covered in the book).

Someone at some point must have thought about this before me.  But I have
looked through Wasserman and Faust and a few recent papers on comparing
networks and I haven't been able to find anything that is doing exactly
what I need it to do.

Any directions you can point me that are more specific than QAP?

Thanks.

Sean




_________________________
Sean Safford
Ph.D. Candidate
MIT Sloan School of Management
- Institute for Work and Employment Research
- Industrial Performance Center
50 Memorial Drive, Suite 580
Cambridge, MA 02142
617 258 9728
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www.mit.edu/~ssafford

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