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I am having some thoughts on certain methodological issues and I would very
much appreciate feedback on it.
The scenario: let's say we have a number of people that know eachother, i.e
a group of friends. These friends make phone calls to eachother and
everytime person A calls person B, this adds to the directional valued
linkage from A to B in the sociomatrix in question.
Although I am only interested in this group of people, they do of course
also call other people and other people call them. These incoming and
outgoing phone calls with non-group people are also important for the
calculation of centrality scores, i.e it shouldn't just be in-group
communication that indicates whether an actor is central and has a brokerage
role. In my model, I have therefore added a "virtual actor", an actor
representing all non-group actors. Then, when calculating centrality indices
(Freeman degree, flow betweenness, Bonacich eigenvector centralities,
Bonacich power and Borgatti/Everett-style continuous c/p fitting), all
non-group actors are represented by this virtual actor.
Is this procedure okay? As I am only interested in how the group members are
stratified w/ regards to different centrality indices, can I just sort of
half-ignore this virtual actor, perhaps just placing how this virtual actor
scored in brackets?
Let's say I want to do a MDS visualisation of the system, beginning from the
original O/D-sociomatrix of the system, with my bunch of people calling
eachother as well as the virtual actor representing the aggregation of
non-group actors. In order to do a MDS visualization, I convert this
sociomatrix of flows (i.e directional calls between actors) to a structural
sociomatrix, by symmetrizing the matrix using the SUM formula. I.e:
...where C is the "structural matrix" and A is the original flow matrix. I
find this to be theoretically underpinned as "[r]egularities or patterns in
interactions give rise to structures" (Wasserman/Faust 1994:5). Structural
values are thus the total number of phone calls made between dyads
(including the virtual actor).
Now, what if I want to do a MDS visualization on this structural matrix and,
once again, only be interested in how the in-group actors relate to
eachother. I can't just rip the virtual actor out as, as said before, phone
calls with external actors are just as important for centrality indicators
and, of course, also affects how the MDS looks like. I can of course MDS the
C matrix above and include the "virtual actor" but I would rather leave it
out as I am only interested in intra-group structure. But I can't, can I? :)
Carl Nordlund, BA, PhD student
Human Ecology Division, Lund university
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