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I have a question on how to statistically analyse intra/intergroup relations
in a network using block models.
Assume that I'll do the following:
From the data, first create a single-relational block model, where each
actor's block membership is determined by an non-relational attribute (e.g.
occupation). Then summarized the number of links within and between all
blocks in a reduced matrix.
Now the question is: For each block (i.e. row in the reduced matrix), is it
possible to statistically test the null hypothesis that all relations are
distibuted randomly on all blocks (i.e. colums)? If the null hypothesis is
valid, then there should not be more within-block relations as compared to
relations to any other block (naturally taken the block sizes into account,
a block with many actors would be expected to have more relations as
compared to smaller blocks). My underlying hypothesis is, however, that my
data should not support the null-hypothesis, i.e. one would expect more
relations within blocks given that the attribute carries some meaning (as
for example occuption, people maybe tends to choose friends within the same
occupation at a higher rate than choosing others with a different
Please note that I do not assume any other similarities, such as
structural/stocastic equivalence, on actors within the same blocks, my only
(underlying) assumption is that actors tend to favorably choose other actors
within the same block.
Any suggestions on papers, books etc are most welcome!
Department of Systems Ecology
106 91 Stockholm
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