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Kerstin,

You might also consider the loglinear modeling approach to this issue. 
In that model, the ties are crosstabulated by ego and alter attributes (in 
your case, team ID), and a loglinear model is fit with terms for the 
margins (which control for differences in team size and, depending on 
parameterization, differences in team mean degree), and one or more terms 
are fit to the diagonals to represent homophily.

The nice thing about this approach is that it has the flexibility of 
fitting more than one homophily term, to represent differences in 
homophily propensity by team, and a statistical framework for testing the 
significance of these differences.

You can find more on this approach in:

1991.  "A log-linear modeling framework for selective mixing."  M. Morris. 
Math Biosc  107:  349-77

1993.  "Epidemiology and Social Networks:  Modeling Structured Diffusion." 
M. Morris.  Soc. Meth. Res.  22 (1):  99-126


These don't address the potential dependence among ties from the same 
node, but that can be handled as a random effect.

best,
Martina

On Fri, 17 Jan 2014, Kerstin Sailer wrote:

> ***** To join INSNA, visit http://www.insna.org ***** Dear All,
> 
> I would like to do a comparison of different organisations and their network
> structures (nodes are people, ties are frequency and usefulness of contacts, sizes
> vary significantly from n=100 to n=1000; data is survey-generated; key question was to
> identify the top 25 contacts from a list of everyone in the organisation and then give
> details on these contacts).
> 
> One of the metrics I would like to compare (and where comparison is not
> straightforward at all, hence my email to ask for help / advice) is the E-I index,
> i.e. the degree to which contacts are within teams or across teams.
> 
> The difficulty is that team sizes and numbers of teams within an organisation differ
> so much. For instance if organisation A has 10 teams of 10 members each, every
> participant would have to nominate members from outside their team to come up with 25
> top contacts, hence the degree of external contact might be higher by default than for
> an organisation B with 2 teams of 50 members each, where each participant could
> possibly nominate all 25 top contacts within their own team.
> This is further complicated by the fact that not everyone participated in the survey
> (i.e. missing ties), that not everyone nominated 25 people (most people don't count
> and just use this as a rough guideline, or insist on nominating fewer or more), so
> outdegree is not always 25 for each member and of course this could vary by team as
> well (so members of one team, e.g. HR might nominate more people disproportionately if
> compared to the organisation's average because of their outreach role).
> 
> Now, if anyone has come across any discussion of those problems in the literature, or
> anyone mathematically minded on the list has an idea on how to normalise these metrics
> so that they become comparable, I'd be very happy to hear about it!
> 
> Thanks in advance!
> Best,
> Kerstin
>
>  -- 
> Dr Kerstin Sailer
> Lecturer in Complex Buildings
> 
> The Bartlett School of Graduate Studies
> Faculty of the Built Environment
> University College London (UCL)
> 14 Upper Woburn Place
> London WC1H 0NN UK
> 
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> W: http://www.bartlett.ucl.ac.uk/people/?school=gs&upi=KSAIL15 
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