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I am a big fan of the odds ratio: AD/BC from table below.  Or the log-odds.  This links to how you would model the effect of team membership on a tie.  Odds ratios are insensitive to marginals.

                                                Tie
                                  No                        yes
                                ------------------------
Same team  No |    A                       B
                        yes |    C                       D
see Goodman, L. and W. Kruskal 1954 "Measures of association for cross classifications." Journal of the American Statistical Association 49: 732-764.



Ken Frank
Professor
Measurement and Quantitative Methods
Counseling, Educational Psychology and Special Education
And
Professor of Fisheries and Wildlife
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Michigan State University
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phone: 517-355-9567 fax: 517-353-6393
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From: Social Networks Discussion Forum [mailto:[log in to unmask]] On Behalf Of Kerstin Sailer
Sent: Friday, January 17, 2014 7:04 AM
To: [log in to unmask]
Subject: Clustering of networks / comparison across organisations

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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)

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