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Christoph
Without knowing the specifics of the research question it is hard to 
provide an answer, but I can offer some suggestions:
1) It would seem that dividing by the overall network size would be 
appropriate and thus get a measure of the proportion of ties that are 
weak. But you say this does not reflect what you want, so
2) You could enter the network size in the regression equation in 
addition to the count of the number that are weak. NB: It doesn't make 
sense to enter both total size and number of strong and weak ties since 
the measures would be co-linear.
3) You might try number (2) above but also include an interaction of 
size and number weak ties to see if the effects are sensitive to size.
4) You might consider treating the data as dyadic to determine if there 
is an association between tie strength and the outcome.
-Tom

Christoph Garbotz wrote:

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>
> Dear Socnet Members,
>
> I have got a set of ego-network data including 103 egos and 590 
> alteris. The data were collected on the basis of a single name 
> generator. The number of alteris that egos could name was restricted 
> to 8 due to the survey design. Relational network measures such as tie 
> strength etc. shall now be used as independent variables in different 
> multiple regression models to explain a dependant variable.
>
> E.g. - Tie strength was measured by assessing the closeness, duration, 
> and frequency of each relationship. Then, ties were categorized as 
> either weak or strong, and after that the number of weak and strong 
> ties was counted. Clearly, the resulting measure is a function of 
> network size
>
> Aim - Test the following hypothesis: The number of weak ties is 
> positively associated with the dependant variable.
>
> My question now is: Do I have to normalize the measures to account for 
> the different ego network sizes? If so, how do I do that? For example, 
> just dividing the number of strong/weak ties by the number of all ties 
> in ego's network does not reflect what I want.
>
> Any help or references to articles where researchers dealt with this 
> problem (ego-network analysis that is not part of a whole network, 
> restriction of alteris) are highly appreciated.
>
> Apologies if the answer might sound too simple to some of you!
>
> Regards,
>
> Christoph
>
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-- 
Thomas W. Valente, PhD
Director, Master of Public Health Program
http://www.usc.edu/medicine/mph/
Department of  Preventive Medicine
Keck  School of Medicine
University of Southern California
1000 S. Fremont Ave., Unit #8
Building A Room 5110		
Alhambra CA 91803		
phone: (626) 457-4139
cell: (626) 429-4123
fax: (626) 457-6699
email: [log in to unmask]

My personal webpage:
http://www-hsc.usc.edu/~tvalente/

The Empirical Networks Project
http://ipr1.hsc.usc.edu/networks/

Evaluating Health Promotion Programs
(Oxford U. Press):
www.oup-usa.org/isbn/0195141768.html

_____________________________________________________________________
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