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Since the error terms will be correlated, you can take
this into account in a regression by specifying the
autocorrelation structure of the error terms. Obviously,
the way in which the error terms are correlated depends on
the network structure and on the way you theorize the
obeservations are related (in terms of power, tie volume,
I have actually written a paper about how you can do
this. It is: Leenders, R.Th.A.J., 2002, “Modeling Social
Influence through Network Autocorrelation: Constructing
-the Weight Matrix.” Social Networks, 24: 21-47.
The weight matrix is what you are looking for. It
represents the autocorrelation structure in your data. The
paper itself focuses on estimating the strength of the
autocorrelation, but the approach would be exactly the
same if your main interest is in the regression
coefficient and you are adding the autocorrelation
structure in order to "remove" its effect from the
Some of the people on this list who have been pivotal in
figuring out how this works includes Patrick Doreian and
Hope this helps.
> On Tue, 30 Nov 2004 13:17:53 -0500
> "Marshall W. Van Alstyne" <[log in to unmask]> wrote:
>> ***** To join INSNA, visit http://www.insna.org *****
>> Greetings SOCNET, I have a question related to the issue
>> among multiplex relations asked a few weeks ago.
>> Since social network measures count agent links, the
>>metrics for connected
>> agents are not independent samples. In regression
>>analysis, this leads to
>> correlated error terms.
>> Does anyone know a good fix for this that will allow you
>>to draw inferences
>> about regression coefficients? Can anyone pls suggest
>> I can think of two methods.
>> Proposed solutions:
>> a) Inflate the standard errors by a factor
>>proportional to the degree or
>> correlation among the social network variables. This
>>would widen the
>> confidence intervals on any regression coefficients.
>> b) We happen to have a very large email dataset.
>> So, perhaps we can draw
>> distinct random samples of email messages from the
>>database for each agent
>> in order that the error terms would not be correlated.
>> The sample sizes
>> would seem to depend on the social network sizes and
>> Given that we have about six dozen people and 45,000
>>email messages, we
>> have a lot of room to draw large quasi-independent
>> Any thoughts or recommendations would be really welcome.
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