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Dear Michael,
You might want to have a look at network autocorrelation models, which build
further on spatial models. Some of the papers that might be interesting are:

Leenders, R.Th.A.J. 2002. “Modelling social influence through network
autocorrelation: Constructing the weight matrix.” Social Networks 24: 21-47.

Mardsen, P.V. & Friedkin, N.E. 1993. “Network studies of social influence.”
Sociological Methods & Research 22, 127-151.

Doreian, P., K. Teuter, C. Wang. 1984. “Network autocorrelation models: Some
Monte Carlo results”. Sociological Methods & Research 13: 155-200.

Doreian, P. 1981. “Estimating linear models with spatially distributed
data”. Sociological Methodology 12:359-388.

Ord, K. 1975. “Estimation methods for models of spatial interaction”.
Journal of the American Statistical Association 70: 120-126.

For the programs in R, there is the "lnam" command in Carter Butts "sna"
package for running a linear network autorrelation model:
http://cran.r-project.org/src/contrib/Descriptions/sna.html

And the spatial regression package in R, which is called "spdep":
http://cran.r-project.org/src/contrib/Descriptions/spdep.html

Filip
_____________

Filip Agneessens
Ghent University
Department of Sociology
Korte Meer 5
B-9000 Gent
Belgium
 
tel. ++32 (0)9 264 91 69
fax ++32 (0)9 264 91 98
e-mail: [log in to unmask]

-----Original Message-----
From: Social Networks Discussion Forum [mailto:[log in to unmask]] On
Behalf Of Michael Haenlein
Sent: woensdag 18 april 2007 22:35
To: [log in to unmask]
Subject: Contagion analysis

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Dear colleagues,

I have a social network consisting of several thousand actors. Besides
knowing something about the social relationships between these actors, I
also have information about a (ratio-scaled) variable for each of them. For
example, assume that I know everyone's income or the amount of chocolate
everyone consumes per month or anything in this spirit.

Based on this data, I want to analyze whether the value of this variable for
a given actor is influenced by the value of this variable among people that
are friends of this actor. For example, is there a relationship between my
income and the income of my friends? The type of question I'd like to answer
is: Are people whose friends are primarily high income more likely to be
high income themselves that people whose friends are low income?

My first idea to do this type of analysis was to run a set of regressions.
For every actor, I could for example run a regression which relates his/ her
income to the average income of his/ her friends. If I have n actors in
total, I would need to run n such regressions. However, the problem is that
these regressions are likely to suffer from an endogeneity bias as the same
variable can appear as a dependent variable in one regression and as an
independent in another. Take the following example: Assume a network that
consists of three actors (Ben, Adam and Chris) that are all related to each
other (i.e. Ben, Adam and Chris form a 3-clique). The three regressions I
would have to run would be:

Income_Adam = Alpha + Beta [(Income_Ben + Income_Chris)/2]
Income_Ben = Alpha + Beta [(Income_Adam + Income_Chris)/2]
Income_Chris = Alpha + Beta [(Income_Adam + Income_Ben)/2]

Adam's income, for example, is a dependent variable in Regression 1 and an
independent one in Regressions 2 and 3. This endogeneity is likely to result
in biased parameter estimates in my regressions.

Does anyone know which approach I can use to overcome this bias?
Are there any software tools and/ or articles that address this issue?
I'm familiar with R, so if anyone could recommend an R Package to do this
type of analysis, that would be great!

Thanks very much for your help,

Michael


Michael Haenlein
Assistant Professor of Marketing
ESCP-EAP European School of Management
79, Avenue de la République | 75011 Paris | France


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