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Contagion analysis

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Wed, 18 Apr 2007 22:34:59 +0200

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 ```***** To join INSNA, visit http://www.insna.org ***** 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 _____________________________________________________________________ SOCNET is a service of INSNA, the professional association for social network researchers (http://www.insna.org). To unsubscribe, send an email message to [log in to unmask] containing the line UNSUBSCRIBE SOCNET in the body of the message.```