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 Prof. Michael Haenlein posted on Sunday, May 20, 2007 - 6:05 am
Dear all,

I'm currently working on a social network analysis project and was wondering whether some of the questions I'm dealing with could also be analyzed using Mplus instead of more "specialized" social network analysis software.

I am working with data from the customer base of a telecommunication service provider. For each observation (i.e. customer) I know the revenue the customer generates per month. I also have information about the social relationships between all people in the dataset. This means I know who is friend with whom and whether two people are close friends are merely acquaintances.

Based on this data I would like to the followin question:

Is there a relationship between the revenue generated by a customer and the average revenue generated by this customer's friends?

If y denotes a (1xn) vector indicating revenue for each customer and W a (nxn) matrix indicating who is friend to whom., this requires estimating a regression of the form: y = Alpha + Beta*W*y. The problem with this regression is that y appears on both sides of the equation, leading to endogeneity problems. In social network analysis such an analysis is done using Network Autocorrelation Models, but I was wondering whether I could also use Mplus to estimate Alpha and Beta?

Thanks very much in advance for your help,

 Linda K. Muthen posted on Sunday, May 20, 2007 - 9:08 am
I would take a simpler approach to this question. I would create a data set where crev represents customer revenue and fave represents average revenue of the customer's friends and then look at either the correlation between the two variables or regress crev on fave.
 Prof. Michael Haenlein posted on Sunday, May 20, 2007 - 10:31 am
Thanks very much for your comment, Linda!

I tried exactly that, i.e. running a regression of the form:
crev = Alpha + Beta*fave

However, when I submitted the paper to a Marketing journal, the reviewers told me that, given the endogeneity issue, my parameter estimates are likely to be wrong.

Is there any way to account for this type of endogeneity within MPlus? I'm a big fan of your software, know it already and, therefore, would like to use it for this question instead of familiarizing myself with another (software) tool ...
 Linda K. Muthen posted on Sunday, May 20, 2007 - 5:42 pm
Mplus does not explicitly handle this endogeneity. How do other programs do this?
 Prof. Michael Haenlein posted on Monday, May 21, 2007 - 12:25 am
Unfortunately, there are not that many software tools that do handle it. One exception is the "sna package" in R, which has the function "lnam" that fits network autocorrelation models. However, it's rather limited in sample size and doesn't work well for more than 400/500 observations. Some references in this context are:

Doreian, Patrick (1981), "Estimating linear models with spatially distributed data," Sociological methodology, 12, 359 - 88.

Leenders, Roger Th. A. J. (2002), "Modeling social influence through network autocorrelation: Constructing the weight matrix," Social networks, 24 (1), 21 - 47.

Ord, Keith (1975), "Estimation methods for models of spatial interaction," Journal of the American statistical association, 70 (349), 120 - 26.

I just wanted to use Mplus because I'm a big fan of your software and though it might have a similar function. Thanks very much for your help!

 Israr Qureshi posted on Monday, June 11, 2007 - 5:23 am
Hello Michael,

I did not see your thread earlier. I think you might need to use UCINET software for this purpose. Not only there is endogeniety issue, there is also issue of non independence of observations in you relationship martix. In the UCINET you can create a matrix of difference of revenue (from your vector of revenue i.e. Y). If your Hypothesis is right then you would expect that closer the relationship is lower will be the difference. This is achieved using QAP regression analysis in UCINET.

Hope this will be helpful.

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