***** To join INSNA, visit http://www.insna.org ***** Emese -

It can be appropriate to use ERGMs to model a complete network based on statistics observed in ego networks, however I think that looking at shared partner effects is problematic in such a context.  Gwdsp is based on the number of dyads with exactly k shared partners, but the ego networks are not going to have the same pattern here as the complete network.  There are two reasons for this.

One is that the ego networks give a downwardly biased estimate of the number of shared partners of two alters, that is we don't know how many shared partners they have where the shared partner does not have a tie to ego and therefore does not appear in the ego network.  

The other is that the sampling design ensures that all alters will have at least one shared partner (ego).  Unless the degree distribution of egos is very small, most dyads are alter-alter pairs.  This will tend to upwardly bias the number of dyads that have 1 or more shared partner. 

Together, that means you have a measure that is biased, but it isn't clear which direction the bias is in, so you can't even regard your estimate as a minimum or maximum.

That may just mean you want to take gwdsp out of your model and fit a different ERGM.  Possibly there is some other way of measuring higher-order structure you could use that would be less problematic. Triangles have a much more natural fit to ego network data than shared partners, for example. If dyadwise shared partners is something that you are truly interested in here, that is problematic and I don't think that a non-ERGM solution would be helpful, as the problems arise from the nature of the data and are not specific to ERGMs.


On Mon, Feb 20, 2012 at 8:52 AM, Emese Domahidi <[log in to unmask]> wrote:
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Dear all,

I am computing ERGM Models for ego networks of approximately 90 egos and
their alteri. The ego networks are not interconnected. I constructed an
overall model for all networks, controlling for different network
structures (e.g. edges and gwdsp) and different individual and dyadic
attributes. The model is converging and the model fit is ok.

My question is whether constructing an overall model instead of looking at
each ego network individually is an appropriate way to model ERGM for
ego networks. I would really appreciate comments on this approach as well as
literature recommendations on ego networks and ERG models.

Cheers, Emese

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