Title:

Inference versus estimation in exponential random graph models.

Authors: 

Alex Stivala (University of Melbourne)
Maksym Byshkin (Universita della Svizzera italiana)
Garry Robins (University of Melbourne)


Abstract:

When using snowball sampling to estimate exponential random graph
model (ERGM) parameters for very large networks, it was observed that
there is a very high Type II error rate (that is, very low power) in
inference on the edge (density) and alternating k-star parameters, as
commonly used in models based on the social circuit dependence
assumption.  However, this problem is not unique to snowball sampling,
and also occurs when using Markov chain Monte Carlo (MCMC) maximum
likelihood estimation (MLE) algorithms and stochastic approximation,
as implemented for example in software packages such as PNet and
statnet, to directly estimate a model for an entire network (not
obtained via sampling from a larger network), even with no missing
data. Here we investigate this issue further and try to explain why
this problem occurs, what the implications are, and how we might try
to mitigate it.