I am pleased to announce the publication of the next paper in JoSS by Tom
Snijders entitled "Markov Chain Monte Carlo Estimation of Exponential
Random Graph Models". It is a powerful demonstration of the value of an
online journal. I draw particular attention to his use of a JAVA applet in
his paper, an applet that allows the user to explore the consequence of a
set of parameter assumptions about a stochastic process in network
formation. The parameters are familiar ones (density, node size,
reciprocity, transitivity, node similarity, twostar). One cannot read this
paper without trying the applet. Indeed, I look forward to seeing if other
readers come to the same conclusion I did about the effect of transitivity
on our models of networks (I will refrain from biasing anyone by announcing
ahead of time what my conclusion was).
To access the paper, go to:
http://www2.heinz.cmu.edu/project/INSNA/joss/index1.html
Abstract
This paper is about estimating the parameters of the exponential
random graph model, also known as the p_ model, using frequentist
Markov chain Monte Carlo (MCMC) methods. The exponential
random graph model is simulated using Gibbs or Metropolis
Hastings sampling. The estimation procedures considered are
based on the RobbinsMonro algorithm for approximating a solution
to the likelihood equation.
A major problem with exponential random graph models resides
in the fact that such models can have, for certain parameter
values, bimodal (or multimodal) distributions for the su_cient
statistics such as the number of ties. The bimodality of the exponential
graph distribution for certain parameter values seems a
severe limitation to its practical usefulness.
The possibility of bi or multimodality is reflected in the
possibility that the outcome space is divided into two (or more)
regions such that the more usual type of MCMC algorithms,
updating only single relations, dyads, or triplets, have extremely
long sojourn times within such regions, and a negligible probability
to move from one region to another. In such situations,
convergence to the target distribution is extremely slow. To
be useful, MCMC algorithms must be able to make transitions
from a given graph to a very different graph. It is proposed to
include transitions to the graph complement as updating steps
to improve the speed of convergence to the target distribution.
Estimation procedures implementing these ideas work satisfactorily
for some data sets and model specifications, but not for all.

David Krackhardt, Professor of Organizations
Academic homepage (address, etc.): http://www.heinz.cmu.edu/~krack/academic/
Journal of Social Structure:
http://www.heinz.cmu.edu/project/INSNA/joss/
