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Hi Stan,
Thanks for the comments, which are helpful. I think we agree that we want
the name to describe statistical exponential family models for distributions
over graphs.
The fundamental issue here is that these models are a general class that are
used in other disciplines. The analogy to linear regression models is
instructive. These can capture a very wide range of structure by appropriate
choice of the regressors. They are used in many scientific fields. If we
choose to call them L* models rather than linear models we would marginalize
ourselves from that community. Most people would not know what we are
talking about, and would not understand that what we are doing is closely
related to what they are doing. This unnecessary marginalization is why I do
not like to use p* and prefer the explicit reference to exponential
families.
That said, I also agree that the ERGM contraction (exponential random graph
models) would be better if it made explicit mention of families. We
originally tried EFRGM (exponential families of random graph models, and I
think most of us used ERGM to make it less cumbersome, while still capturing
the generality. In retrospect, I prefer the longer version. Of course, the
papers make explicit reference to the statistical exponential families when
the name is introduced, so there is no ambiguity in the content.
Best,
Mark
On 2/11/07 3:01 PM, "Stanley Wasserman" <[log in to unmask]> wrote:
> Mark:
>
> Thanks for correcting me on the dependence structure for p2 --- indeed,
> it is a model based on dyadic independence, conditional on the nodal
> attribute variables.
>
> With respect to names of distributions .... I suppose I am a
> traditional guy who feels that original names do not necessarily have to
> be changed. Paul Holland named p1, who told me that he viewed it as
> the first cool graph distribution. p* was named to get away from
> Ove Frank and David Strauss' "Markov random graph" label, since one
> does not have to have Markov distribution, and because the distribution
> was so cool, cooler and better than p1, that it deserved a star.
>
> As for ERGs ---- if only its practitioners retained the important "family"
part
> of the name.
>
> As far as I know, everyone calls it simply an "exponential random graph"
> model, which is perhaps the most uninformative name of all. All
> (almost all?) probability mass functions for graphs can be made
> exponential --- but clearly not all are special exponential FAMILIES.
>
> p1, p*, and so forth, refer to specific distributions; the label
exponential
> can be applied to
> all random graph distributions.
>
> I do wish that this class of models was referred to as an exponential
> family (a special beast in statistics), but not even the recent
> literature does so. I believe that the recent literature does not call
> this an exponential family. For example,
>
> Snijders, T.A.B., Pattison, P., Robins, G.L., & Handock, M. (In press). New
> specifications for exponential random graph models. Sociological Methodology.
>
> Robins, G., Pattison, P., Kalish, Y., & Lusher, D. (2005). A workshop on
> exponential random graph (p*) models for social networks. Social Networks.
>
> Robins, G., Snijders, T., Wang, P., Handcock, M., & Pattison, P. (2005).
> Recent developments in Exponential Random Graph (p*) Models for Social
> Networks. Social Networks.
>
> Some of us use the rather long, but certainly more accurate and
> informative phrase "p*, an exponential family of random graphs".
>
> So, since Mark inquired, those are the reasons I do not use this uninformative
> and uninstructive ERG label. Where's that necessary "family" noun?
>
>
> It would be preferable, and an nice tribute I think, henceforth to refer
> to this exponential family as Frank-Strauss random graphs, to honor
> David (and especially Ove) who first used these ideas in network
> science. We network statisticians owe much to Ove.
>
>
> SW
>
>
> > On Feb 9, 2007, at 9:03 PM, Mark S. Handcock wrote:
> >
> > ***** To join INSNA, visit http://www.insna.org *****
> >
> > To add to Stanley's notes:
> >
> > The p2 model does not assume dyad independence. It is explicitly a dyad
> > dependence model, although there is conditional independence given the
> > node-specific random effects.
> >
> > The naming of the exponential family models for networks is a bit
> > problematic. Historically, Holland, Leinhardt and others presented them as
> > exponential families of distributions over the space of graphs. The
> > so-called "p1" model was a particularly useful class presented in their
> > seminal paper with an unfortunately uninstructive name (a non-name really!).
> > The generalization by Frank and Strauss is a general statistical exponential
> > family of distributions over graphs. The specification of the statistics
> > constitutes the modeling part. This is the reason recent work references
> > them as (statistical) exponential family models. A number of acronyms or
> > combination of terms to capture this make sense, and constructively describe
> > the statistical roots and connections of the model class. The utility of the
> > "p*" name is unclear to me (perhaps Stanley can describe why he prefers it
> > to the earlier name?).
> >
> > Cheers,
> >
> > Mark
> >
> > -------------------------------------------------
> > Mark S. Handcock
> > Professor of Statistics
> > Department of Statistics, C014-B Padelford Hall
> > University of Washington, Box 354322 Phone: (206) 221-6930
> > Seattle, WA 98195-4322. FAX: (360) 365-6324
> > Web: www.stat.washington.edu/~handcock
> > internet: [log in to unmask]
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