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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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