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Mark:

Thanks for your reply.

I am disappointed that  you did not like my suggestion to name these  
models after
	Frank and Strauss.   It would be a nice idea to
	 honor the authors of the first paper that applied
	this class of models to networks.   We would have a Frank-Strauss
	distribution, which could stand beside the well-known Erdos-
	Renyi random graph distribution.


As you mentioned, the dependence assumptions and dependence graph,  
leading to
	the Hammersley-Clifford Theorem, are common to many fields (as
	David Strauss pointed out in his 1992 American Statistician article),
	yet the resulting distribution has different names in its different
	incarnations.   For example, in statistical physics, the  
distribution has
	one name, in communication theory, another.   There appears to be no
	commonality (as my physicists friends tell me).   I don't see how  
there can
	be any marginalization given that there are so many names and labels.
	Statistics is of course full of labels for distributions, models,  
properties,
	and so forth.

The acronym "ERG" is unfortunate, as I mentioned in my previous email.
I see many researchers referring to the class of models as
	"exponential random graphs", an uninformative name.

The papers that I have read often do not mention exponential families  
at all,
	even the papers you have co-authored (see those in the forthcoming
	special issue of Social Networks, where the phrase "exponential family"
	can only be found in the references).   I am afraid that everyone will
	forget the "family"  part, and simply refer to this class of models as
	"exponential".   If everyone understood the difference between an
	exponential distribution and an exponential family, then I would not
	feel that this is important.    But the current "ERG"   label is  
misleading
	and does not do justice to the family of models.


I think we should begin calling the normal distribution an
	"exponential random variable" (ERV) model, ignoring the
	earlier name given to it in the literature ---- after all, it too
	has an exponential function in it.   And let's not call it
	Gaussian either.    Even referring to it as an "exponential family
	of random variables", and using the "ERV" acronym, is not
	terribly informative, since there are zillions of other exponential
	families out there.   And why should we call it "N(mu,sigma)"??


Enough said .... I will once again get off my soapbox.




SW


On Feb 13, 2007, at 1:33 PM, Mark S. Handcock wrote:

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

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