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Hi Stan, Mark, and other readers,
A bit belated let me also go to the soapbox. In my understanding, if
anybody talks about the Frank-Strauss family of probability
distributions I would assume they are talking about the Markov random
graph family which they introduced in their 1986 JASA paper. So I would
say that the name of Frank-Strauss is already attached to a family of
distributions.
Of course I agree that what now often has been called ERGM is a family
of distributions, and also that some articles may have been sloppy in
describing this. By the way, we talk about the normal distribution when
we refer to a family of Normal(mu, sigma^2) distributions, which
indicates that skipping between levels where mathematical objects are
defined is not so rare.
A statistical model is always a family of distributions, so whereas
<<ERG distribution>> is nonsense, <<ERG model>> is not. However, "ERG
model" does not specify the model, but only a class of models (where I
define a model as a family of probability distributions all defined on
the same outcome space), since you need to specify the sufficient
statistics. Mark points out the analogy to linear models. ERGM has the
same level of generality as General Linear Model (GLM) or Structural
Equation Model (SEM), which also leave open which variables are used (in
the GLM) or which linear equations are used (for the SEM). GLM and SEM
also are called models, where <<model>> stands for <<families of
families of probability distributions>>. So here we are also used to
skipping between levels when using the word <<(statistical) model>>.
I fully agree with Stan that we should not talk about exponential random
graphs. But I do not see why ERGM would be a misleading name.
Best regards to all,
Tom
Stanley Wasserman wrote:
> ---------------------- Information from the mail header -----------------------
> Sender: Social Networks Discussion Forum <[log in to unmask]>
> Poster: Stanley Wasserman <[log in to unmask]>
> Subject: Re: you call them ERGs, we call them p* .... how about
> Frank-Strauss??
> -------------------------------------------------------------------------------
>
> ***** To join INSNA, visit http://www.insna.org *****
>
> 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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--
==============================================
Tom A.B. Snijders
Professor of Statistics in the Social Sciences
University of Oxford
Professor of Statistics and Methodology
Department of Sociology
University of Groningen
http://stat.gamma.rug.nl/snijders/
==============================================
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