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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?).
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
internet: [log in to unmask]
On 2/8/07 9:31 AM, "Stanley Wasserman" <[log in to unmask]> wrote:
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> Dear all:
> p1 is now 30 years old, and research has progressed considerably over
> the past
> two decades ... see for example the chapters on statistical
> models in
> Carrington, et al. (2005).
> p1, as well as p2, assumes dyadic independence, which is a rather
> simplifying assumption.
> The new models, all based on the p* framework first proposed by Frank
> and Strauss
> in 1986, have opened up network research to realistic and
> interesting statistical
> parametric structures. And we now have good estimation techniques
> for the
> As Tom says here, p* (which is more accurately an exponential family
> of random graphs, rather than
> an "ERG" or an "ERGM") is a hot topic and one can do lots of cool
> things with it
> (if you are careful).
> On Feb 8, 2007, at 4:53 AM, Tom Snijders wrote:
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>> Hi readers,
>> Christophe, the use of the p1 model for modeling the effects of
>> node level independent variables on binary dyadic (relational)
>> dependent variables is not such a good idea any more. Better than
>> the p1 model is the p2 model, see
>> Duijn, M.A.J. van, Snijders, T.A.B. & Zijlstra, B.J.H., (2004). P2:
>> a random effects model with covariates for directed graphs.
>> Statistica Neerlandica, 58, 234-254.
>> which is part of the Stocnet suite, see http://stat.gamma.rug.nl/
>> ; and the ERG model, see the papers-in-press of the special issue
>> of Social Networks edited by Garry Robins and Martina Morris. The
>> ERG model represents network structure such as triadic closure,
>> while the p2 model is restricted to modeling differences in
>> popularity and acitivity of nodes (like p1). Estimation for the
>> ERGM is implemented in SIENA (again, in the Stocnet suite) and in
>> Statnet (an R package).
>> Best wishes,
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