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Dear Kim and social networkers,

p* and p2 do not contain each other either way. p* has an in principle 
unlimited possibility for network effects (and p2 doesn't); the 
practical limitation resides in the estimability of these effects (cf. 
Snijders, Pattison, Robins, Handcock,  New specifications for 
exponential random graph models; To be published, Sociological 
Methodology; downloadable from
http://stat.gamma.rug.nl/sprh_f.pdf
p* now is often referred to as ergm (exponential random graph model).

On the other hand, p2 has random effects for representing between-actor 
differences (and p* doesn't). However, in/out/mixed-twostars effects in 
p* have to some degree a similar functionality; but the interpretability 
of unexplained variances at the actor level, which is a feature of p2, 
is not available in p*.

The focus of p2 is on testing effects of covariates, which can be 
actor-bound or dyad-bound, and which can interact with reciprocity; 
while controlling for differential actor tendencies to sending and 
receiving ties, and for reciprocity. The focus of p*/ergm is on 
structurally modeling networks (which may include covariate effects).

For p2, better estimation methods have been an advantage; recently there 
have been advances in estimation methods for both p*/ergm and p2, and 
p*/ergm now is in much better shape than with the earlier 
pseudolikelihood methods. I think that with recent and almost finished 
work on multivariate and multilevel p2, p2 retains an advantage 
concerning availability of good estimation methods across a range of 
model extensions. (The new January 2006 release of Stocnet will contain 
a new p2 version with multivariate and multilevel options.) p*/ergm has 
the advantage of a much better representation of structural network effects.

Best regards,
Tom


Kim Se Kwon wrote:
> ---------------------- Information from the mail header -----------------------
> Sender:       Social Networks Discussion Forum <[log in to unmask]>
> Poster:       Kim Se Kwon <[log in to unmask]>
> Subject:      Does p* contain p2?
> -------------------------------------------------------------------------------
> 
> *****  To join INSNA, visit http://www.insna.org  *****
> 
> I've read some papers about p* and one paper about p2.
> 
> If I've read correctly, Equation 4 of reference 2 ;extends ;first p* 
> (equation 1) to contain covariates. And p2 is 'the extension of p1 that 
> doesn't assume dyadic independence and accounts for nodal & dyadic 
> covariates.'
> 
> Does p* (equation 4 in reference 2) contain p2? Because p* has p1 as 
> submodels, p2's model equation is very similar to p*'s. If not, what is the 
> unique features of p2?
> 
> Thanks in advance for any comments.
> 
> --- Equations ---
> Equation 1 of Reference 2 ; : ; P(X = x) ;= exp(theta' * ;t(x)) / c(theta)
> Equation 4 of Reference 2 ; : ; P(X = x) = exp(vec(x)' Z beta + sum of 
> alpha_k * d_k(x) + theta' * t(x)) / c(alpha, beta, theta) ; (d_k : the 
> number of individuals with exactly k links, Z : exogenous dyadic 
> covariates)
> 
> 
> --- References ---
> 1. Logit models and logistic regressions for social networks : I An 
> Introduction to markov graphs and p*. Stanley ;Wasserman...
> 2. statnet: An R package for the Statistical Analysis and Simulation of 
> Social Networks, Mark S. Handcock...
> 3. p2: a random effects model with covariates for directed graphs. Marijtje 
> A. J. van Duijn...
> 
> 
> Best Regards
> Se Kwon, Kim
> 
> -------------
> KAIST (Korean Advanced Institute of Science & Technology)
> Mathematics Student
> http://math.kaist.ac.kr
> 
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-- 
Tom A.B. Snijders
Professor of Statistics and Methodology
Scientific Director, ICS
Department of Sociology, University of Groningen
Grote Rozenstraat 31
9712 TG Groningen
The Netherlands
+31-(0)50-3636188/6216
http://stat.gamma.rug.nl/snijders/
Note: new email address: [log in to unmask]

_____________________________________________________________________
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