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The paper that Jim mentions is very brief, and a bit thin on actual methods, being a note in Nature and all. Perhaps the more useful paper is:

Handcock, M. S., and J.H. Jones. 2004. Likelihood-based inference for stochastic models of sexual network evolution. Theoretical Population Biology. 65:413-422.

All the distributions that we tested in this paper are implemented in the package Martina mentioned (degreenet) earlier in this thread.

The basic take-home messages were: (1) don't test for a power law using OLS regression of the truncated log-survival function of the degree distribution against the degree distribution, (2) maximum likelihood estimation of degree distributions is straightforward and allows you to easily compare different models, (3) it isn't much of a test unless you test against alternative models, and (4) sexual networks don't show a lot of evidence of power-law behavior -- alternative models are more behaviorally plausible and fit the observed degree distributions better.

Cheers,
J
--
James Holland Jones
Associate Professor of Anthropology &
Senior Fellow, Woods Institute for the Environment

450 Serra Mall
Building 50
Stanford, CA 94305-2034

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> On Mar 15, 2015, at 6:40 AM, James Moody <[log in to unmask]> wrote:
> 
> *****  To join INSNA, visit http://www.insna.org  *****
> 
> Hey - 
> See also:
> 	Jones, J.H. and M.S. Handcock. (2003) Sexual contacts and epidemic thresholds. Nature. 423: 605-606.
> 
> I believe they have a package to estimate/fit/test distributional forms as well.
> PTs
> Jim
> 
> -----Original Message-----
> From: Social Networks Discussion Forum [mailto:[log in to unmask]] On Behalf Of Jen Badham
> Sent: Sunday, March 15, 2015 12:17 AM
> To: [log in to unmask]
> Subject: Re: Testing power law vs exponential tail
> 
> *****  To join INSNA, visit http://www.insna.org  *****
> 
> There is an excellent paper specifically on this question: Clauset, A.; Shalizi, C. R. & Newman, M. E. J. Power-law distributions in empirical data SIAM Review, 2009, 51, 661- 703. The toolkits they and others developed are available in several statistical languages from Clauset’s website at http://tuvalu.santafe.edu/~aaronc/powerlaws/
> 
> Jennifer Badham
> Centre for Research in Social Simulation University of Surrey
> 
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