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

An answer to some of your questions may be in
 Tom A.B. Snijders. (2011). Statistical Models for Social Networks . Annual Review of Sociology, 37, 129-151.
DOI: http://dx.doi.org/10.1146/annurev.soc.012809.102709

For the rest, the reasoning is based on issues of statistical modeling. The basic principle here is that if your model is misspecified (and departs too strongly form the probabilistic system that may reasonably have generated the data), results in terms of standard errors and hypothesis tests may be unreliable, and sometimes wildly off. The statistical literature is full of results implying that especially if the correlations in the system generating the data are not represented by the statistical model, there will be this kind of unreliability. The evidence here for a broad variety of statistical models is so strong, that for statisticians this is a foregone conclusion.

I remember having seen some examples where results from a model with independent residuals were compared with results from a network model, and mostly the differences were indeed large. But I do not remember where. Perhaps somebody else can give a reference to such an example?

Best wishes,
Tom


Best,
Tom

=========================================
Tom A.B. Snijders
Professor of Statistics and Methodology, Dept of Sociology, University of Groningen
Emeritus Fellow, Nuffield College, University of Oxford
http://www.stats.ox.ac.uk/~snijders

On Wed, Jun 24, 2015 at 3:36 AM, Momin M. Malik <[log in to unmask]> wrote:
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Poster:       "Momin M. Malik" <[log in to unmask]>
Subject:      Why, exactly, do we need special statistical models for networks?
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Dear SOCNETters,

I think I am not alone in not fully appreciating why there is a need for
special statistical models for networks (ERGMs, SIENA, etc.). I can *accept=
*
that there is such a need, but I'd like to understand what dependencies
between observations do to traditional models or obvious approaches.

E.g., in a March 16th email, Elly Power had asked about using centrality as
a covariate; there were helpful replies from Philip Leifeld, Tom Snijders,
and Phillip Bonacich, but aside from there being more suitable
alternatives, the effects of dependencies are still opaque to me.

Does anybody know of literature or resources that explain this?

In what I've found so far, the network autocorrelation literature (and
'Galton's problem') from Dow and colleagues in the 80s helps a lot for
understanding problems with regression on node attributes, as does Shalizi
& Thomas (2011) for C&F's 'network effects' approach. Still, I'd like to
see similar explorations for other obvious approaches including using
centrality as a covariate, or doing a logistic regression on the
presence/absence of individual edges (not pairs of edges as in p1), or
perhaps doing a regression with network-level measures of ego networks.
What would we be missing? How misleading could results be?

As a related point, does anybody know of introductions that gather up and
compare *all* approaches to network statistics? E.g., I don't think I've
seen any introduction that has even just ERGMs and SIENA side-by-side, let
alone network autocorrelation with those two, even if just to say what the
differences are in modeling goals and assumptions (or, for the former two,
to note the range of Tom Snijders' contributions!).

Thank you!

Partial list of what I've been searching through:

   - Aral, S., Muchnik, L., and Sundararajan, A. (2009). Distinguishing
   influence-based contagion from homophily-driven diffusion in dynamic
   networks. *Proceedings of the National Academy of Sciences*, *106*
   (51):21544=E2=80=9321549. http://www.pnas.org/content/106/51/21544.abstr=
act
   - Chatterjee, S., Diaconis, P., and Sly, A. (2011). Random graphs with a
   given degree sequence. *The Annals of Applied Probability*, *21*
   (4):1400=E2=80=931435. http://projecteuclid.org/euclid.aoap/1312818840
   - Dekker, D., Krackhardt, D., and Snijders, T. (2007). Sensitivity of
   MRQAP tests to collinearity and autocorrelation conditions.
   *Psychometrika*, *72*(4):563=E2=80=93581.
   http://link.springer.com/article/10.1007%2Fs11336-007-9016-1
   - Dow, M. M. (2007). Galton=E2=80=99s problem as multiple network
   autocorrelation effects: Cultural trait transmission and ecological
   constraint. *Cross-Cultural Research*, *41*(4):336=E2=80=93363.
   http://ccr.sagepub.com/content/41/4/336.abstract
   - Dow, M. M., Burton, M. L., and White, D. R. (1982). Network
   autocorrelation: A simulation study of a foundational problem in regress=
ion
   and survey research. *Social Networks*, *4*(2):169=E2=80=93200.
   http://www.sciencedirect.com/science/article/pii/0378873382900314
   - Dow, M. M., Burton, M. L., White, D. R., and Reitz, K. P. (1984).
   Galton=E2=80=99s problem as network autocorrelation. *American Ethnologi=
st*, *11*
   (4):754=E2=80=93770.
   http://onlinelibrary.wiley.com/doi/10.1525/ae.1984.11.4.02a00080/abstrac=
t
   - Dow, M. M., White, D. R., and Burton, M. L. (1982). Multivariate
   modeling with interdependent network data. *Cross-Cultural Research*,
   *17*(3-4):216=E2=80=93245. http://ccr.sagepub.com/content/17/3-4/216.abs=
tract
   - Fienberg, S. E. (2012). A brief history of statistical models for
   network analysis and open challenges. *Journal of Computational and
   Graphical Statistics*, *21*(4):825=E2=80=93839.
   http://www.tandfonline.com/doi/abs/10.1080/10618600.2012.738106
   - Goldenberg, A., Zheng, A. X., Fienberg, S. E., and Airoldi, E. M.
   (2010). A survey of statistical network models. *Foundations and Trends
   in Machine Learning*, *2*(2):129=E2=80=93233. http://arxiv.org/abs/0912.=
5410
   - Hanneman, R. A. and Riddle, M. (2005). Chapter 18: Some statistical
   tools. In *Introduction to social network methods*. University of
   California, Riverside.
   http://faculty.ucr.edu/~hanneman/nettext/C18_Statistics.html
   - Holland, P. W., & Leinhardt, S. (1981). An exponential family of
   probability distributions for directed graphs. *Journal of the American
   Statistical Association*, *76*(373):33-50.
   http://www.jstor.org/stable/2287037
   - Hunter, D. R., Krivitsky, P. N., and Schweinberger, M. (2012).
   Computational statistical methods for social network models. *Journal of
   Computational and Graphical Statistics*, *21*(4):856=E2=80=93882.
   http://www.tandfonline.com/doi/abs/10.1080/10618600.2012.732921
   - Knoke, D. and Yang, S. (2008). Chapter 5: Advanced methods for
   analyzing networks. In *Social Network Analysis* (pp. 91=E2=80=93117), 2=
nd ed.
   Quantitative Applications in the Social Sciences, no. 154. SAGE
   Publications.
   - Kolaczyk, E. D. (2009). *Statistical analysis of network data: Methods
   and models*. Springer Series in Statistics. Springer-Verlag.
   http://www.springer.com/us/book/9780387881454
   - Kolaczyk, E. D. and Cs=C3=A1rdi, G. (2014). *Statistical analysis of
   network data with R*. Use R!, volume 65. Springer-Verlag.
   http://www.springer.com/us/book/9781493909827
   - Krackardt, D. (1987). QAP partialling as a test of spuriousness. *Soci=
al
   Networks*, *9*(2):171=E2=80=93186.
   http://www.sciencedirect.com/science/article/pii/0378873387900128
   - Krackhardt, D. (1988). Predicting with networks: Nonparametric
   multiple regression analysis of dyadic data. *Social Networks*, *10*
   (4):359=E2=80=93381.
   http://www.sciencedirect.com/science/article/pii/0378873388900044
   - Laumann, E. O., Marsden, P. V., and Galaskiewicz, J. (1977).
   Community-elite influence structures: Extension of a network
approach. *American
   Journal of Sociology*, *83*(3):594=E2=80=93631.
   http://www.jstor.org/stable/2778146
   - Leenders, R. T. (2002). Modeling social influence through network
   autocorrelation: Constructing the weight matrix. *Social Networks*, *24*
   (1):21=E2=80=9347.
   http://www.sciencedirect.com/science/article/pii/S0378873301000491
   - Lusher, D., Koskinen, J., and Robins, G. (2012). *Exponential Random
   Graph Models for social networks: Theory, methods, and applications*.
   Structural Analysis in the Social Sciences. Cambridge University Press.
   - Pattison, P., and Robins, G. (2008). Chapter 18: Probabilistic network
   analysis. In T. Rudas (Ed.), *Handbook of Probability: Theory and
   Applications* (pp. 291=E2=80=93313). SAGE Publications.
   http://dx.doi.org/10.4135/9781452226620
   - Prell, C. (2011). Chapter 10: Statistical models for social networks.
   In *Social Network Analysis: History, theory and methodology* (pp.
   199=E2=80=93220). SAGE Publications.
   - Rinaldo, A., Petrovic, S., and Fienberg, S. E. (2013). Maximum
   lilkelihood estimation in the =CE=B2-model. *The Annals of Statistics*, =
*41*
   (3):1085=E2=80=931110. http://projecteuclid.org/euclid.aos/1371150894
   - Robins, G. (2012). Exponential random graph (p*) models for social
   networks. In R. A. Meyers (Ed.), *Computational Complexity* (pp.
   2953=E2=80=932967). Springer New York.
   http://link.springer.com/referenceworkentry/10.1007%2F978-1-4614-1800-9_=
182
   - Robins, G. (2013). A tutorial on methods for the modeling and analysis
   of social network data. *Journal of Mathematical Psychology*, *57*
   (6):261=E2=80=93274.
   - Robins, G. (2014). Exponential random graph models for social
   networks. In J. Scott and P. J. Carrington (Eds.), *The SAGE Handbook of
   Social Network Analysis *(pp. 484=E2=80=93501). SAGE Publications.
   http://www.sciencedirect.com/science/article/pii/S0022249613000126
   - Robins, G., Pattison, P., Kalish, Y., and Lusher, D. (2007). An
   introduction to exponential random graph (p*) models for social
networks. *Social
   Networks*, *29*(2):173=E2=80=93191. Special Section: Advances in Exponen=
tial
   Random Graph (p*) Models.
   http://www.sciencedirect.com/science/article/pii/S0378873306000372
   - Shalizi, C. R. and Thomas, A. C. (2011). Homophily and contagion are
   generically confounded in observational social network studies.
*Sociological
   Methods & Research*, *40*(2):211=E2=80=93239.
   http://smr.sagepub.com/content/40/2/211.abstract
   - Snijders, T. A. (2011). Statistical models for social networks. *Annua=
l
   Review of Sociology*, *37*(1):131=E2=80=93153.
   http://www.annualreviews.org/doi/abs/10.1146/annurev.soc.012809.102709
   - Snijders, T. A. and Borgatti, S. P. (1999). Non-parametric standard
   errors and tests for network statistics. *Connections*, *22*(2):61=E2=80=
=9370.
   http://www.insna.org/PDF/Connections/v22/1999_I-2_61-70.pdf
   - Snijders, T. A., van de Bunt, G. G., and Steglich, C. E. (2010).
   Introduction to stochastic actor-based models for network dynamics. *Soc=
ial
   Networks*, *32*(1):44=E2=80=9360.
   http://www.sciencedirect.com/science/article/pii/S0378873309000069
   - Snijders, T. A. B. (2014). Network dynamics. In J. Scott and P. J.
   Carrington (Eds.), *The SAGE Handbook of Social Network Analysis* (pp.
   501=E2=80=93513). SAGE Publications.
   - Snijders, T. A. B., Koskinen, J., and Schweinberger, M. (2010b).
   Maximum likelihood estimation for social network dynamics. *The Annals
   of Applied Statistics*, *4*(2):567=E2=80=93588.
   http://projecteuclid.org/euclid.aoas/1280842131
   - Steglich, C., Snijders, T. A. B., and Pearson, M. (2010). Dynamic
   networks and behavior: Separating selection from influence. *Sociologica=
l
   Methodology*, *40*(1):329=E2=80=93393. http://smx.sagepub.com/content/40=
/1/329

   - van Duijn, M. A. J. and Huisman, M. (2014). Statistical models for
   ties and actors. In J. Scott and P. J. Carrington (Eds.), *The SAGE
   Handbook of Social Network Analysis* (pp. 459=E2=80=93483). SAGE Publica=
tions.

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*****  To join INSNA, visit http://www.insna.org  *****
<div dir=3D"ltr"><div class=3D"gmail_quote"><div dir=3D"ltr">Dear SOCNETter=
s,<div><br></div><div>I think I am not alone in not fully appreciating why =
there is a need for special statistical models for networks (ERGMs, SIENA, =
etc.). I can <i>accept</i> that there is such a need, but I&#39;d like to u=
nderstand what dependencies between observations do to traditional models o=
r obvious approaches.=C2=A0</div><div><br></div><div>E.g., in a March 16th =
email, Elly Power had asked about using centrality as a covariate; there we=
re helpful replies from Philip Leifeld, Tom Snijders, and Phillip Bonacich,=
 but aside from there being=C2=A0more suitable alternatives, the effects of=
 dependencies are still opaque to me.=C2=A0</div><div><br></div><div>Does a=
nybody know of literature or resources that explain this?</div><div><br></d=
iv><div>In what I&#39;ve found so far, the network autocorrelation literatu=
re (and &#39;Galton&#39;s problem&#39;) from Dow and colleagues in the 80s =
helps a lot for understanding problems with regression on node attributes, =
as does Shalizi &amp; Thomas (2011) for C&amp;F&#39;s &#39;network effects&=
#39; approach. Still, I&#39;d like to see similar explorations for other ob=
vious approaches including using centrality as a covariate, or doing a logi=
stic regression on the presence/absence of individual edges (not pairs of e=
dges as in p1), or perhaps doing a regression with network-level measures o=
f ego networks. What would we be missing? How misleading could results be?<=
/div><div><br></div><div>As a related point, does anybody know of introduct=
ions that gather up and compare=C2=A0<i>all</i>=C2=A0approaches to network =
statistics? E.g., I don&#39;t think I&#39;ve seen any introduction that has=
 even just ERGMs and SIENA side-by-side, let alone network autocorrelation =
with those two, even if just to say what the differences are in modeling go=
als and assumptions (or, for the former two, to note the range of Tom Snijd=
ers&#39; contributions!).=C2=A0<br></div><div><br></div><div>Thank you!</di=
v><div><br></div><div>Partial list of what I&#39;ve been searching through:=
</div><ul><li>Aral, S., Muchnik, L., and Sundararajan, A. (2009). Distingui=
shing influence-based contagion from homophily-driven diffusion in dynamic =
networks. <i>Proceedings of the National Academy of Sciences</i>, <i>106</i=
>(51):21544=E2=80=9321549.=C2=A0<a href=3D"http://www.pnas.org/content/106/=
51/21544.abstract
" target=3D"_blank">http://www.pnas.org/content/106/51/215=
44.abstract</a><br></li><li>Chatterjee, S., Diaconis, P., and Sly, A. (2011=
). Random graphs with a given degree sequence. <i>The Annals of Applied Pro=
bability</i>, <i>21</i>(4):1400=E2=80=931435.=C2=A0<a href=3D"http://projec=
teuclid.org/euclid.aoap/1312818840" target=3D"_blank">http://projecteuclid.=
org/euclid.aoap/1312818840</a><br></li><li>Dekker, D., Krackhardt, D., and =
Snijders, T. (2007). Sensitivity of MRQAP tests to collinearity and autocor=
relation conditions. <i>Psychometrika</i>, <i>72</i>(4):563=E2=80=93581.=C2=
=A0<a href=3D"http://link.springer.com/article/10.1007%2Fs11336-007-9016-1"=
 target=3D"_blank">http://link.springer.com/article/10.1007%2Fs11336-007-90=
16-1
</a><br></li><li>Dow, M. M. (2007). Galton=E2=80=99s problem as multipl=
e network autocorrelation effects: Cultural trait transmission and ecologic=
al constraint. <i>Cross-Cultural Research</i>, <i>41</i>(4):336=E2=80=93363=
.=C2=A0<a href=3D"http://ccr.sagepub.com/content/41/4/336.abstract" target=
=3D"_blank">http://ccr.sagepub.com/content/41/4/336.abstract</a><br></li><l=
i>Dow, M. M., Burton, M. L., and White, D. R. (1982). Network autocorrelati=
on: A simulation study of a foundational problem in regression and survey r=
esearch. <i>Social Networks</i>, <i>4</i>(2):169=E2=80=93200.=C2=A0<a href=
=3D"http://www.sciencedirect.com/science/article/pii/0378873382900314" targ=
et=3D"_blank">http://www.sciencedirect.com/science/article/pii/037887338290=
0314</a><br></li><li>Dow, M. M., Burton, M. L., White, D. R., and Reitz, K.=
 P. (1984). Galton=E2=80=99s problem as network autocorrelation. <i>America=
n Ethnologist</i>, <i>11</i>(4):754=E2=80=93770.=C2=A0<a href=3D"http://onl=
inelibrary.wiley.com/doi/10.1525/ae.1984.11.4.02a00080/abstract" target=3D"=
_blank">http://onlinelibrary.wiley.com/doi/10.1525/ae.1984.11.4.02a00080/ab=
stract</a><br></li><li>Dow, M. M., White, D. R., and Burton, M. L. (1982). =
Multivariate modeling with interdependent network data. <i>Cross-Cultural R=
esearch</i>, <i>17</i>(3-4):216=E2=80=93245.=C2=A0<a href=3D"http://ccr.sag=
epub.com/content/17/3-4/216.abstract" target=3D"_blank">http://ccr.sagepub.=
com/content/17/3-4/216.abstract</a><br></li><li>Fienberg, S. E. (2012). A b=
rief history of statistical models for network analysis and open challenges=
. <i>Journal of Computational and Graphical Statistics</i>, <i>21</i>(4):82=
5=E2=80=93839.=C2=A0<a href=3D"http://www.tandfonline.com/doi/abs/10.1080/1=
0618600.2012.738106" target=3D"_blank">http://www.tandfonline.com/doi/abs/1=
0.1080/10618600.2012.738106</a><br></li><li>Goldenberg, A., Zheng, A. X., F=
ienberg, S. E., and Airoldi, E. M. (2010). A survey of statistical network =
models. <i>Foundations and Trends in Machine Learning</i>, <i>2</i>(2):129=
=E2=80=93233.=C2=A0<a href=3D"http://arxiv.org/abs/0912.5410" target=3D"_bl=
ank">http://arxiv.org/abs/0912.5410</a><br></li><li>Hanneman, R. A. and Rid=
dle, M. (2005). Chapter 18: Some statistical tools. In <i>Introduction to s=
ocial network methods</i>. University of California, Riverside.=C2=A0<a hre=
f=3D"http://faculty.ucr.edu/~hanneman/nettext/C18_Statistics.html" target=
=3D"_blank">http://faculty.ucr.edu/~hanneman/nettext/C18_Statistics.html</a=
><br></li><li>Holland, P. W., &amp; Leinhardt, S. (1981). An exponential fa=
mily of probability distributions for directed graphs. <i>Journal of the Am=
erican Statistical Association</i>, <i>76</i>(373):33-50.=C2=A0<a href=3D"h=
ttp://www.jstor.org/stable/2287037" target=3D"_blank">http://www.jstor.org/=
stable/2287037
</a></li><li>Hunter, D. R., Krivitsky, P. N., and Schweinberg=
er, M. (2012). Computational statistical methods for social network models.=
 <i>Journal of Computational and Graphical Statistics</i>, <i>21</i>(4):856=
=E2=80=93882.=C2=A0<a href=3D"http://www.tandfonline.com/doi/abs/10.1080/10=
618600.2012.732921" target=3D"_blank">http://www.tandfonline.com/doi/abs/10=
.1080/10618600.2012.732921</a><br></li><li>Knoke, D. and Yang, S. (2008). C=
hapter 5: Advanced methods for analyzing networks. In <i>Social Network Ana=
lysis</i> (pp. 91=E2=80=93117), 2nd ed. Quantitative Applications in the So=
cial Sciences, no. 154. SAGE Publications.=C2=A0<br></li><li>Kolaczyk, E. D=
. (2009). <i>Statistical analysis of network data: Methods and models</i>. =
Springer Series in Statistics. Springer-Verlag.=C2=A0<a href=3D"http://www.=
springer.com/us/book/9780387881454" target=3D"_blank">http://www.springer.c=
om/us/book/9780387881454</a><br></li><li>Kolaczyk, E. D. and Cs=C3=A1rdi, G=
. (2014). <i>Statistical analysis of network data with R</i>. Use R!, volum=
e 65. Springer-Verlag.=C2=A0<a href=3D"http://www.springer.com/us/book/9781=
493909827" target=3D"_blank">http://www.springer.com/us/book/9781493909827<=
/a><br></li><li>Krackardt, D. (1987). QAP partialling as a test of spurious=
ness. <i>Social Networks</i>, <i>9</i>(2):171=E2=80=93186.=C2=A0<a href=3D"=
http://www.sciencedirect.com/science/article/pii/0378873387900128" target=
=3D"_blank">http://www.sciencedirect.com/science/article/pii/03788733879001=
28</a><br></li><li>Krackhardt, D. (1988). Predicting with networks: Nonpara=
metric multiple regression analysis of dyadic data. <i>Social Networks</i>,=
 <i>10</i>(4):359=E2=80=93381.=C2=A0<a href=3D"http://www.sciencedirect.com=
/science/article/pii/0378873388900044" target=3D"_blank">http://www.science=
direct.com/science/article/pii/0378873388900044</a><br></li><li>Laumann, E.=
 O., Marsden, P. V., and Galaskiewicz, J. (1977). Community-elite influence=
 structures: Extension of a network approach. <i>American Journal of Sociol=
ogy</i>, <i>83</i>(3):594=E2=80=93631.=C2=A0<a href=3D"http://www.jstor.org=
/stable/2778146" target=3D"_blank">http://www.jstor.org/stable/2778146</a><=
br></li><li>Leenders, R. T. (2002). Modeling social influence through netwo=
rk autocorrelation: Constructing the weight matrix. <i>Social Networks</i>,=
 <i>24</i>(1):21=E2=80=9347.=C2=A0<a href=3D"http://www.sciencedirect.com/s=
cience/article/pii/S0378873301000491
" target=3D"_blank">http://www.scienced=
irect.com/science/article/pii/S0378873301000491</a><br></li><li>Lusher, D.,=
 Koskinen, J., and Robins, G. (2012). <i>Exponential Random Graph Models fo=
r social networks: Theory, methods, and applications</i>. Structural Analys=
is in the Social Sciences. Cambridge University Press.<br></li><li>Pattison=
, P., and Robins, G. (2008). Chapter 18: Probabilistic network analysis. In=
 T. Rudas (Ed.),=C2=A0<i>Handbook of Probability: Theory and Applications</=
i> (pp. 291=E2=80=93313). SAGE Publications.=C2=A0<a href=3D"http://dx.doi.=
org/10.4135/9781452226620" target=3D"_blank">http://dx.doi.org/10.4135/9781=
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