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Dear Tom,

What you describe seems to fit:

Dow, M. M., Burton, M. L., and White, D. R. (1982). Network
autocorrelation: A simulation study of a foundational problem in regression
and survey research. *Social Networks*, *4*(2):169–200.
http://www.sciencedirect.com/science/article/pii/0378873382900314

Is that perhaps what you are remembering?

Indeed, even among the generally help work from Dow and colleagues, this is
probably the single article that has helped me the most so far. Still, it
isn't exactly what I am looking for, since their purpose is investigating
finite-sample properties of two specific estimators rather than on
demonstrating the effect of not accounting for dependencies in general
(their method is to simulate data from a network autocorrelation model to
show that a network-autocorrelation-inspired estimator is better than OLS;
perfectly appropriate for advancing research, but somewhat circular and too
focused for my purposes of understanding basic statistical issues).

However, what you say about the statistical literature being full of
results about the unreliability of models that do not represent the system
generating the data, such that statisticians take that unreliability as a
foregone conclusion, is very helpful. I think that now I have a better idea
of what I can expect to find and not expect to find, and why.

And it seems then that the kind of resources I am looking for (and again, I
think I am not alone) don't exist. I think I know enough to start setting
up simulations, and working through some formal arguments, to try to figure
things out myself; if I can manage this, hopefully I can then attempt to
make something to share with others.

It would still help to see some examples of the evidence you mention. Would
you, or anybody on the list, be able to recommend good textbooks or other
resources for statistical model-building in general (beyond regression
modeling)? Something I could look through for discussions not just of
misspecification of terms in a given model, but also of when models
themselves depart too far from the actual underlying probabilistic system?

Thank you!
Momin


(For the record, other particularly helpful articles from the bibliography
I forwarded: for the problem of dependencies, see all of the Dow et al.
articles, and especially the "simulation study of a foundational problem" I
mention above; for anybody who knows about bootstrapping and nonparametric
permutation tests and wonder how they could apply to networks, see Tom's
work with Steve Borgatti in Snijders and Borgatti, as well as Krackhardt's
QAP articles; for those who know about graphical models for causality,
see Shalizi
and Thomas; for an example of an ERGM worked through by hand, see Knoke and
Yang; and for perhaps the earliest recognition by social scientists of the
subtlety of problem, see the footnotes in Laumann et al. And, after taking
another look at Tom's *Annual Review of Sociology* article, it is indeed
probably the best place to start for finding out about models, as it covers
every model I've seen used and provides a breakdown of the various models'
goals and assumptions.)


On Thu, Jun 25, 2015 at 5:39 AM, Snijders, T.A.B. <[log in to unmask]>
wrote:

> ***** 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:
>
>> ---------------------- Information from the mail header
>> -----------------------
>> Sender:       Social Networks Discussion Forum <[log in to unmask]>
>> Poster:       "Momin M. Malik" <[log in to unmask]>
>> Subject:      Why, exactly, do we need special statistical models for
>> networks?
>>
>> -------------------------------------------------------------------------------
>>
>> --001a113cd112c204f30519398853
>> Content-Type: text/plain; charset=UTF-8
>> Content-Transfer-Encoding: quoted-printable
>>
>> *****  To join INSNA, visit http://www.insna.org  *****
>>
>> 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 <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.
>>
>> _____________________________________________________________________
>> SOCNET is a service of INSNA, the professional association for social
>> network researchers (http://www.insna.org). To unsubscribe, send
>> an email message to [log in to unmask] containing the line
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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 <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 <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=
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