diff --git a/inst/REFERENCES.bib b/inst/REFERENCES.bib index 10076cd2..7914566f 100644 --- a/inst/REFERENCES.bib +++ b/inst/REFERENCES.bib @@ -1,4 +1,4 @@ -% Encoding: ISO-8859-1 +% Encoding: UTF-8 @Article{KrHu23e, author = {Pavel N. Krivitsky and David R. Hunter and Martina Morris and Chad Klumb}, @@ -35,12 +35,14 @@ @Article{DuGi09f } @InProceedings{ScDe17e, - author = {Schmid, Christian S and Desmarais, Bruce A}, - title = {Exponential random graph models with big networks: Maximum pseudolikelihood estimation and the parametric bootstrap}, - booktitle = {2017 IEEE international conference on big data (Big Data)}, - year = {2017}, - pages = {116--121}, - organization = {IEEE}, + author = {Schmid, Christian S. and Desmarais, Bruce A.}, + title = {Exponential random graph models with big networks: Maximum pseudolikelihood estimation and the parametric bootstrap}, + booktitle = {2017 IEEE International Conference on Big Data (Big Data)}, + year = {2017}, + pages = {116--121}, + month = dec, + publisher = {IEEE}, + doi = {10.1109/bigdata.2017.8257919}, } @Article{ScHu23c, @@ -55,30 +57,26 @@ @Article{ScHu23c } @Article{HuHu12i, - author = {Hummel, Ruth M. and Hunter, David R. and Handcock, Mark S.}, - title = {Improving Simulation-based Algorithms for Fitting {ERGMs}}, - journal = {Journal of Computational and Graphical Statistics}, - year = {2012}, - volume = {21}, - number = {4}, - pages = {920--939}, - abstract = { Markov chain Monte Carlo methods can be used to approximate the intractable normalizing constants that arise in likelihood calculations for many exponential-family random graph models for networks. However, in practice, the resulting approximations degrade as parameter values move away from the value used to define the Markov chain, even in cases where the chain produces perfectly efficient samples. We introduce a new approximation method along with a novel method of moving toward a maximum likelihood estimator (MLE) from an arbitrary starting parameter value in a series of steps based on alternating between the canonical exponential-family parameterization and the mean-value parameterization. This technique enables us to find an approximate MLE in many cases where this was previously not possible. We illustrate these methods on a model for a transcriptional regulation network for E. coli, an example where previous attempts to approximate an MLE had failed, and a model for a well-known social network dataset involving friendships among workers in a tailor shop. These methods are implemented in the publicly available ergm package for R, and computer code to duplicate the results of this article is included in the online supplementary materials. }, - doi = {10.1080/10618600.2012.679224}, - file = {HuHu12i.pdf:/home/pavel/Documents/Research/References/HuHu12i.pdf:PDF}, + author = {Hummel, Ruth M. and Hunter, David R. and Handcock, Mark S.}, + title = {Improving Simulation-based Algorithms for Fitting {ERGMs}}, + journal = {Journal of Computational and Graphical Statistics}, + year = {2012}, + volume = {21}, + number = {4}, + pages = {920--939}, + doi = {10.1080/10618600.2012.679224}, } @Article{HaGi10m, - author = {Handcock, Mark S. and Gile, Krista J.}, - title = {Modeling Social Networks from Sampled Data}, - journal = {Annals of Applied Statistics}, - year = {2010}, - volume = {4}, - number = {1}, - pages = {5--25}, - issn = {1932-6157}, - abstract = {Network models are widely used to represent relational information among interacting units and the structural implications of these relations. Recently, social network studies have focused a great deal of attention on random graph models of networks whose nodes represent individual social actors and whose edges represent a specified relationship between the actors. Most inference for social network models assumes that the presence or absence of all possible links is observed, that the information is completely reliable, and that there are no measurement (e.g., recording) errors. This is clearly not true in practice, as much network data is collected though sample surveys. In addition even if a census of a population is attempted, individuals and links between individuals are missed (i.e., do not appear in the recorded data). In this paper we develop the conceptual and computational theory for inference based on sampled network information. We first review forms of network sampling designs used in practice. We consider inference from the likelihood framework, and develop a typology of network data that reflects their treatment within this frame. We then develop inference for social network models based on information from adaptive network designs. We motivate and illustrate these ideas by analyzing the effect of link-tracing sampling designs on a collaboration network.}, - doi = {10.1214/08-AOAS221}, - file = {:HaGi10m.pdf:PDF}, + author = {Handcock, Mark S. and Gile, Krista J.}, + title = {Modeling Social Networks from Sampled Data}, + journal = {Annals of Applied Statistics}, + year = {2010}, + volume = {4}, + number = {1}, + pages = {5--25}, + issn = {1932-6157}, + doi = {10.1214/08-AOAS221}, } @Article{HuHa06i, @@ -91,7 +89,6 @@ @Article{HuHa06i pages = {565--583}, issn = {1061-8600}, doi = {10.1198/106186006X133069}, - file = {:HuHa06i.pdf:PDF}, publisher = {American Statistical Association}, } @@ -102,18 +99,20 @@ @Article{Sn02m year = {2002}, volume = {3}, number = {2}, - file = {:Sn02m.pdf:PDF}, } @Article{StIk90p, - author = {Strauss, David and Ikeda, Michael}, - title = {Pseudolikelihood Estimation for Social Networks}, - journal = {Journal of the American Statistical Association}, - year = {1990}, - volume = {85}, - number = {409}, - pages = {204--212}, - issn = {0162-1459}, + author = {Strauss, David and Ikeda, Michael}, + title = {Pseudolikelihood Estimation for Social Networks}, + journal = {Journal of the American Statistical Association}, + year = {1990}, + volume = {85}, + number = {409}, + pages = {204--212}, + month = mar, + issn = {0162-1459}, + doi = {10.1080/01621459.1990.10475327}, + publisher = {Informa UK Limited}, } @Article{RoMo51s, @@ -126,9 +125,7 @@ @Article{RoMo51s pages = {400--407}, month = sep, issn = {00034851}, - abstract = {Let M(x) denote the expected value at level x of the response to a certain experiment. M(x) is assumed to be a monotone function of x but is unknown to the experimenter, and it is desired to find the solution x = θ of the equation M(x) = α, where α is a given constant. We give a method for making successive experiments at levels x1,x2,⋯ in such a way that xn will tend to θ in probability.}, - copyright = {Copyright © 1951 Institute of Mathematical Statistics}, - file = {:RoMo51s.pdf:PDF}, + copyright = {Copyright © 1951 Institute of Mathematical Statistics}, publisher = {Institute of Mathematical Statistics}, } @@ -153,7 +150,6 @@ @Article{FrSt86m pages = {832--842}, issn = {0162-1459}, doi = {10.1080/01621459.1986.10478342}, - file = {:FrSt86m.pdf:PDF}, } @Article{Kr17u, @@ -165,7 +161,6 @@ @Article{Kr17u pages = {149--161}, month = mar, doi = {10.1016/j.csda.2016.10.015}, - file = {Kr17u.pdf:Mine/Kr17u.pdf:PDF}, } @Article{KrKu23l, @@ -181,17 +176,16 @@ @Article{KrKu23l publisher = {Institute of Mathematical Statistics}, } -@article{VaFl15m, - author = {Vats, Dootika and Flegal, James M. and Jones, Galin L.}, - title = {Multivariate output analysis for {Markov} chain {Monte} {Carlo}}, - journal = {Biometrika}, - volume = {106}, - number = {2}, - pages = {321-337}, - year = {2019}, - month = {04}, - abstract = {Markov chain Monte Carlo produces a correlated sample which may be used for estimating expectations with respect to a target distribution. A fundamental question is: when should sampling stop so that we have good estimates of the desired quantities? The key to answering this question lies in assessing the Monte Carlo error through a multivariate Markov chain central limit theorem. The multivariate nature of this Monte Carlo error has been largely ignored in the literature. We present a multivariate framework for terminating a simulation in Markov chain Monte Carlo. We define a multivariate effective sample size, the estimation of which requires strongly consistent estimators of the covariance matrix in the Markov chain central limit theorem, a property we show for the multivariate batch means estimator. We then provide a lower bound on the number of minimum effective samples required for a desired level of precision. This lower bound does not depend on the underlying stochastic process and can be calculated a priori. This result is obtained by drawing a connection between terminating simulation via effective sample size and terminating simulation using a relative standard deviation fixed-volume sequential stopping rule, which we demonstrate is an asymptotically valid procedure. The finite-sample properties of the proposed method are demonstrated in a variety of examples.}, - doi = {10.1093/biomet/asz002}, +@Article{VaFl15m, + author = {Vats, Dootika and Flegal, James M. and Jones, Galin L.}, + title = {Multivariate output analysis for {Markov} chain {Monte} {Carlo}}, + journal = {Biometrika}, + year = {2019}, + volume = {106}, + number = {2}, + pages = {321-337}, + month = {04}, + doi = {10.1093/biomet/asz002}, } @Article{WaAt13a, @@ -208,4 +202,142 @@ @Article{WaAt13a publisher = {Informa UK Limited}, } +@Article{GoKi09b, + author = {Goodreau, Steven M. and Kitts, James A. and Morris, Martina}, + title = {Birds of a Feather, or Friend of a Friend? {Using} Exponential Random Graph Models to Investigate Adolescent Social Networks}, + journal = {Demography}, + year = {2009}, + volume = {46}, + number = {1}, + pages = {103--125}, + month = feb, + doi = {10.1353/dem.0.0045}, +} + +@Article{HuGo08g, + author = {Hunter, David R. and Goodreau, Steven M. and Handcock, Mark S.}, + title = {Goodness of Fit for Social Network Models}, + journal = {Journal of the American Statistical Association}, + year = {2008}, + volume = {103}, + number = {481}, + pages = {248--258}, + month = mar, + issn = {0162-1459}, + doi = {10.1198/016214507000000446}, +} + +@Article{Sc11i, + author = {Schweinberger, Michael}, + title = {Instability, Sensitivity, and Degeneracy of Discrete Exponential Families}, + journal = {Journal of the American Statistical Association}, + year = {2011}, + volume = {106}, + number = {496}, + pages = {1361--1370}, + doi = {10.1198/jasa.2011.tm10747}, +} + +@Article{SnPa06n, + author = {Snijders, Tom A. B. and Pattison, Philippa E. and Robins, Garry L. and Handcock, Mark S.}, + title = {New Specifications for Exponential Random Graph Models}, + journal = {Sociological Methodology}, + year = {2006}, + volume = {36}, + number = {1}, + pages = {99--153}, + month = aug, + issn = {1467-9531}, + doi = {10.1111/j.1467-9531.2006.00176.x}, + publisher = {Blackwell Synergy}, +} + +@Article{MoHa08s, + author = {Morris, Martina and Handcock, Mark S. and Hunter, David R.}, + title = {Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects}, + journal = {Journal of Statistical Software}, + year = {2008}, + volume = {24}, + number = {4}, + pages = {1--24}, + month = may, + issn = {1548-7660}, + doi = {10.18637/jss.v024.i04}, + publisher = {Foundation for Open Access Statistic}, +} + +@Article{Hu07c, + author = {Hunter, David R.}, + title = {Curved Exponential Family Models for Social Networks}, + journal = {Social Networks}, + year = {2007}, + volume = {29}, + pages = {216--230}, + issn = {0378-8733}, + doi = {10.1016/j.socnet.2006.08.005}, +} + +@TechReport{Ha03a, + author = {Handcock, Mark S.}, + title = {Assessing Degeneracy in Statistical Models of Social Networks}, + institution = {Center for Statistics and the Social Sciences, University of Washington}, + year = {2003}, + type = {Working Paper}, + number = {39}, + address = {Seattle, WA}, + month = dec, + url = {https://csss.uw.edu/research/working-papers/assessing-degeneracy-statistical-models-social-networks}, +} + +@Article{KrHa11a, + author = {Krivitsky, Pavel N. and Handcock, Mark S. and Morris, Martina}, + title = {Adjusting for Network Size and Composition Effects in Exponential-family Random Graph Models}, + journal = {Statistical Methodology}, + year = {2011}, + volume = {8}, + number = {4}, + pages = {319--339}, + month = jul, + issn = {1572-3127}, + doi = {10.1016/j.stamet.2011.01.005}, + keywords = {network size; ERGM; random graph; egocentrically-sampled data}, +} + +@Article{KrMo17i, + author = {Pavel N. Krivitsky and Martina Morris}, + title = {Inference for Social Network Models from Egocentrically-sampled Data, with Application to Understanding Persistent Racial Disparities in {HIV} Prevalence in the {US}}, + journal = {Annals of Applied Statistics}, + year = {2017}, + volume = {11}, + number = {1}, + pages = {427--455}, + doi = {10.1214/16-AOAS1010}, + journaltitle = {Annals of Applied Statistics}, + keywords = {social network; ERGM; random graph; egocentrically-sampled data; pseudo maximum likelihood; pseudo likelihood}, +} + +@Article{KrHa14s, + author = {Krivitsky, Pavel N. and Handcock, Mark S.}, + title = {A Separable Model for Dynamic Networks}, + journal = {Journal of the Royal Statistical Society, Series B}, + year = {2014}, + volume = {76}, + number = {1}, + pages = {29--46}, + doi = {10.1111/rssb.12014}, + keywords = {Social networks; Longitudinal; Exponential random graph model; Markov chain Monte Carlo; Maximum likelihood estimation}, +} + +@Article{HuGo13e, + author = {Hunter, David R. and Goodreau, Steven M. and Handcock, Mark S.}, + title = {Ergm.userterms: {A} Template Package for Extending Statnet}, + journal = {Journal of Statistical Software}, + year = {2013}, + volume = {52}, + number = {2}, + pages = {1--25}, + issn = {1548-7660}, + doi = {10.18637/jss.v052.i02}, +} + @Comment{jabref-meta: databaseType:bibtex;} diff --git a/vignettes/ergm.Rmd b/vignettes/ergm.Rmd index 5e5e1f10..30c95056 100644 --- a/vignettes/ergm.Rmd +++ b/vignettes/ergm.Rmd @@ -3,7 +3,7 @@ title: "Introduction to Exponential-family Random Graph Models with `ergm`" author: "The Statnet Development Team" date: "`ergm` version `r packageVersion('ergm')` (`r Sys.Date()`)" output: rmarkdown::html_vignette - +bibliography: ../inst/REFERENCES.bib vignette: > %\VignetteIndexEntry{Introduction to Exponential-family Random Graph Models with ergm} %\VignetteEngine{knitr::rmarkdown} @@ -32,10 +32,10 @@ This vignette provides an introduction to statistical modeling of network data with *Exponential family Random Graph Models* (ERGMs) using `ergm` package. It is based on the `ergm` tutorial used in the `statnet` workshops, but covers a subset of that material. -The complete tutorial can be found on the [`statnet` workshop wiki](https://github.com/statnet/Workshops/wiki/). +The complete tutorial can be found on the [`statnet` workshops page](https://statnet.org/workshops/). A more complete overview of the advanced functionality available in the -`ergm` package can be found in [this preprint](http://arxiv.org/abs/2106.04997). +`ergm` package can be found in @KrHu23e. ### Software installation @@ -58,7 +58,7 @@ set.seed(0) ## 1. Statistical network modeling with ERGMs -This is a *very brief* overview of the modeling framework, as the primary purpose of this tutorial is to show how to implement statistical analysis of network data with ERGMs using the `ergm` package. For more detail (and to really understand ERGMs) please see the [references](ergm_tutorial.html#references) at the end of this tutorial. +This is a *very brief* overview of the modeling framework, as the primary purpose of this tutorial is to show how to implement statistical analysis of network data with ERGMs using the `ergm` package. For more detail (and to really understand ERGMs) please see [further reading](#further-reading) at the end of this tutorial. Exponential-family random graph models (ERGMs) are a general class of models based on exponential-family theory @@ -104,7 +104,7 @@ The statistics $g(y)$ can be thought of as the "covariates" in the model. In th As a result, every term in an ERGM must have an associated algorithm for computing its value for your network. The `ergm` package in `statnet` includes about 150 term-computing algorithms. We will explore some of these terms in this tutorial, and links to more information are provided in -[section 3.](#model-terms-available-for-ergm-estimation-and-simulation). +[section 3](#model-terms-available-for-ergm-estimation-and-simulation). You can get the list of all available terms, and the syntax for using them, by typing: ```{r, eval=FALSE} @@ -131,9 +131,7 @@ One key distinction in model terms is worth keeping in mind: terms are either _ * Dyad _dependent_ terms (like degree terms, or triad terms), by contrast, imply dependence between dyads. Such terms have very different effects, and much of what is different about network models comes from these terms. They introduce complex cascading effects that can often lead to counter-intuitive and highly non-linear outcomes. In addition, a model with dyad dependent terms requires a different estimation algorithm, so when we use them below you will see some different components in the output. -An overview and discussion of many of these terms can be found in -the 'Specifications' -paper in the [*Journal of Statistical Software v24(4)*](http://www.jstatsoft.org/v24/i04) +An overview and discussion of many of these terms can be found in @MoHa08s. #### ERGM probabilities: at the tie-level @@ -504,11 +502,10 @@ There is a `statnet` package --- `ergm.userterms` --- that facilitates the writing of new `ergm` terms. The package is available [on GitHub](https://github.com/statnet/ergm.userterms), and installing it will include the tutorial (ergmuserterms.pdf). The tutorial can -also be found in the -[*Journal of Statistical Software 52(2)*](http://www.jstatsoft.org/v52/i02), +also be found in @HuGo13e, and some introductory slides and installation instructions from the workshop we teach on coding `ergm` terms can be found -[here](https://github.com/statnet/Workshops/tree/master/ergm.userterms). +[here](https://statnet.org/workshops/). For the most recent API available for implementing terms, see the Terms API vignette. Note that writing up new `ergm` terms requires some knowledge of C and the ability @@ -616,9 +613,7 @@ plot(mesamodel.02.gof) ``` For a good example of model exploration and fitting for the Add Health -Friendship networks, see [Goodreau, Kitts & Morris, *Demography* 2009](http://link.springer.com/article/10.1353/dem.0.0045). -For more technical details on the approach, see -[Hunter, Goodreau and Handcock *JASA* 2008](http://amstat.tandfonline.com/doi/abs/10.1198/016214507000000446?journalCode=uasa20#.U7HZgPldWSo) +Friendship networks, see @GoKi09b. For more technical details on the approach, see @HuGo08g. ## 7. Diagnostics: troubleshooting and checking for model degeneracy @@ -754,7 +749,7 @@ mcmc.diagnostics(fit) Success! Of course, in real life one might have a lot more trial and error. -Degeneracy is often an indicator of a poorly specified model. It is not a property of all ERGMs, but it is associated with some dyadic-dependent terms, in particular, the reduced homogenous Markov specifications (e.g., 2-stars and triangle terms). For a good technical discussion of unstable terms see [Schweinberger 2012.](http://www.tandfonline.com/doi/abs/10.1198/jasa.2011.tm10747#.U6R2FvldWSo) For a discussion of alternative terms that exhibit more stable behavior see [Snijders et al. 2006.](http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9531.2006.00176.x/abstract) and for the gwesp term (and the curved exponential family terms in general) see [Hunter and Handcock 2006.](http://amstat.tandfonline.com/doi/abs/10.1198/106186006X133069#.U7MxWPldWSo) +Degeneracy is often an indicator of a poorly specified model. It is not a property of all ERGMs, but it is associated with some dyadic-dependent terms, in particular, the reduced homogenous Markov specifications (e.g., 2-stars and triangle terms). For a good technical discussion of unstable terms see @Sc11i. For a discussion of alternative terms that exhibit more stable behavior see @SnPa06n and for the `gwesp` term (and the curved exponential family terms in general) see @HuHa06i. @@ -762,12 +757,12 @@ Degeneracy is often an indicator of a poorly specified model. It is not a prope One of the most powerful features of ERGMs is that they can be used to estimate models from from egocentrically sampled data, and the fitted models can then be used to simulate complete networks (of any size) that will have the properties of the original network that are observed and represented in the model. -The egocentric estimation/simulation framework extends to temporal ERGMs ("TERGMs") as well, with the minimal addition of an estimate of partnership duration. This makes it possible to simulate complete dynamic networks from a single cross-sectional egocentrically sampled network. For an example of what you can do with this, check out the network movie we developed to explore the impact of dynamic network structure on HIV transmission, see http://statnet.org/movies +The egocentric estimation/simulation framework extends to temporal ERGMs ("TERGMs") as well, with the minimal addition of an estimate of partnership duration. This makes it possible to simulate complete dynamic networks from a single cross-sectional egocentrically sampled network. For an example of what you can do with this, check out the network movie we developed to explore the impact of dynamic network structure on HIV transmission, see https://statnet.org/movies/ . While the `ergm` package can be used with egocentric data, we recommend instead to use the package `ergm.ego`. This package includes accurate statistical inference and many utilities that simplify the task of reading in the data, conducting exploratory analyses, calculating the sample "target statistics", and specifying model options. -We have a workshop/tutorial for `ergm.ego` at the [statnet Workshops wiki](https://github.com/statnet/Workshops/wiki). +We have a workshop/tutorial for `ergm.ego` at the [statnet Workshops site](https://statnet.org/workshops/). ## 9. Additional functionality in statnet and other package @@ -776,7 +771,7 @@ We have a workshop/tutorial for `ergm.ego` at the [statnet Workshops wiki](https All of these packages can be downloaded from CRAN. For more detailed information, please visit the `statnet` -webpage [www.statnet.org](http://statnet.org). +webpage [www.statnet.org](https://statnet.org/). ### Current statnet packages @@ -785,15 +780,16 @@ Packages developed by statnet team that are not covered in this tutorial: * `sna` -- classical social network analysis utilities * `tsna` -- descriptive statistics for temporal network data -* `tergm` -- temporal ergms for dynamic networks +* `tergm` -- temporal ERGMs for dynamic networks * `ergm.ego`-- estimation/simulation of ergms from egocentrically sampled data * `ergm.count` -- models for tie count network data * `ergm.rank` -- models for tie rank network data +* `ergm.multi` -- models of multilayer networks and for samples of networks * `relevent` -- relational event models for networks * `latentnet` -- latent space and latent cluster analysis * `degreenet` -- MLE estimation for degree distributions (negative binomial, Poisson, scale-free, etc.) * `networksis` -- simulation of bipartite networks with given degree distributions -* `ndtv` package -- network movie maker +* `ndtv` -- network movie maker * `EpiModel` -- network modeling of infectious disease and social diffusion processes @@ -806,8 +802,7 @@ Packages developed by statnet team that are not covered in this tutorial: There are now a number of excellent packages developed by others that extend the functionality of statnet. The easiest way to find these is to -look at the "reverse depends" of the `ergm` package on -[CRAN](https://cran.org/packages). Examples include: +look at the "reverse depends" of the `ergm` package on CRAN. Examples include: * `Bergm` -- Bayesian Exponential Random Graph Models * `btergm` -- Temporal Exponential Random Graph Models by Bootstrapped Pseudolikelihood @@ -825,8 +820,7 @@ Steven M. Goodreau goodreau@u.washington.edu Skye Bender-deMoll skyebend@skyeome.net Samuel M. Jenness samuel.m.jenness@emory.edu - -## References +## Further reading The best place to start is the special issue of the *Journal of Statistical Software* (JSS) devoted to `statnet`: [link](https://www.jstatsoft.org/issue/view/v024) @@ -834,45 +828,28 @@ The nine papers in this issue cover a wide range of theoretical and practical to HOWEVER: Note that this issue was written in 2008. The statnet code base has evolved considerably since that time, so some of the syntax specified in the articles may no longer work (in most cases because it has been replace with something better). -An overview of most recent update, `ergm 4`, can be found in here: [link](http://arxiv.org/abs/2106.04997). - -For social scientists, a good introductory application paper is: +An overview of most recent update, `ergm 4`, can be found at @KrHu23e. -Goodreau, S., J. Kitts and M. Morris (2009). -Birds of a Feather, or Friend of a Friend? Using Statistical Network Analysis to Investigate Adolescent Social Networks. -*Demography* 46(1): 103-125. [link](http://link.springer.com/article/10.1353/dem.0.0045) +For social scientists, a good introductory application paper is @GoKi09b. +### Dealing with Model Degeneracy -**Dealing with Model Degeneracy** +@Ha03a -Handcock MS (2003a). -"Assessing Degeneracy in Statistical Models of Social Networks." -Working Paper 39, Center for Statistics and the Social Sciences, University of Washington. [link](https://csss.uw.edu/research/working-papers/assessing-degeneracy-statistical-models-social-networks) +@Sc11i -Schweinberger, Michael (2011) Instability, Sensitivity, and Degeneracy of Discrete Exponential Families *JASA* 106(496): 1361-1370. [link](http://www.tandfonline.com/doi/abs/10.1198/jasa.2011.tm10747#.U7M4A_ldWSo) +@SnPa06n -Snijders, TAB et al (2006) -New Specifications For Exponential Random Graph Models -*Sociological Methodology* 36(1): 99-153 [link](http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9531.2006.00176.x/abstract) +@Hu07c -Hunter, D. R. (2007). -Curved Exponential Family Models for Social Networks. -*Social Networks*, 29(2), 216-230.[link](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2031865/) +### Temporal ERGMs +@KrHa14s -**Temporal ERGMs** +### Egocentric ERGMS -Krivitsky, P.N., Handcock, M.S,(2014). -A separable model for dynamic networks -*JRSS Series B-Statistical Methodology*, 76(1):29-46; 10.1111/rssb.12014 JAN 2014 [link](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3891677/) +@KrHa11a -Krivitsky, P. N., M. S. Handcock and M. Morris (2011). -Adjusting for Network Size and Composition Effects in Exponential-family Random Graph Models, -*Statistical Methodology* 8(4): 319-339, ISSN 1572-3127 [link](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3117581/) - -**Egocentric ERGMS** - -Krivitsky, P. N., & Morris, M. (2017). -Inference for social network models from egocentrically sampled data, with application to understanding persistent racial disparities in HIV prevalence in the US. -*Annals of Applied Statistics*, 11(1), 427-455.[link](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5737754/) +@KrMo17i +## References