tergm-package {tergm}

Fit, Simulate and Diagnose Dynamic Network Models derived from Exponential-Family Random Graph Models

Description

tergm is a collection of extensions to the ergm package to fit, diagnose, and simulate models for dynamic networks — networks that evolve over time — based on exponential-family random graph models (ERGMs). For a list of functions type help(package='tergm')

Details

When publishing results obtained using this package, please cite the original authors as described in citation(package="tergm").

All programs derived from this package must cite it.

An exponential-family random graph model (ERGM) postulates an exponential family over the sample space of networks of interest, and ergm package implements a suite of tools for modeling single networks using ERGMs.

There have been a number of extensions of ERGMs for modeling the evolution of networks, including the temporal ERGM (TERGM) of Hanneke et al. (2010) and the separable termporal ERGM (STERGM) of Krivitsky and Handcock (2014). The latter model allows familiar ERGM terms and statistics to be reused in a dynamic context, interpreted in terms of formation and dissolution (persistence) of ties. Krivitsky (2012) suggested a method for fitting dynamic models when only a cross-sectional network is available, provided some temporal information for it is available as well.

This package aims to implement these and other ERGM-based models for network evolution. At this time, it implements, via the tergm function, a general framework for modeling tie dynamics in temporal networks with flexible model specification (including (S)TERGMs). Estimation options include a conditional MLE (CMLE) approach for fitting to a series of networks and an Equilibrium Generalized Method of Moments Estimation (EGMME) for fitting to a single network with temporal information. For further development, see the referenced papers.

Temporal model specification in tergm

The operator terms implemented by tergm are Form(), Persist(), Diss(), Cross(), and Change(). These are used to specify how the ergm terms (ergmTerm) in a formula are evaluated across a network time-series. Note, you cannot use one of these operators within another temporal, so Cross(~Form(~edges)) is not a valid specification. (Generally, nesting these operators within other operators will often not work; nesting other operators within them will almost always work, however.)

The durational terms are distinguished either by their name, mean.age, or their name extensions: ⁠<name>.ages⁠, ⁠<name>.mean.age⁠, and ⁠<name>.age.interval⁠. In contrast to their eponymous terms in ergm, these durational terms take into account the elapsed time since each (term-relevant) dyad in the network was last toggled.

As currently implemented, the package does not support use of many durational terms during estimation, though it may work with some. But durational terms may be used as targets, monitors, or summary statistics. The ability to use these terms in the estimation of models is under development.

Compatibility with previous versions

If you previously used the stergm() function in this package, please note that stergm() has been superceded by the new tergm function, and has been deprecated. The dissolution formula in stergm() maps to the new Persist() operator in the tergm() function, not the Diss() operator.

For detailed information on how to download and install the software, go to the Statnet project website: https://statnet.org. A tutorial, support newsgroup, references and links to further resources are provided there.

References

Hanneke S, Fu W and Xing EP (2010). Discrete Temporal Models of Social Networks. Electronic Journal of Statistics, 2010, 4, 585-605. doi:10.1214/09-EJS548

Krackhardt, D and Handcock, MS (2006) Heider vs Simmel: Emergent features in dynamic structures. ICML Workshop on Statistical Network Analysis. Springer, Berlin, Heidelberg, 2006.

Krivitsky PN & Handcock MS (2014) A Separable Model for Dynamic Networks. Journal of the Royal Statistical Society, Series B, 76(1): 29-46. doi:10.1111/rssb.12014

Krivitsky, PN (2012). Modeling of Dynamic Networks based on Egocentric Data with Durational Information. Pennsylvania State University Department of Statistics Technical Report, 2012(2012-01). https://web.archive.org/web/20170830053722/https://stat.psu.edu/research/technical-report-files/2012-technical-reports/TR1201A.pdf

Butts CT (2008). network: A Package for Managing Relational Data in . Journal of Statistical Software, 24(2). doi:10.18637/jss.v024.i02

Goodreau SM, Handcock MS, Hunter DR, Butts CT, Morris M (2008a). A statnet Tutorial. Journal of Statistical Software, 24(8). doi:10.18637/jss.v024.i08

Hunter, D. R. and Handcock, M. S. (2006) Inference in curved exponential family models for networks, Journal of Computational and Graphical Statistics, 15: 565-583

Hunter DR, Handcock MS, Butts CT, Goodreau SM, Morris M (2008b). ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. Journal of Statistical Software, 24(3). doi:10.18637/jss.v024.i03

Morris M, Handcock MS, Hunter DR (2008). Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects. Journal of Statistical Software, 24(4). doi:10.18637/jss.v024.i04