New topics in network modeling

1st Chilean Summer School about Social Network Research

George G. Vega Yon, Ph.D.

The University of Utah

Booz Allen Hamilton

2024-01-12

Overview

  • With more data and computing resources, the things that we can ask and do with networks are becoming increasingly (even more) exciting and complex.

  • In this section, I will introduce some of the latest advancements and forthcoming topics in network modeling.

Part I: New models and extensions

Mutli-ERGMs

  • In Krivitsky, Coletti, and Hens (2023a), the authors present a start-to-finish pooled ERGM example featuring heterogeneous data sources.

  • They increase power and allow exploring heterogeneous effects across types/classes of networks.

Statistical power of SOAM

  • SOAM Stadtfeld et al. (2020) proposes ways to perform power analysis for Siena models. At the center of their six-step approach is simulation.

Bayesian ALAAM

Ever wondered how to model influence exclusively?

  • The Auto-Logistic Actor Attribute Model [ALAAM] is a model that allows us to do just that.
  • Koskinen and Daraganova (2022) extends the ALAAM model to a Bayesian framework.
  • It provides greater flexibility to accommodate more complicated models and add extensions such as hierarchical models. Figure 1 reproduced from A. D. Stivala et al. (2020)

Relational Event Models

  • REMs are great for modeling sequences of ties (instead of panel or cross-sectional.)

  • Butts et al. (2023) provides a general overview of Relational Event Models [REMs,] new methods, and future steps.

Figure 3 reproduced from Brandenberger (2020)

Big ERGMs

  • ERGMs In A. Stivala, Robins, and Lomi (2020), a new method is proposed to estimate large ERGMs (featuring millions of nodes).

Partial map of the Internet based on the January 15, 2005 data found on opte.org. – Wiki

Exponential Random Network Models

  • Wang, Fellows, and Handcock recently published a re-introduction of the ERNM framework (Wang, Fellows, and Handcock 2023).

  • ERNMs generalize ERGMs to incorporate behavior and are the cross-sectional causing of SIENA models.

\begin{align*} \text{ER\textbf{G}M}: & P_{\mathcal{Y}, \bm{\theta}}(\bm{Y}=\bm{y} | \bm{X}=\bm{x}) \\ \text{ER\textbf{N}M}: & P_{\mathcal{Y}, \bm{\theta}}(\bm{Y}=\bm{y}, \bm{X}=\bm{x}) \end{align*}

Part II: Shameless self-promotion

ERGMitos: Small ERGMs

Five small networks from the ergmito R package

Discrete Exponential-family Models

  • ERGMs are a particular case of Random Markov fields.

  • We can use the ERGM framework for modeling vectors of binary outcomes, e.g., the consumption of \{tobacco, MJ, alcohol\}

Power analysis in ERGMs

  • Using conditional ERGMs (closely related to constrained), we can do power analysis for network samples (Vega Yon 2023).

Reproduced from Krivitsky, Coletti, and Hens (2023b)

Two-step estimation ERGMs

  • Conditioning the ERGM on an observed statistic “drops” the associated coefficient.

  • Hypothesis: As n increases, conditional ERGM estimates are consistent with the full model:

Simulation study trying to demonstrate the concept (Work in progress)

Thanks!

Bonus track: Why network scientists don’t use ERGMs?

Attempts to overcome these problems by extending the blockmodel have focused particularly on the use of (more complicated) p∗ or exponential random graph models, but while these are conceptually appealing, they quickly lose the analytic tractability of the original blockmodel as their complexity increases.

– Karrer and Newman (2011)

References

New topics in network modeling – https://ggvy.cl

Brandenberger, Laurence. 2020. “Interdependencies in Conflict Dynamics: Analyzing Endogenous Patterns in Conflict Event Data Using Relational Event Models.” In Computational Conflict Research, edited by Emanuel Deutschmann, Jan Lorenz, Luis G. Nardin, Davide Natalini, and Adalbert F. X. Wilhelm, 67–80. Computational Social Sciences. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-29333-8_4.
Butts, Carter T., Alessandro Lomi, Tom A. B. Snijders, and Christoph Stadtfeld. 2023. “Relational Event Models in Network Science.” Network Science 11 (2): 175–83. https://doi.org/10.1017/nws.2023.9.
Karrer, Brian, and M. E. J. Newman. 2011. “Stochastic Blockmodels and Community Structure in Networks.” Physical Review E 83 (1): 016107. https://doi.org/10.1103/PhysRevE.83.016107.
Koskinen, Johan, and Galina Daraganova. 2022. “Bayesian Analysis of Social Influence.” Journal of the Royal Statistical Society Series A: Statistics in Society 185 (4): 1855–81. https://doi.org/10.1111/rssa.12844.
Krivitsky, Pavel N., Pietro Coletti, and Niel Hens. 2023a. “A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks.” Journal of the American Statistical Association 0 (0): 1–21. https://doi.org/10.1080/01621459.2023.2242627.
———. 2023b. “Rejoinder to Discussion of ‘A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks’.” Journal of the American Statistical Association 118 (544): 2235–38. https://doi.org/10.1080/01621459.2023.2280383.
Stadtfeld, Christoph, Tom A. B. Snijders, Christian Steglich, and Marijtje van Duijn. 2020. “Statistical Power in Longitudinal Network Studies.” Sociological Methods & Research 49 (4): 1103–32. https://doi.org/10.1177/0049124118769113.
Stivala, Alex D., H. Colin Gallagher, David A. Rolls, Peng Wang, and Garry L. Robins. 2020. “Using Sampled Network Data With The Autologistic Actor Attribute Model.” arXiv. https://doi.org/10.48550/arXiv.2002.00849.
Stivala, Alex, Garry Robins, and Alessandro Lomi. 2020. “Exponential Random Graph Model Parameter Estimation for Very Large Directed Networks.” PLoS ONE 15 (1): 1–23. https://doi.org/10.1371/journal.pone.0227804.
Vega Yon, George G. 2023. “Power and Multicollinearity in Small Networks: A Discussion of ‘Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks’ by Krivitsky, Coletti & Hens.” Journal Of The American Statistical Association.
Vega Yon, George G., Andrew Slaughter, and Kayla de la Haye. 2021. “Exponential Random Graph Models for Little Networks.” Social Networks 64 (August 2020): 225–38. https://doi.org/10.1016/j.socnet.2020.07.005.
Wang, Zeyi, Ian E. Fellows, and Mark S. Handcock. 2023. “Understanding Networks with Exponential-Family Random Network Models.” Social Networks, August, S0378873323000497. https://doi.org/10.1016/j.socnet.2023.07.003.