ergm.multi-package {ergm.multi}R Documentation

ergm.multi: Fit, Simulate and Diagnose Exponential-Family Models for Multiple or Multilayer Networks

Description

A set of extensions for the 'ergm' package to fit multilayer/multiplex/multirelational networks and samples of multiple networks. 'ergm.multi' is a part of the Statnet suite of packages for network analysis. See Krivitsky, Koehly, and Marcum (2020) doi:10.1007/s11336-020-09720-7 and Krivitsky, Coletti, and Hens (2023) doi:10.1080/01621459.2023.2242627.

Multilayer network models

Also known as multiplex, multirelational, or multivariate networks, in a multilayer network a pair of actors can have multiple simultaneous relations of different types. For example, in the Lazega lawyer data set included with this package, each pair of lawyers in the firm can have an advice relationship, a coworking relationship, a friendship relationship, or any combination thereof. Application of ERGMs to multilayer networks has a long history (Pattison and Wasserman 1999; Lazega and Pattison 1999), and a number of R packages exist for analysing and estimating them.

ergm.multi implements the general approach of Krivitsky et al. (2020) for specifying multilayer ERGMs, including Layer Logic and the various cross-layer specifications. Its features include:

seamless integration with ergm():

Multilayer specification is contained entirely in an ergm()-style formula and can be nested with any other ergm() terms, including dynamic and multi-network.

unlimited layers:

The number of layers in the modeled network is limited only by computing power.

flexibility and simplicity:

Any valid binary ERGM can be specified for any layer or a logical combination of layers using simple term operators.

heterogeneous layers:

A network can have directed and undirected layers, which can be modeled jointly.

multimode/multilevel support (experimental):

With some care, it is possible to specify models for unipartite and bipartie layers over different subsets of actors, which can be used to specify multimode models.

See Layer() and ergmTerm?L for examples.

Multi-network models

Joint modeling of independent samples of networks on disjoint sets of actors have a long history as well (Zijlstra et al. 2006, Slaughter and Koehly 2016, Stewart et al. 2019, and Vega Yon et al. 2021, for example). ergm.multi facilitates fixed-effect models for samples of networks (possibly heterogeneous in size and composition), using a multivariate linear model for each network's ERGM parameters, with network-level attributes serving as predictors, as formulated by Slaughter and Koehly (2016) and Krivitsky et al. (2023).

Its features include:

seamless integration with ergm():

Multi-network model specification is contained entirely in an ergm()-style formula and can be nested with any other ergm() terms, including dynamic and multilayer.

flexibility and simplicity:

Any valid binary or valued ERGM can be specified for the networks, using simple term operators and the network-level specification with an lm()-style formula.

See Networks(), ergmTerm?N for specification, gofN() for diagnostic facilities, and vignette("Goeyvaerts_reproduction") for a demonstration.

Author(s)

Maintainer: Pavel N. Krivitsky pavel@statnet.org (ORCID)

Other contributors:

References

Krivitsky PN, Coletti P, Hens N (2023). “A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks.” Journal of the American Statistical Association, 118(544), 2213-2224. doi:10.1080/01621459.2023.2242627.

Krivitsky PN, Koehly LM, Marcum CS (2020). “Exponential-family Random Graph Models for Multi-layer Networks.” Psychometrika, 85(3), 630–659. doi:10.1007/s11336-020-09720-7.

Lazega E, Pattison PE (1999). “Multiplexity, Generalized Exchange and Cooperation in Organizations: A Case Study.” Social Networks, 21(1), 67–90. doi:10.1016/S0378-8733(99)00002-7.

Pattison P, Wasserman S (1999). “Logit Models and Logistic Regressions for Social Networks: II. Multivariate Relations.” British Journal of Mathematical and Statistical Psychology, 52(2), 169–193.

Slaughter AJ, Koehly LM (2016). “Multilevel Models for Social Networks: Hierarchical Bayesian Approaches to Exponential Random Graph Modeling.” Social Networks, 44, 334–345. doi:10.1016/j.socnet.2015.11.002.

Stewart J, Schweinberger M, Bojanowski M, Morris M (2019). “Multilevel Network Data Facilitate Statistical Inference for Curved ERGMs with Geometrically Weighted Terms.” Social Networks, 59, 98–119. doi:10.1016/j.socnet.2018.11.003.

Vega Yon GG, Slaughter A, de la Haye K (2021). “Exponential Random Graph Models for Little Networks.” Social Networks, 64, 225–238. doi:10.1016/j.socnet.2020.07.005.

Zijlstra BJH, Van Duijn MAJ, Snijders TAB (2006). “The Multilevel p_2 Model: A Random Effects Model for the Analysis of Multiple Social Networks.” Methodology, 2(1), 42.

See Also

Useful links:

[Package ergm.multi version 0.2.1 Index]