<b>ergm</b>: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks

Hunter, David R.; Handcock, Mark S.; Butts, Carter T.; Goodreau, Steven M.; Morris, Martina

doi:10.18637/jss.v024.i03

Cited by 863 publications

(767 citation statements)

References 35 publications

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“…A large set of local structures are provided in the literature to use with exponential random graph models (Hunter et al, 2009). Two previous studies (Simpson et al, , 2012 .…”

Section: Local Structure Definitionsmentioning

confidence: 99%

“…We then compared the observed network with the simulated network based on three global descriptive network characteristics: degree (connectivity), geodic distance (shortest path) and edge-wise shared partners (clustering) from the Bergm package (Caimo and Friel, 2014). Additionally, we implemented the triad census (i.e., subset of motifs), that determines the contributions, as a probability, of one, two or three connections between all possible node triples (Hunter et al, 2009;Morris et al, 2008), and compared these contributions between the observed and simulated networks.…”

Section: Goodness-of-fitmentioning

confidence: 99%

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Bayesian exponential random graph modeling of whole-brain structural networks across lifespan

Sinke

Dijkhuizen

Caimo³

et al. 2016

NeuroImage

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a b s t r a c t a r t i c l e i n f oDescriptive neural network analyses have provided important insights into the organization of structural and functional networks in the human brain. However, these analyses have limitations for inter-subject or between-group comparisons in which network sizes and edge densities may differ, such as in studies on neurodevelopment or brain diseases. Furthermore, descriptive neural network analyses lack an appropriate generic null model and a unifying framework. These issues may be solved with an alternative framework based on a Bayesian generative modeling approach, i.e. Bayesian exponential random graph modeling (ERGM), which explains an observed network by the joint contribution of local network structures or features (for which we chose neurobiologically meaningful constructs such as connectedness, local clustering or global efficiency). We aimed to identify how these local network structures (or features) are evolving across the life-span, and how sensitive these features are to random and targeted lesions. To that aim we applied Bayesian exponential random graph modeling on structural networks derived from whole-brain diffusion tensor imaging-based tractography of 382 healthy adult subjects (age range: 20.2-86.2 years), with and without lesion simulations. Networks were successfully generated from four local network structures that resulted in excellent goodness-of-fit, i.e. measures of connectedness, local clustering, global efficiency and intrahemispheric connectivity. We found that local structures (i.e. connectedness, local clustering and global efficiency), which give rise to the global network topology, were stable even after lesion simulations across the lifespan, in contrast to overall descriptive network changes -e.g. lower network density and higher clustering -during aging, and despite clear effects of hub damage on network topologies. Our study demonstrates the potential of Bayesian generative modeling to characterize the underlying network structures that drive the brain's global network topology at different developmental stages and/or under pathological conditions.

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“…A large set of local structures are provided in the literature to use with exponential random graph models (Hunter et al, 2009). Two previous studies (Simpson et al, , 2012 .…”

Section: Local Structure Definitionsmentioning

confidence: 99%

Section: Goodness-of-fitmentioning

confidence: 99%

Bayesian exponential random graph modeling of whole-brain structural networks across lifespan

Sinke

Dijkhuizen

Caimo³

et al. 2016

NeuroImage

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“…For details about interpreting the output above, see similar models in other articles in this journal volume -e.g., model3 in Hunter et al (2008b) or model2 in Goodreau et al (2008a) -and read the descriptions of the edges and nodematch terms below.…”

Section: Terms Used In Exponential-family Random Graph Modelsmentioning

confidence: 99%

“…These terms are used in calls to the ergm function, to fit an ergm model; calls to simulate, to simulate networks from an ergm model fit; and calls to summary, to obtain measurements of network statistics on a dataset. See Hunter et al (2008b) and Goodreau, Handcock, Hunter, Butts, and Morris (2008a) for examples of these functions. The terms described below are also available to the other packages in the statnet suite.…”

Section: Introductionmentioning

confidence: 99%

Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects

Morris¹,

Handcock²,

Hunter³

2008

J. Stat. Soft.

Self Cite

336

270

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Exponential-family random graph models (ERGMs) represent the processes that govern the formation of links in networks through the terms selected by the user. The terms specify network statistics that are sufficient to represent the probability distribution over the space of networks of that size. Many classes of statistics can be used. In this article we describe the classes of statistics that are currently available in the ergm package. We also describe means for controlling the Markov chain Monte Carlo (MCMC) algorithm that the package uses for estimation. These controls affect either the proposal distribution on the sample space used by the underlying Metropolis-Hastings algorithm or the constraints on the sample space itself. Finally, we describe various other arguments to core functions of the ergm package.

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“…that enable the fitting of ERGMs (see Table 1). Basic ERGMs, including for bipartite 236 networks, can be fitted using the package ergm Hunter et al, 2008). 237 We provide an example demonstrating the model output, convergence diagnostics and These diverse applications demonstrate that ERGMs can be used to model affiliative 294 and antagonistic networks, to analyse differences within and among-populations, and to 295 understand dyadic and whole network-level processes.…”

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confidence: 99%

Understanding animal social structure: exponential random graph models in animal behaviour research

Silk

Fisher

2017

Animal Behaviour

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4The social environment is a pervasive influence on the ecological and evolutionary dynamics 5 of animal populations. Recently, social network analysis has provided an increasingly 6 powerful and diverse toolset to enable animal behaviour researchers to quantify the social 7 environment of animals and the impact that it has on ecological and evolutionary processes. 8 However, there is considerable scope for improving these methods further. We outline an 9 approach specifically designed to model the formation of network links, exponential random 10 graph models (ERGMs), which have great potential for modelling animal social structure. 11ERGMs are generative models that treat network topology as a response variable. This 12 makes them ideal for answering questions related directly to how and why social 13 associations or interactions occur, from the modelling of population-level transmission, 14 through within-group behavioural dynamics to social evolutionary processes. We discuss 15 how ERGMs have been used to study animal behaviour previously, and how recent 16 developments in the ERGM framework can increase the scope of their use further. We also 17 highlight the strengths and weaknesses of this approach relative to more conventional 18 methods, and provide some guidance on the situations and research areas in which they can 19 be used appropriately. ERGMs have the potential to be an important part of an animal 20 behaviour researcher's toolkit and fully integrating them into the field should enhance our 21 ability to understand what shapes animal social interactions, and identify the underlying 22 processes that lead to the social structure of animal populations. Randomisation-based analyses have many strengths, especially in animal social 64 network studies in which complex sampling issues often have to be controlled for (Farine & 65 Whitehead, 2015). However, using this approach controls for, rather than models, the 66 biological processes, such as site use, that generate network structure. Often these 67 processes can be directly of interest, yet treating them as a nuisance factor prevents us 68 from more fully understanding the role they play in shaping animal social systems. In this article we review the use of one of the more highly developed and flexible of 86 these statistical network approaches, exponential random graph models (ERGMs) (Lusher et 87 al., 2013;Robins et al., 2007). We start by providing a basic verbal description of the 88 modelling approach, illustrating some of the key aspects of model fitting with a toy 89 example. We then describe the previous uses of these models in the study of animal social 90 behaviour, before going on to discuss its strengths and weaknesses as a method to model 91 animal social networks and how these models can be extended to understand more 92 complex network datasets that are increasingly used to study animal behaviour (temporally 93 dynamic, bipartite and multilayer networks). Finally, we set an agenda for future research:

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ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks

Cited by 863 publications

References 35 publications

Bayesian exponential random graph modeling of whole-brain structural networks across lifespan

Bayesian exponential random graph modeling of whole-brain structural networks across lifespan

Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects

Understanding animal social structure: exponential random graph models in animal behaviour research

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