Inference in Curved Exponential Family Models for Networks

Hunter, David R.; Handcock, Mark S.

doi:10.1198/106186006x133069

Cited by 448 publications

(498 citation statements)

References 12 publications

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“…Although fitting exponential random graphs using this pseudolikelihood estimation is computationally relatively easy, the properties of the estimator are not well understood and the estimated θ are known to be inaccurate in many cases (Robins et al, 2007a). An alternative and more straightforward method to fit exponential random graph models is by means of Monte Carlo maximum likelihood estimation (Hunter and Handcock, 2006). This form of estimation simulates a distribution of random networks from a starting set of model parameters, θ 0 , and subsequently refines the parameter values by comparing the distribution of networks against the measured network x obs .…”

Section: Bayesian Exponential Random Graph Modelingmentioning

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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Section: Bayesian Exponential Random Graph Modelingmentioning

confidence: 99%

“…(3) and (4) dampens the effect of large changes in the statistics of higher k and was in this study fixed to 0.75 so that the model remains a regular exponential random graph model (Hunter and Handcock, 2006).…”

Section: Local Structure Definitionsmentioning

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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“…Markov chain Monte Carlo maximum likelihood estimation (MCMC-MLE) is the preferred method for estimating cross-sectional (single network at a single time period) ERGMs (Geyer and Thompson 1992;Hunter and Handcock 2006;Snijders 2002;Snijders et al 2006;van Duijn, Gile, and Handcock 2009). An alternative method of estimation is called maximum pseudolikelihood estimation (MPLE) (Hyvarinen 2006;Strauss and Ikeda 1990).…”

Section: Exponential Random Graph Modelsmentioning

confidence: 99%

Navigating the Range of Statistical Tools for Inferential Network Analysis

Cranmer

Leifeld

McClurg³

et al. 2016

American J Political Sci

174

158

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“…See the "Remark" in Section 3 of that paper to see why it is used rather than the version given in Snijders, Pattison, Robins, and Handcock (2006). The optional argument fixed indicates whether the scale parameter lambda is to be fit as a curved exponential-family model (see Hunter and Handcock 2006). The default is FALSE, which means the scale parameter is not fixed and thus the model is a CEF model.…”

Section: Parametric Formsmentioning

confidence: 99%

“…New specifications for non-degenerate models of triad-based clustering have been developed (Snijders et al 2006;Hunter and Handcock 2006) and used with some success Goodreau, Kitts, and Morris 2008b). These are dyad-based configurations, rather than node-based, and count the number of times that both nodes have a tie to a third node.…”

Section: Shared Partner Distributionsmentioning

confidence: 99%

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

Morris¹,

Handcock²,

Hunter³

2008

J. Stat. Soft.

331

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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Inference in Curved Exponential Family Models for Networks

Cited by 448 publications

References 12 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

Navigating the Range of Statistical Tools for Inferential Network Analysis

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

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