Models of dynamic networks—networks that evolve over time—have manifold applications. We develop a discrete time generative model for social network evolution that inherits the richness and flexibility of the class of exponential family random-graph models. The model—a separable temporal exponential family random-graph model—facilitates separable modelling of the tie duration distributions and the structural dynamics of tie formation. We develop likelihood-based inference for the model and provide computational algorithms for maximum likelihood estimation. We illustrate the interpretability of the model in analysing a longitudinal network of friendship ties within a school.
Model‐based clustering of semiparametric temporal exponential‐family random graph models
Model‐based clustering of time‐evolving networks has emerged as one of the important research topics in statistical network analysis. It is a fundamental research question to model time‐varying network parameters. However, due to difficulties in modelling functional network parameters, there is little progress in the current literature to model time‐varying network parameters effectively. In this work, we model network parameters as univariate nonparametric functions instead of constants. We effectively estimate those functional network parameters in temporal exponential‐family random graph models using a kernel regression technique and a local likelihood approach. Furthermore, we propose a semiparametric finite mixture of temporal exponential‐family random graph models by adopting finite mixture models, which simultaneously allows both modelling and detecting groups in time‐evolving networks. Also, we use a conditional likelihood to construct an effective model selection criterion and network cross‐validation to choose an optimal bandwidth. The power of our method is demonstrated in simulation studies and real‐world applications to dynamic international trade networks and dynamic arm trade networks.
more » « less- NSF-PAR ID:
- 10380544
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Stat
- Volume:
- 11
- Issue:
- 1
- ISSN:
- 2049-1573
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Low‐dimensional parametric models for network dynamics have been successful as inferentially efficient and interpretable tools for modelling network evolution but have difficulty in settings with strong time inhomogeneity (particularly when sharp variation in parameters is possible and covariates are limited). Here, we propose to address this problem via a novel family of block‐structured dynamic exponential‐family random graph models (ERGMs), where the time domain is divided into consecutive blocks and the network parameters are assumed to evolve smoothly within each block. In particular, we let the latent ERGM parameters follow a piecewise polynomial model with an unknown block structure (e.g., change points). We propose an iterative estimation procedure that involves estimating the block structure using trend filtering and fitting ERGMs for networks belonging to the same time block. We demonstrate the utility of the proposed approach using simulation studies and applications to interbank transaction networks and citations among political blogs over the course of an electoral cycle.
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Policy Points Promoting healthy public policies is a national priority, but state policy adoption is driven by a complex set of internal and external factors.
This study employs new social network methods to identify underlying connections among states and to predict the likelihood of new firearm‐related policy adoption given changes to this interstate network.
This approach could be used to assess the likelihood that a given state will adopt a specific new firearm‐related law and to identify points of influence that could either inhibit or promote wider diffusion of specific laws.
Context US states are largely responsible for the regulation of firearms within their borders. Each state has developed a different legal environment with regard to firearms based on different values and beliefs of citizens, legislators, governors, and other stakeholders. Predicting the types of firearm laws that states may adopt is therefore challenging.
Methods We propose a parsimonious model for this complex process and provide credible predictions of state firearm laws by estimating the likelihood they will be passed in the future. We employ a temporal exponential‐family random graph model to capture the bipartite state law–state network data over time, allowing for complex interdependencies and their temporal evolution. Using data on all state firearm laws over the period 1979–2020, we estimate these models’ parameters while controlling for factors associated with firearm law adoption, including internal and external state characteristics. Predictions of future firearm law passage are then calculated based on a number of scenarios to assess the effects of a given type of firearm law being passed in the future by a given state.
Findings Results show that a set of internal state factors are important predictors of firearm law adoption, but the actions of neighboring states may be just as important. Analysis of scenarios provide insights into the mechanics of how adoption of laws by specific states (or groups of states) may perturb the rest of the network structure and alter the likelihood that new laws would become more (or less) likely to continue to diffuse to other states.
Conclusions The methods used here outperform standard approaches for policy diffusion studies and afford predictions that are superior to those of an ensemble of machine learning tools. The proposed framework could have applications for the study of policy diffusion in other domains.
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De Vico Fallani, Fabrizio (Ed.)The exponential family random graph modeling (ERGM) framework provides a highly flexible approach for the statistical analysis of networks (i.e., graphs). As ERGMs with dyadic dependence involve normalizing factors that are extremely costly to compute, practical strategies for ERGMs inference generally employ a variety of approximations or other workarounds. Markov Chain Monte Carlo maximum likelihood (MCMC MLE) provides a powerful tool to approximate the maximum likelihood estimator (MLE) of ERGM parameters, and is generally feasible for typical models on single networks with as many as a few thousand nodes. MCMC-based algorithms for Bayesian analysis are more expensive, and high-quality answers are challenging to obtain on large graphs. For both strategies, extension to the pooled case—in which we observe multiple networks from a common generative process—adds further computational cost, with both time and memory scaling linearly in the number of graphs. This becomes prohibitive for large networks, or cases in which large numbers of graph observations are available. Here, we exploit some basic properties of the discrete exponential families to develop an approach for ERGM inference in the pooled case that (where applicable) allows an arbitrarily large number of graph observations to be fit at no additional computational cost beyond preprocessing the data itself. Moreover, a variant of our approach can also be used to perform Bayesian inference under conjugate priors, again with no additional computational cost in the estimation phase. The latter can be employed either for single graph observations, or for observations from graph sets. As we show, the conjugate prior is easily specified, and is well-suited to applications such as regularization. Simulation studies show that the pooled method leads to estimates with good frequentist properties, and posterior estimates under the conjugate prior are well-behaved. We demonstrate the usefulness of our approach with applications to pooled analysis of brain functional connectivity networks and to replicated x-ray crystal structures of hen egg-white lysozyme.more » « less
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Abstract Dynamic community detection provides a coherent description of network clusters over time, allowing one to track the growth and death of communities as the network evolves. However, modularity maximization, a popular method for performing multilayer community detection, requires the specification of an appropriate null network as well as resolution and interlayer coupling parameters. Importantly, the ability of the algorithm to accurately detect community evolution is dependent on the choice of these parameters. In functional temporal networks, where evolving communities reflect changing functional relationships between network nodes, it is especially important that the detected communities reflect any state changes of the system. Here, we present analytical work suggesting that a uniform null network provides improved sensitivity to the detection of small evolving communities in temporal networks with positive edge weights bounded above by 1, such as certain types of correlation networks. We then propose a method for increasing the sensitivity of modularity maximization to state changes in nodal dynamics by modelling self-identity links between layers based on the self-similarity of the network nodes between layers. This method is more appropriate for functional temporal networks from both a modelling and mathematical perspective, as it incorporates the dynamic nature of network nodes. We motivate our method based on applications in neuroscience where network nodes represent neurons and functional edges represent similarity of firing patterns in time. We show that in simulated data sets of neuronal spike trains, updating interlayer links based on the firing properties of the neurons provides superior community detection of evolving network structure when groups of neurons change their firing properties over time. Finally, we apply our method to experimental calcium imaging data that monitors the spiking activity of hundreds of neurons to track the evolution of neuronal communities during a state change from the awake to anaesthetized state.
