Micro‐Level Interpretation of Exponential Random Graph Models with Application to Estuary Networks

Advances in exponential random graph ( p*) models applied to a large social network

Synthetic power grids enable real-world energy system simulations and are crucial for algorithm testing, resilience assessment, and policy formulation. We propose a novel method for the generation of synthetic transmission power grids using exponential random graph (ERG) models. Our two main contributions are (1) the formulation of an ERG model tailored specifically for capturing the topological nuances of power grids and (2) a general procedure for estimating the parameters of such a model conditioned on working with connected graphs. From a modeling perspective, we identify edge counts per bus type and k-triangles as crucial topological characteristics for synthetic power-grid generation. From a technical perspective, we develop a rigorous methodology to estimate the parameters of an ERG constrained to the space of connected graphs. The proposed model is flexible, easy to implement, and successfully captures the desired topological properties of power grids. Published by the American Physical Society 2024

Background: The relationship between policy networks and policy development among local health departments (LHDs) is a growing area of interest to public health practitioners and researchers alike. In this study, we examine policy activity and ties between public health leadership across large urban health departments. Methods: This study uses data from a national profile of local health departments as well as responses from a survey sent to three staff members (local health official, chief of policy, chief science officer) in each of 16 urban health departments in the United States. Network questions related to frequency of contact with health department personnel in other cities. Using exponential random graph models, network density and centrality were examined, as were patterns of communication among those working on several policy areas using exponential random graph models. Results: All 16 LHDs were active in communicating about chronic disease as well as about use of alcohol, tobacco, and other drugs (ATOD). Connectedness was highest among local health officials (density = .55), and slightly lower for chief science officers (d = .33) and chiefs of policy (d = .29). After accounting for organizational characteristics, policy homophily (i.e., when two network members match on a single characteristic) and tenure were the most significant predictors of formation of network ties. Conclusion: Networking across health departments has the potential for accelerating the adoption of public health policies. This study suggests similar policy interests and formation of connections among senior leadership can potentially drive greater connectedness among other staff.

Exponential random graph models (ERGMs) provide conceptually elegant recipes for generating soft-constrained random graphs. This chapter begins by explaining the theory and describing how to properly specify an ERGM, including demonstrating Lagrange’s method to derive the values of the model parameters that correspond to the desired constraints. Three ERGMs, all with constraints depending linearly on the adjacency matrix, are solved exactly: the targeted total number of links, targeted individual node degrees and targeted number of two-way links in a directed graph. However, when the controlled features become more complicated, ERGMs have a tendency to produce graphs in extreme phases (very dense or very sparse). The two-star model and the Strauss model are worked through in detail using advanced techniques from statistical mechanics in order to analyze the phase transitions. The chapter closes with a discussion of the strengths and weaknesses of ERGMs as null models.

Exponential random graph models (ERGMs) are increasingly applied to observed network data and are central to understanding social structure and network processes. The chapters in this edited volume provide a self-contained, exhaustive account of the theoretical and methodological underpinnings of ERGMs, including models for univariate, multivariate, bipartite, longitudinal and social-influence type ERGMs. Each method is applied in individual case studies illustrating how social science theories may be examined empirically using ERGMs. The authors supply the reader with sufficient detail to specify ERGMs, fit them to data with any of the available software packages and interpret the results.

Social network analysis is a suite of approaches for exploring relational data. Two approaches commonly used to analyze animal social network data are permutation-based tests of significance and exponential random graph models. However, the performance of these approaches when analyzing different types of network data has not been simultaneously evaluated. Here we test both approaches to determine their performance when analyzing a range of biologically realistic simulated animal social networks. We examined the false positive and false negative error rate of an effect of a two-level explanatory variable (e.g., sex) on the number and combined strength of an individual’s network connections. We measured error rates for two types of simulated data collection methods in a range of network structures, and with/without a confounding effect and missing observations. Both methods performed consistently well in networks of dyadic interactions, and worse on networks constructed using observations of individuals in groups. Exponential random graph models had a marginally lower rate of false positives than permutations in most cases. Phenotypic assortativity had a large influence on the false positive rate, and a smaller effect on the false negative rate for both methods in all network types. Aspects of within- and between-group network structure influenced error rates, but not to the same extent. In "grouping event-based" networks, increased sampling effort marginally decreased rates of false negatives, but increased rates of false positives for both analysis methods. These results provide guidelines for biologists analyzing and interpreting their own network data using these methods.

Understanding the impact of engineering design on product competitions is imperative for product designers to better address customer needs and develop more competitive products. In this paper, we propose a dynamic network-based approach for modeling and analyzing the evolution of product competitions using multi-year buyer survey data. The product co-consideration network, formed based on the likelihood of two products being co-considered from survey data, is treated as a proxy of products’ competition relations in a market. The separate temporal exponential random graph model (STERGM) is employed as the dynamic network modeling technique to model the evolution of network as two separate processes: link formation and link dissolution. We use China’s automotive market as a case study to illustrate the implementation of the proposed approach and the benefits of dynamic network models compared to the static network modeling approach based on an exponential random graph model (ERGM). The results show that since STERGM takes preexisting competition relations into account, it provides a pathway to gain insights into why a product may maintain or lose its competitiveness over time. These driving factors include both product attributes (e.g., fuel consumption) as well as current market structures (e.g., the centralization effect). With the proposed dynamic network-based approach, the insights gained from this paper can help designers better interpret the temporal changes of product competition relations to support product design decisions.

By introducing the statistical network method of Exponential Random Graph Modelling (ERGM) we adhere to the call of Lucarelli and Brorström (2013) in The Marketing Review to think of new ways to analyse and make inferences about participatory processes of place branding. The ERGM is more suited for studying the interactive dynamics in participatory processes of place branding than traditional methods like case study research or regression analysis. ERGM is a relatively new methodology. Only a few scholars in the neurosciences, international relations, and political sciences have worked with the inferential social network method. We show that the new ERGM methodology helps to gain more insights into the social processes and tie-formation mechanisms which generate emergent interaction patterns in participatory processes of place branding. Hence, this article brings a novel methodology to the area of place branding.

Network data often contain sensitive relational information. One approach to protecting sensitive information while offering flexibility for network analysis is to share synthesized networks based on the information in originally observed networks. We employ differential privacy (DP) and exponential random graph models (ERGMs) and propose the DP-ERGM method to synthesize network data. We apply DP-ERGM to two real-world networks. We then compare the utility of synthesized networks generated by DP-ERGM, the DyadWise Randomized Response (DWRR) approach, and the Synthesis through Conditional distribution of Edge given nodal Attribute (SCEA) approach. In general, the results suggest that DP-ERGM preserves the original information significantly better than two other approaches in network structural statistics and inference for ERGMs and latent space models. Furthermore, DP-ERGM satisfies node DP through modeling the global network structure with ERGM, a stronger notion of privacy than the edge DP under which DWRR and SCEA operate.

The global trade network has significant importance in analyzing countries’ economic exchanges. Therefore, studying the global trade network and the factors influencing its structure is helpful for both economists and political decision makers. Putting these in mind, we try to analyze the global trade network from various viewpoints. We use the backbone filtering methods to construct a network of essential trades between countries. We analyze the structural, economic, geographical, political, and cultural factors and their effect on the global trade network using exponential random graph models. Additionally, we analyze the global trade network evolution using the separable temporal exponential random models. Our results show multiple structural, economic, geographical, and political factors affect the global trade network structure.

Ecological associations between hosts and parasites are influenced by host exposure and susceptibility to parasites, and by parasite traits, such as transmission mode. Advances in network analysis allow us to answer questions about the causes and consequences of traits in ecological networks in ways that could not be addressed in the past. We used a network-based framework (exponential random graph models or ERGMs) to investigate the biogeographic, phylogenetic and ecological characteristics of hosts and parasites that affect the probability of interactions among nonhuman primates and their parasites. Parasites included arthropods, bacteria, fungi, protozoa, viruses and helminths. We investigated existing hypotheses, along with new predictors and an expanded host-parasite database that included 213 primate nodes, 763 parasite nodes and 2319 edges among them. Analyses also investigated phylogenetic relatedness, sampling effort and spatial overlap among hosts. In addition to supporting some previous findings, our ERGM approach demonstrated that more threatened hosts had fewer parasites, and notably, that this effect was independent of hosts also having a smaller geographic range. Despite having fewer parasites, threatened host species shared more parasites with other hosts, consistent with loss of specialist parasites and threat arising from generalist parasites that can be maintained in other, non-threatened hosts. Viruses, protozoa and helminths had broader host ranges than bacteria, or fungi, and parasites that infect non-primates had a higher probability of infecting more primate species. The value of the ERGM approach for investigating the processes structing host-parasite networks provided a more complete view on the biogeographic, phylogenetic and ecological traits that influence parasite species richness and parasite sharing among hosts. The results supported some previous analyses and revealed new associations that warrant future research, thus revealing how hosts and parasites interact to form ecological networks.

In most European countries, data regarding movements of live animals are routinely collected and can greatly aid predictive epidemic modeling. However, the use of complete movements’ dataset to conduct policy-relevant predictions has been so far limited by the massive amount of data that have to be processed (e.g., in intensive commercial systems) or the restricted availability of timely and updated records on animal movements (e.g., in areas where small-scale or extensive production is predominant). The aim of this study was to use exponential random graph models (ERGMs) to reproduce, understand, and predict pig trade networks in different European production systems. Three trade networks were built by aggregating movements of pig batches among premises (farms and trade operators) over 2011 in Bulgaria, Extremadura (Spain), and Côtes-d’Armor (France), where small-scale, extensive, and intensive pig production are predominant, respectively. Three ERGMs were fitted to each network with various demographic and geographic attributes of the nodes as well as six internal network configurations. Several statistical and graphical diagnostic methods were applied to assess the goodness of fit of the models. For all systems, both exogenous (attribute-based) and endogenous (network-based) processes appeared to govern the structure of pig trade network, and neither alone were capable of capturing all aspects of the network structure. Geographic mixing patterns strongly structured pig trade organization in the small-scale production system, whereas belonging to the same company or keeping pigs in the same housing system appeared to be key drivers of pig trade, in intensive and extensive production systems, respectively. Heterogeneous mixing between types of production also explained a part of network structure, whichever production system considered. Limited information is thus needed to capture most of the global structure of pig trade networks. Such findings will be useful to simplify trade networks analysis and better inform European policy makers on risk-based and more cost-effective prevention and control against swine diseases such as African swine fever, classical swine fever, or porcine reproductive and respiratory syndrome.

Social network analysis has typically concerned analysis of one type of tie connecting nodes of the same type. It has however been recognised that people are connected through multiple types of ties and that people in addition are affiliated with multiple types of non-people nodes. Exponential random graph models (ERGM) is a family of statistical models for social networks that at this point allows for a number of different types of network data, including one-mode networks, bipartite networks, multiplex data, as well as multilevel network data. Multilevel networks have been proposed as a joint representation of associations between multiple types of entities or nodes, such as people and organization, where two types of nodes gives rise to three distinct types of ties. The typical roster data collection method may be impractical or infeasible when the node sets are hard to detect or define or because of the cognitive demands on respondents. Multilevel multilayered networks allow us to consider a multitude of different sources of data and to sample on different types of nodes and relations. We consider modelling multilevel multilayered networks using exponential random graph models and extend a recently developed Bayesian data-augmentation scheme to allow for partially missing data. We illustrate the proposed inference procedures for the case of multilevel snowball sampling and sampling with error based on the Noordin Top network.

The world is currently facing the worst migration crisis on record. Violent conflicts around the globe have forced over 65 million people to flee their homes, and receiving countries are struggling to support the massive influx of refugees. Lack of preparation and disorganization have only worsened the situation, and there is a pressing need to better understand refugee migration patterns in order to inform policy decisions and improve humanitarian efforts. In previous migration research, gravity models have been one of the classical methods for investigating determinants of migration, however this approach fails to take into account the interdependent nature of migration. To address this weakness, we apply statistical network analysis, which takes into account this interdependency, in order to quantify the influence of certain economic, political, social, and geographical factors on refugee migration. We create four different networks in order to investigate forced migration patterns surrounding four countries that are currently experiencing violent conflicts: Syria, Ukraine, the Democratic Republic of Congo (DRC), and Myanmar. Each network includes 12 nodes: the respective country of interest and the eleven countries hosting the most refugees from that country in 2015. Weighted directed edges represent the number of refugees from the origin country living in the host country in 2015. In order to quantify the influence of chosen factors on refugee migration in the context of the specific countries and conflicts of interest, we apply two different network models to each of the four networks —the exponential random graph model (ERGM) adapted for binary edges, and the generalized exponential random graph model (GERGM) adapted for weighted edges. Our results indicate that the ERGM is a poor choice for modeling this specific problem since the thresholding required to coerce weighted edges into binary edges results in a failure to capture the vastly different magnitudes of refugee migration present in the networks. The GERGM proved to be a much better model. Our final GERGM produced vastly different results for each of the four networks, suggesting that refugee migration patterns differ greatly for different countries and conflicts. Our results also suggest that the influence of determinants of migration on refugee flow patterns differs greatly for outmigration and in-migration. We speculate that determinants of migration have a greater influence on out migration than in-migration in the context of more recent conflicts. On the other hand, we speculate that determinants of migration have an influence on both out-migration and

Understanding user-to-User interaction on government microblogs: An exponential random graph model with the homophily and emotional effect