Exponential random graph models for multilevel networks

Modern multilevel analysis, whereby outcomes of individuals within groups take into account group membership, has been accompanied by impressive theoretical development (e.g. Kozlowski and Klein, 2000) and sophisticated methodology (e.g. Snijders and Bosker, 2012). But typically the approach assumes that links between groups are non-existent, and interdependence among the individuals derives solely from common group membership. It is not plausible that such groups have no internal structure nor they have no links between each other. Networks provide a more complex representation of interdependence. Drawing on a small but crucial body of existing work, we present a general formulation of a multilevel network structure. We extend exponential random graph models (ERGMs) to multilevel networks, and investigate the properties of the proposed models using simulations which show that even very simple meso effects can create structure at one or both levels. We use an empirical example of a collaboration network about French cancer research elites and their affiliations (0125 and 0120) to demonstrate that a full understanding of the network structure requires the cross-level parameters. We see these as the first steps in a full elaboration for general multilevel network analysis using ERGMs.     

k-means-based algorithm for blockmodeling linked networks

The paper presents a k-means-based algorithm for blockmodeling linked networks where linked networks are defined as a collection of one-mode and two-mode networks in which units from different one-mode networks are connected through two-mode networks. The reason for this is that a faster algorithm is needed for blockmodeling linked networks that can better scale to larger networks. Examples of linked networks include multilevel networks, dynamic networks, dynamic multilevel networks, and meta-networks. Generalized blockmodeling has been developed for linked/multilevel networks, yet the generalized blockmodeling approach is too slow for analyzing larger networks. Therefore, the flexibility of generalized blockmodeling is sacrificed for the speed of k-means-based approaches, thus allowing the analysis of larger networks. The presented algorithm is based on the two-mode k-means (or KL-means) algorithm for two-mode networks or matrices. As a side product, an algorithm for one-mode blockmodeling of one-mode networks is presented. The algorithm’s use on a dynamic multilevel network with more than 400 units is presented. A situation study is also conducted which shows that k-means based algorithms are superior to relocation algorithm-based methods for larger networks (e.g. larger than 800 units) and never much worse.     

Cluster analysis of multiplex networks: Defining composite network measures

Social relations are multiplex by nature: actors in a group are tied together by various types of relationships. To understand and explain group processes it is, therefore, important to study multiple social networks simultaneously in a given group. However, with multiplexity the complexity of data also increases. Although some multivariate network methods (e.g. Exponential Random Graph Models, Stochastic Actor-oriented Models) allow to jointly analyze multiple networks, modeling becomes complicated when it focuses on more than a few (2–4) network dimensions. In such cases, dimension reduction methods are called for to obtain a manageable set of variables. Drawing on existing statistical methods and measures, we propose a procedure to reduce the dimensions of multiplex network data measured in multiple groups. We achieve this by clustering the networks using their pairwise similarities, and constructing composite network measures as combinations of the networks in each resulting cluster. The procedure is demonstrated on a dataset of 21 interpersonal network dimensions in 18 Hungarian high-school classrooms. The results indicate that the network items organize into three well-interpretable clusters: positive, negative, and social role attributions. We show that the composite networks defined on these three relationship groups overlap but do not fully coincide with the network measures most often used in adolescent research, such as friendship and dislike.     

The co-evolution of gossip and friendship in workplace social networks

This study investigates the co-evolution of friendship and gossip in organizations. Two contradicting perspectives are tested. The social capital perspective predicts that friendship causes gossip between employees, defined as informal evaluative talking about absent colleagues. The evolutionary perspective reverses this causality claiming that gossiping facilitates friendship. The data comprises of three observations of a complete organizational network, allowing longitudinal social network analyses. Gossip and friendship are modeled as both explanatory and outcome networks with RSiena. Results support the evolutionary perspective in that gossip between two individuals increases the likelihood of their future friendship formation. However, individuals with disproportionately high gossip activity have fewer friends in the network, suggesting that the use of gossiping to attract friends has a limit.     

Multilevel models for social networks: Hierarchical Bayesian approaches to exponential random graph modeling

In many applications, researchers may be interested in studying patterns of dyadic relationships that involve multiple groups, with a focus on modeling the systematic patterns within groups and how these structural patterns differ across groups. A number of different models – many of them potentially quite powerful – have been developed that allow for researchers to study these differences. However, as with any set of models, these are limited in ways that constrain the types of questions researchers may ask, such as those involving the variance in group-wise structural features. In this paper, we demonstrate some of the ways in which multilevel models based on a hierarchical Bayesian approach might be used to further develop and extend existing exponential random graph models to address such constraints. These include random coefficient extensions to the standard ERGM for sets of multiple unconnected or connected networks and examples of multilevel models that allow for the estimation of structural entrainment among connected groups. We demonstrate the application of these models to real-world and simulated data sets.     

A model for the multiplex dynamics of two-mode and one-mode networks,with an application to employment preference,friendship, and advice

We propose a new stochastic actor-oriented model for the co-evolution of two-mode and one-mode networks. The model posits that activities of a set of actors, represented in the two-mode network, co-evolve with exchanges and interactions between the actors, as represented in the one-mode network. The model assumes that the actors, not the activities, have agency.     

Effects of competition on collective learning in advice networks

This paper looks at the effect of identifying alters as direct competitors on their selection as advisors. We differentiate between two kinds of competition: cut-throat vs friendly. We argue that, unlike cut-throat competition, friendly competition makes collective learning possible as a social process: when knowledge is built in interactions that are able to mitigate the negative effects of status competition and take place in homophilous social niches; and when the quality of this knowledge is guaranteed by members with epistemic status in these niches. Social niches and status facilitate advice seeking and collective learning because advice seeking between direct competitors is not obvious even when members have a common interest in sharing advice – a learning-related dilemma of collective action. We apply this reasoning to a network dataset combining identification of direct competitors and selection of advisors among the elite of cancer researchers in France. We use a procedure of multiplex stochastic block-modeling designed by Barbillon et al. (2015) to measure the effect of these identifications of direct competitors on the structure of the advice network. Results obtained with this dataset support our theory.     

The embeddedness of organizational performance: Multiple Membership Multiple Classification Models for the analysis of multilevel networks

We present a Multiple Membership Multiple Classification (MMMC) model for analysing variation in the performance of organizational sub-units embedded in a multilevel network. The model postulates that the performance of organizational sub-units varies across network levels defined in terms of: (i) direct relations between organizational sub-units; (ii) relations between organizations containing the sub-units, and (iii) cross-level relations between sub-units and organizations. We demonstrate the empirical merits of the model in an analysis of inter-hospital patient mobility within a regional community of health care organizations. In the empirical case study we develop, organizational sub-units are departments of emergency medicine (EDs) located within hospitals (organizations). Networks within and across levels are delineated in terms of patient transfer relations between EDs (lower-level, emergency transfers), hospitals (higher-level, elective transfers), and between EDs and hospitals (cross-level, non-emergency transfers). Our main analytical objective is to examine the association of these interdependent and partially nested levels of action with variation in waiting time among EDs – one of the most commonly adopted and accepted measures of ED performance. We find evidence that variation in ED waiting time is associated with various components of the multilevel network in which the EDs are embedded. Before allowing for various characteristics of EDs and the hospitals in which they are located, we find, for the null models, that most of the network variation is at the hospital level. After adding these characteristics to the model, we find that hospital capacity and ED uncertainty are significantly associated with ED waiting time. We also find that the overall variation in ED waiting time is reduced to less than a half of its estimated value from the null models, and that a greater share of the residual network variation for these models is at the ED level and cross level, rather than the hospital level. This suggests that the covariates explain some of the network variation, and shift the relative share of residual variation away from hospital networks. We discuss further extensions to the model for more general analyses of multilevel network dependencies in variables of interest for the lower level nodes of these social structures.     

Stakeholder influence,government power,and new opportunities for Chinese Internet companies: A multilevel network analysis of cross-sector networks

In recent decades, Chinese Internet companies have experienced exponential growth. As the Internet industry increasingly commends tremendous financial resources, they also face growing stakeholder expectations for corporate social responsibility (CSR) actions. One way through which Chinese Internet companies conduct CSR is by building cross-sectoral collaborations with nonprofit and nongovernmental organizations (NGOs) and governmental agencies. Aiming to understand Internet companies’ strategic relationship building on CSR issues, the researchers drew from stakeholder influence theory and research on a network approach to stakeholder influence, and applied multilevel network analysis to model three networks related to Chinese Internet companies’ CSR collaborations. Specifically, we found that power and urgency are significant predictors of the structure of Internet companies’ cross-sector CSR alliance network. Organizations affiliated or endorsed by the central Chinese government are the most desirable CSR stakeholders. Additionally, the study also revealed that for Internet companies, devoting their attention to Internet-related social issues could increase their desirability as strategic stakeholders from other sectors and among Internet companies.     

Random alliance networks

The morphological properties of kinship and marriage alliance networks, such as circuits, are typically considered as indicators of sociological phenomena — yet, they may also be partly coincidental. To assert the contribution of chance to these morphological features, we develop a standardized method where empirical alliance networks are compared with a random baseline. We apply our framework to a variety of empirical cases and show that some corpuses are remarkably well reconstructed by our random model, while others still feature significant divergencies which may be partly connected to field-based experience. On the whole, our approach may be used to scrutinize the matrimonial role of social groups as asserted by native or ethnological theory.     

Basic notions for the analysis of large two-mode networks

Many large real-world networks actually have a two-mode nature: their nodes may be separated into two classes, the links being between nodes of different classes only. Despite this, and despite the fact that many ad hoc tools have been designed for the study of special cases, very few exist to analyse (describe, extract relevant information) such networks in a systematic way. We propose here an extension of the most basic notions used nowadays to analyse large one-mode networks (the classical case) to the two-mode case. To achieve this, we introduce a set of simple statistics, which we discuss by comparing their values on a representative set of real-world networks and on their random versions. This makes it possible to evaluate their relevance in capturing properties of interest in two-mode networks.     

Dynamic exchange networks

Considering the theoretical and empirical untenability of static exchange networks, researchers have asked how exchange outcomes change when links are added or deleted. The present paper assesses the validity of seemingly sensible propositions concerning the effects of adding and deleting a link on (i) the payoffs of the actors in the link, (ii) the payoffs of actors in neighboring links and (iii) the variance of payoffs in the exchange network. The propositions were examined by applying expected value theory (EVT) to all 13,597 networks up to size 8. All propositions were falsified. Some falsifications of propositions could be attributed to EVTs prediction that actors use sub-optimal exchange relations. Since other well-known theories of exchange, like power-dependence theory and network exchange theory, also predict that actors use sub-optimal relations, these results are robust to selection of the theory of exchange.     

How interrank contacts benefit masters in a Buddhist monastery: Comparing the effects of ascribed Dharma titles and perceived status

Social interactions within modern Buddhist communities reflect two hierarchical rules. First, the Dharma titles ordained to specific masters affect how they interact with one another. Second, as more Buddhist organizations adapt to secular society, their members also network along nonreligious hierarchies. To capture how such changing social hierarchies shape masters’ social networks, this study examines the “status effects” embedded in social interactions within Foothills, a Buddhist monastery in Taiwan, based on contact diaries recorded over twenty-eight months. Multilevel analyses that focus on 102,254 contacts nested in 582 interpersonal ties among 53 Buddhist masters indicate that nearly all pairings of the ascribed Dharma titles had significant effects on emotional gain, and perceived status was not significant. In addition, contact with the highest ascribed title was clearly more important for instrumental gain, whereas the pattern of the perceived status effect was ambiguous. While the modern monastery has incorporated task-oriented work from secular society, the ordained titles continue to generate more profound effects than perceived status.     

Measuring knowledge and experience in two mode temporal networks

Two mode social network data consisting of actors attending events is a common type of social network data. For these kinds of data it is also common to have additional information about the timing or sequence of the events. We call data of this type two-mode temporal data. We explore the idea that actors attending events gain information from the event in two ways. Firstly the event itself may provide information or training; secondly, as co-attendees interact, they may pass on skills or information they have gleaned from other events. We propose a method of measuring these gains and demonstrate its usefulness using the classic Southern Women Data and a covert network dataset.     

Duality of departmental specializations and PhD exchange: A Weberian analysis of status in interaction using multilevel exponential random graph models (mERGM)

Weber proposes that lifestyle similarities preserve status by producing interactional closure between status similar actors. I investigate this theory on academic status hierarchies by conceptualizing sub-disciplinary specializations as departmental lifestyles and PhD exchange networks as interdepartmental interactions. Multilevel exponential random graph models (mERGM) reveal that the more specializations departments share, the more likely they are to exchange personnel. On the flip side, departments that do not share specializations are less likely to exchange doctoral candidates. Moreover, shared specializations are key determinants of closure between elite departments. These results support Weber’s theory and suggest that shared specializations preserve existing patterns of inequality between elite and non-elite departments.     

Clustering in weighted networks

In recent years, researchers have investigated a growing number of weighted networks where ties are differentiated according to their strength or capacity. Yet, most network measures do not take weights into consideration, and thus do not fully capture the richness of the information contained in the data. In this paper, we focus on a measure originally defined for unweighted networks: the global clustering coefficient. We propose a generalization of this coefficient that retains the information encoded in the weights of ties. We then undertake a comparative assessment by applying the standard and generalized coefficients to a number of network datasets.     

Emergent stakeholders: Using multi-stakeholder issue networks to gain legitimacy in corporate networks

Multi-stakeholder issue networks (MSINs) are models of cross-sector cooperation dedicated to resolving a specific issue. Research to date has not demonstrated the reasons for collaboration (Sun et al., 2021). This paper merges public relations and organizational communication scholarship to theorize that MSINs are one way that marginalized groups achieve salience in corporate networks. Stakeholder salience theory (SST) states that corporations balance stakeholder claims using a manager-defined calculus of legitimacy, urgency, and power. Because these attributes are defined by managers in relation to corporate interests, corporations deny legitimacy to historically, socially, and geographically marginalized groups. MSINs that emerge to highlight the needs of these marginalized groups decenter corporations by constraining corporations’ ability to ignore the needs of groups previously dismissed as nonstakeholders. As MSINs become more active within the corporate ecology, they further limit corporate activity and encourage management to not only to see the legitimacy, urgency, and power of emergent stakeholder claims, but to act upon them. Examples in case-based studies illustrate the emergent stakeholder concept.     

Beyond interviewer effects in the standardized measurement of ego-centric networks

The effects which interviewers exert on the collection of ego-centric networks have recently come into the focus of methodological considerations. Studies consistently show that the size of networks varies depending on the interviewer. We would like to expand on this research strand by pointing to different aspects which have so far gone unremarked in the discussion. First, size is mainly analysed as a network measure which is influenced during data collection, while other common measures such as network density or composition have not received sufficient consideration. Second, large-scale surveys using face-to-face interviews usually allocate interviewers to a single sampling point. Differences between sampling points (locality effects) are attributed to interviewer effects. Hence, we disentangle the effects of the locality and interviewer. Third, the discussion on interviewer effects often follows an “actor-oriented” consideration of how data collection situations are structured by interviewers. Expanding this approach from a relational perspective, we consider the relationship between the interviewers and respondents and whether this relationship influences the collection of network data. To test our hypotheses about the influence of interviewers, the locality and the interviewer-respondent relationship on different network measures, we use data from the 2010 German General Social Survey (n = 2827 respondents, n = 220 interviewers). The multilevel analyses show that the relationship between the interviewer and the respondent is not very relevant. Furthermore, the analyses show that interviewers have an influence on the network size but not on measures of their composition. However, evidence on the prevalence of locality or interviewer effects is mixed. Finally, homophilous interviewer-respondent relationships have very little effect on network characteristics. We find evidence of training and fatigue effects on network size. However, much of the variation in network size caused by the interviewer still remains unexplained. We draw conclusions on how to organize interview situations in surveys.