Analysing networks of networks

We consider data with multiple observations or reports on a network in the case when these networks themselves are connected through some form of network ties. We could take the example of a cognitive social structure where there is another type of tie connecting the actors that provide the reports; or the study of interpersonal spillover effects from one cultural domain to another facilitated by the social ties. Another example is when the individual semantic structures are represented as semantic networks of a group of actors and connected through these actors’ social ties to constitute knowledge of a social group. How to jointly represent the two types of networks is not trivial as the layers and not the nodes of the layers of the reported networks are coupled through a network on the reports. We propose to transform the different multiple networks using line graphs, where actors are affiliated with ties represented as nodes, and represent the totality of the different types of ties as a multilevel network. This affords studying the associations between the social network and the reports as well as the alignment of the reports to a criterion graph. We illustrate how the procedure can be applied to studying the social construction of knowledge in local flood management groups. Here we use multilevel exponential random graph models but the representation also lends itself to stochastic actor-oriented models, multilevel blockmodels, and any model capable of handling multilevel networks.     

Discrete-Time Multilevel Hazard Analysis

Combining innovations in hazard modeling with those in multilevel modeling, we develop a method to estimate discrete-time multilevel hazard models. We derive the likelihood of and formulate assumptions for a discrete-time multilevel hazard model with time-varying covariates at two levels. We pay special attention to assumptions justifying the estimation method. Next, we demonstrate file construction and estimation of the models using two common software packages, HLM and MLN. We also illustrate the use of both packages by estimating a model of the hazard of contraceptive use in rural Nepal using time-varying covariates at both individual and neighborhood levels.     

Actors and networks as objects

This paper explores the application of two contemporary computational methods to the development of sociological theory. Specifically, we combine the methods of object-orientation with discrete event simulation. This approach has several advantages for constructing and evaluating dynamic social theories.In object-oriented program design, objects combine and integrate the traditional concepts of data structures and algorithms, the building blocks of structured programming. Algorithms associated with objects are called methods or member functions. Constructing social actors as objects involves defining both their data attributes and the methods associated with these attributes. We also treat a social network as a computational object. It has data types of nodes and ties. As an object, the network must also have methods that add and delete nodes and ties. Once a network exists, we can create other data types and methods that describe and analyze the network. For example, networks have in-degree and out-degree vectors, and measures of hierarchy. In principle, we can create attributes of networks for all of the structural measures we use to describe networks.We use actor and network objects in a discrete event simulation of a process of formation of dominance structures, exploring several dynamic variations of the underlying theoretical model.     

Reliability and validity of egocentered network data collected via web: A meta-analysis of multilevel multitrait multimethod studies

Our goal in this article is to assess reliability and validity of egocentered network data collected through web surveys using multilevel confirmatory factor analysis under the multitrait multimethod approach.In this study, we analyze a questionnaire of social support of Ph.D. students in three European countries. The traits used are the frequency of social contact questions. The methods used are web survey design variants.We consider egocentered network data as hierarchical; therefore, a multilevel analysis is required. Within and between-ego reliabilities and validities are defined and interpreted.Afterwards, we proceed to a meta-analysis of the results of the three countries where within and between-ego validities and reliabilities are predicted from survey design variables which have to do with question order (by questions or by alters), response category labels (end labels or all labels) and lay-out of the questionnaire (graphical display or plain text). Results show that question order by questions, all-labeled response categories and a graphical display lay-out with images lead to a better data quality. Our basic approach consisting on multilevel and meta-analysis can be applied to evaluate the quality of any type of egocentered network questionnaire, regardless of the data collection mode.     

Multilevel embeddedness: The case of the global fisheries governance complex

This paper explores how bilateral and multilateral clustering are embedded in a multilevel system of interdependent networks. We argue that in complex systems in which bilateral and multilateral relations are themselves interrelated, such as global fisheries governance, embeddedness cannot be reduced to unipartite or bipartite clustering but implicates multilevel closure. We elaborate expectations for ties’ multilevel embeddedness based on network theory and substantive considerations and explore them using a multilevel ERGM. We find states’ bilateral ties are embedded in their shared membership in multilateral fisheries agreements, which is itself clustered around foci represented by similar content and treaty secretariats.     

Using modern methods for missing data analysis with the social relations model: A bridge to social network analysis

Social network analysis identifies social ties, and perceptual measures identify peer norms. The social relations model (SRM) can decompose interval-level perceptual measures among all dyads in a network into multiple person- and dyad-level components. This study demonstrates how to accommodate missing round-robin data using Bayesian data augmentation, including how to incorporate partially observed covariates as auxiliary correlates or as substantive predictors. We discuss how data augmentation opens the possibility to fit SRM to network ties (potentially without boundaries) rather than round-robin data. An illustrative application explores the relationship between sorority members’ self-reported body comparisons and perceptions of friends’ body talk.     

Whom do we lose? The case of dissimilarity in personal networks

Previous research finds that individuals tend to form ties with similar others much more often than with dissimilar others. However, we know relatively little about tie loss and to what extent this is driven by (dis)similarity. In this paper, we argue that ties to persons who are dissimilar with regard to gender, age, ethnicity, and education are lost faster than ties to similar persons – and we test three explanations for this faster decay of ties with dissimilar others: lack of meeting opportunities, preferences for similarity, and lower network embeddedness. To test these explanations, we analysed two waves of the Survey on the Social Networks of the Dutch (SSND, 2007, 2014). These SSND-waves contain comprehensive longitudinal panel data on ego networks of 441 respondents, who were interviewed about a wide range of relationships, their alters’ sociodemographic characteristics, where and when they met their alters, as well as how and whether they maintain these relationships. We modelled tie loss by event history analyses. Results show that ties to persons who were dissimilar are more likely to be lost faster, and that tie loss occurs mostly in the early years of a relationship. However, meeting opportunities, preferences for similarity, and network embeddedness are unable to explain why ties to dissimilar others are lost faster. We conclude that dissimilarity is a powerful driver of tie loss, and that more arguments and research are needed to fully understand the underlying mechanisms.     

Keep around,drop, or revise? exploring what becomes of difficult ties in personal networks

Previous studies increasingly recognize the presence and impact of difficult individuals within personal networks. However, current research sheds little light on the turnover, retention, and change in quality of such difficult ties. The current study addresses this gap by focusing on two distinct forms of network change. We examine how role relationships, support exchange, relational homophily, and personal characteristics are associated with these processes. Data are drawn from three waves of the University of California Social Network Study (UCNets), a project containing comprehensive longitudinal data on ego networks among two adult cohorts. Findings indicate that over time, 34% of difficult ties re-appear in people’s networks as sources of aggravation; 26% of difficult ties are removed from the network; and 40% can no longer be verified as problematic network members. Most ties no longer deemed difficult are identified as providing one or more supportive functions. Multinomial multilevel models reveal that exchanging support tends to anchor difficult ties in the network. Kinship, meanwhile, plays a large role in whether difficult ties remain or get dropped. Personal characteristics such as gender, income, and relocation also play a role in these processes. Overall, we conclude that the turnover dynamics of difficult ties are similar to other ties, and the apparent change from negative to positive suggests that many ties hold ambivalent properties that make shedding such ties less common than may be expected.     

Logit Models for Affiliation Networks

Once confined to networks in which dyads could be reasonably assumed to be independent, the statistical analysis of network data has blossomed in recent years. New modeling and estimation strategies have made it possible to propose and evaluate very complex structures of dependency between and among ties in social networks. These advances have focused exclusively on one-mode networks—that is, networks of direct ties between actors. We generalize these models to affiliation networks, networks in which actors are tied to each other only indirectly through belonging to some group or event. We formulate models that allow us to study the (log) odds of an actor's belonging to an event (or an event including an actor) as a function of properties of the two-mode network of actors' memberships in events. We also provide illustrative analysis of some classic data sets on affiliation networks.     

The Statistical Evaluation of Social Network Dynamics

A class of statistical models is proposed for longitudinal network data. The dependent variable is the changing (or evolving) relation network, represented by two or more observations of a directed graph with a fixed set of actors. The network evolution is modeled as the consequence of the actors making new choices, or withdrawing existing choices, on the basis of functions, with fixed and random components, that the actors try to maximize. Individual and dyadic exogenous variables can be used as covariates. The change in the network is modeled as the stochastic result of network effects (reciprocity, transitivity, etc.) and these covariates. The existing network structure is a dynamic constraint for the evolution of the structure itself. The models are continuous-time Markov chain models that can be implemented as simulation models. The model parameters are estimated from observed data. For estimating and testing these models, statistical procedures are proposed that are based on the method of moments. The statistical procedures are implemented using a stochastic approximation algorithm based on computer simulations of the network evolution process.     

Modeling Repeatable Events Using Discrete‐Time Data: Predicting Marital Dissolution

I join two methodologies by illustrating the application of multilevel modeling principles to hazard‐rate models with an emphasis on procedures for discrete‐time data that contain repeatable events. I demonstrate this application using data taken from the 1995 National Survey of Family Growth (NSFG) to ascertain the relationship between multiple covariates and risk of subsequent marital dissolution. I consider both fixed‐ and random‐effects versions of the multilevel model, as well as a Generalized Estimating Equation alternative to estimating random effects. I compare results obtained from the various estimators, noting why differences occur, and recommend when to choose the various alternatives. I also provide a set of SAS and STATA programs that can be used to analyze the NSFG data.     

Vorwort

Although the concept of tie strength plausibly extends opinion leadership theory, prior studies have indicated that tie strength is of minor importance for opinion leadership. The paper argues that strong ties and weak ties play major roles in the process of opinion leadership that prior studies have insufficiently differentiated due to methodological limitations. Against this background, a methodologically more rigorous reassessment of the association between tie strength and opinion leadership is conducted. The reassessment centers on the combination of ego-centered network analyses with statistical methods of multilevel analysis. These are applied to original data of a study by Schenk (2006) on financial opinion leadership in Germany (n?=?10,100 survey respondents) which has previously been considered as an important indication for tie strength’s minor importance. Empirical results show that strong ties and weak ties are remarkably more important in the process of opinion leadership than previously known. Opinion leaders benefit from strong ties, because personal influence can be carried through them comparatively easily. By contrast, weak ties foster opinion leadership in a structural manner by catalyzing the influence that opinion leaders can exert through strong ties.     

A Multivariate, Multilevel Rasch Model with Application to Self–Reported Criminal Behavior

In studying correlates of social behavior, attitudes, and beliefs, a measurement model is required to combine information across a large number of item responses. Multiple constructs are often of interest, and covariates are often multilevel (e.g., measured at the person and neighborhood level). Some item–level missing data can be expected. This paper proposes a multivariate, multilevel Rasch model with random effects for these purposes and illustrates its application to self–reports of criminal behavior. Under assumptions of conditional independence and additivity, the approach enables the investigator to calibrate the items and persons on an interval scale, assess reliability at the person and neighborhood levels, study the correlations among crime types at each level, assess the proportion of variation in each crime type that lies at each level, incorporate covariates at each level, and accommodate data missing at random. Using data on 20 item responses from 2842 adolescents ages 9 to 18 nested within 196 census tracts in Chicago, we illustrate how to test key assumptions, how to adjust the model in light of diagnostic analyses, and how to interpret parameter estimates.     

Networks containing negative ties

Social network analysts have often collected data on negative relations such as dislike, avoidance, and conflict. Most often, the ties are analyzed in such a way that the fact that they are negative is of no consequence. For example, they have often been used in blockmodeling analyses where many different kinds of ties are used together and all ties are treated the same, regardless of meaning. However, sometimes we may wish to apply other network analysis concepts, such as centrality or cohesive subgroups. The question arises whether all extant techniques are applicable to negative tie data. In this paper, we consider in a systematic way which standard techniques are applicable to negative ties and what changes in interpretation have to be made because of the nature of the ties. We also introduce some new techniques specifically designed for negative ties. Finally we show how one of these techniques for centrality can be extended to networks with both positive and negative ties to give a new centrality measure (PN centrality) that is applicable to directed valued data with both positive and negative ties.     

Analyzing event stream dynamics in two-mode networks: An exploratory analysis of private communication in a question and answer community

Information about social networks can often be collected as event stream data. However, most methods in social network analysis are defined for static network snapshots or for panel data. We propose an actor oriented Markov process framework to analyze the structural dynamics in event streams. Estimated parameters are similar to what is known from exponential random graph models or stochastic actor oriented models as implemented in SIENA. We apply the methodology on a question and answer web community and show how the relevance of different kinds of one- and two-mode network structures can be tested using a new software.     

The Social Relationships and Social Support of Aging Mothers Whose Adult Daughters Are Mentally Ill

Guided by a conceptual framework highlighting multiple facets of social relationships and social support, this study examined the extent to which aging mothers of adult daughters with a serious mental illness were socially integrated with members of their network. It further examined the relational content of these mothers’ social ties as tangible or intangible support and the nature of their supportive exchanges with network members, particularly their adult daughters with mental illness. A structured face-to-face interview was conducted with 22 aging mothers of these adult daughters. Two methods of analysis were used to analyze data: counting and content analysis. Findings showed aging mothers of daughters with mental illness were socially integrated with relatives and nonrelatives, evidenced relational content of tangible and intangible support in their social ties and engaged in bidirectional and asymmetrical support exchanges with network members, including their daughters with mental illness. These findings suggest that social resources in the form of social relationships and support are embedded in the networks of aging mothers who have adult daughters with serious mental illness. Practitioners should assess support contributions to the aging mothers of adult daughters with serious mental illness from a wide range of social relationships including their daughters.     

Introduction to stochastic actor-based models for network dynamics

Stochastic actor-based models are models for network dynamics that can represent a wide variety of influences on network change, and allow to estimate parameters expressing such influences, and test corresponding hypotheses. The nodes in the network represent social actors, and the collection of ties represents a social relation. The assumptions posit that the network evolves as a stochastic process ‘driven by the actors’, i.e., the model lends itself especially for representing theories about how actors change their outgoing ties. The probabilities of tie changes are in part endogenously determined, i.e., as a function of the current network structure itself, and in part exogenously, as a function of characteristics of the nodes (‘actor covariates’) and of characteristics of pairs of nodes (‘dyadic covariates’). In an extended form, stochastic actor-based models can be used to analyze longitudinal data on social networks jointly with changing attributes of the actors: dynamics of networks and behavior.     

MULTILEVEL COVARIANCE STRUCTURE ANALYSIS BY FITTING MULTIPLE SINGLE-LEVEL MODELS

Data in social and behavioral sciences are often hierarchically organized. Multilevel statistical procedures have been developed to analyze such data while taking into account the dependence of observations. When simultaneously evaluating models at all levels, a significant statistic provides no information on the level at which the model is misspecified. Model misspecification can exist at one or several levels simultaneously. When one level is misspecified, the other levels may be affected even when they are correctly specified. Motivated by these observations, we propose to separate a multilevel covariance structure into multiple single-level covariance structure models and to fit these single-level models as in conventional covariance structure analysis. A procedure for segregating the multilevel model into single-level models is developed. Five test statistics for evaluating a model at each level are provided. Standard error formulas for the separate estimators are also provided, and their efficiency is compared to simultaneous estimators. Empirical and Monte Carlo results demonstrate the advantages of the segregated procedure over the simultaneous procedure. Computer programs that will allow the developed procedure to be used in practice are also presented.     

Information seeking in secondary schools: A multilevel network approach

In this study, we investigate information seeking interactions in secondary schools from a multilevel network approach. Based on network-related theories, we examine the facilitating role of formal subunits. We apply exponential random graph models for multilevel networks and summarize our findings by using a meta-analysis technique. Our results indicate that formal subunits (e.g. subject departments) can, to some extent, facilitate interactions, in loosely coupled organizations (e.g. secondary schools). Finally, this study shows that a multilevel network approach can provide a more informative representation of information seeking ties in knowledge-intensive organizations.     

Who “Fills in” for Siblings and How? A Multilevel Analysis of Personal Network Composition and Its Relationship to Sibling Size1

In the midst of widespread fertility decline, I examine the relationship between sibling number and support network composition using multilevel regression on data from 25 countries. A fundamental structural effect of having fewer siblings is that individuals have a smaller pool of available close‐kin alters with whom to construct support networks. Consequently, networks of people with fewer siblings should be composed of different sorts of relations. Results confirm that such compositional adjustment occurs in systematic ways. Compared to those with three or more siblings, adults with none to two siblings (as separate categories) are more likely to expect support from parents, extended kin, and close friends but not more likely to do so from spouses/partners and children. Single children are also more likely to include neighbors and have smaller‐sized and/or impersonal networks. These findings contradict the primacy of familial ties in social support networks. Moreover, adjustment of support networks towards nonsibling ties occurs in culturally expected ways. Those with fewer siblings are generally only more likely to turn to ties for the types of support typically associated with those relations—parents for instrumental and financial support and friends for emotional support. Single children, however, also violate institutionalized expectations of social support by turning to ties for a wider range of social support. The results suggest that continuing declines in fertility could bring about both reinforcement and rearticulation of the sociocultural framing of close personal relationships. Moreover, consistent with recent research, the results show that personal networks are influenced more by individual‐level than country‐level factors.