Stochastic a posteriori blockmodels: Construction and assessment

In 1983, Holland, Laskey, and Leinhardt, using the ideas of Holland and Leinhardt, and Fienberg and Wasserman, introduced the notion of a stochastic blockmodel. The mathematics for stochastic a priori blockmodels, in which exogenous actor attribute data are used to partition actors independently of any statistical analysis of the available relational data, have been refined by several researchers and the resulting models used by many. Attempts to simultaneously partition actors and to perform relational data analyses using statistical methods that yield stochastic a posteriori blockmodels are still quite rare. In this paper, we discuss some old suggestions for producing such posterior blockmodels, and comment on other new suggestions based on multiple comparisons of model parameters, log-linear models for ordinal categorical data, and correspondence analysis. We also review measures for goodness-of-fit of a blockmodel, and we describe a natural approach to this problem using likelihood-ratio statistics generated from a popular model for relational data.     

A p* primer: logit models for social networks

A major criticism of the statistical models for analyzing social networks developed by Holland, Leinhardt, and others [Holland, P.W., Leinhardt, S., 1977. Notes on the statistical analysis of social network data; Holland, P.W., Leinhardt, S., 1981. An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association. 76, pp. 33–65 (with discussion); Fienberg, S.E., Wasserman, S., 1981. Categorical data analysis of single sociometric relations. In: Leinhardt, S. (Ed.), Sociological Methodology 1981, San Francisco: Jossey-Bass, pp. 156–192; Fienberg, S.E., Meyer, M.M., Wasserman, S., 1985. Statistical analysis of multiple sociometric relations. Journal of the American Statistical Association, 80, pp. 51–67; Wasserman, S., Weaver, S., 1985. Statistical analysis of binary relational data: Parameter estimation. Journal of Mathematical Psychology. 29, pp. 406–427; Wasserman, S., 1987. Conformity of two sociometric relations. Psychometrika. 52, pp. 3–18] is the very strong independence assumption made on interacting individuals or units within a network or group. This limiting assumption is no longer necessary given recent developments on models for random graphs made by Frank and Strauss [Frank, O., Strauss, D., 1986. Markov graphs. Journal of the American Statistical Association. 81, pp. 832–842] and Strauss and Ikeda [Strauss, D., Ikeda, M., 1990. Pseudolikelihood estimation for social networks. Journal of the American Statistical Association. 85, pp. 204–212]. The resulting models are extremely flexible and easy to fit to data. Although Wasserman and Pattison [Wasserman, S., Pattison, P., 1996. Logit models and logistic regressions for social networks: I. An introduction to Markov random graphs and p*. Psychometrika. 60, pp. 401–426] present a derivation and extension of these models, this paper is a primer on how to use these important breakthroughs to model the relationships between actors (individuals, units) within a single network and provides an extension of the models to multiple networks. The models for multiple networks permit researchers to study how groups are similar and/or how they are different. The models for single and multiple networks and the modeling process are illustrated using friendship data from elementary school children from a study by Parker and Asher [Parker, J.G., Asher, S.R., 1993. Friendship and friendship quality in middle childhood: Links with peer group acceptance and feelings of loneliness and social dissatisfaction. Developmental Psychology. 29, pp. 611–621].     

Measurement quality issues in dyadic models of relationships

Interpersonal relationships are an important and integral part of numerous social science research agendas. Analytical tools have been created in the last 10 years that model dyadic interactions. In particular, this article focuses on the dyadic models of Fienberg and Wasserman [Fienberg, S.E., Wasserman, S., 1981. Categorical data analysis of single sociometric relations. In: Leinhardt, S. (Ed.), Sociological Methodology. Jossey-Bass, San Francisco.], Holland and Leinhardt [Holland, P.W., Leinhardt, S., 1981. An exponential family of probability densities for directed graphs. Journal of the American Statistical Association 76 (1981) 33–51.], Iacobucci and Wasserman [Iacobucci, D., Wasserman, S., 1988. A general framework for the statistical analysis of sequential dyadic interaction data. Psychological Bulletin 103 (1988) 379–390.] and Wasserman and Iacobucci [Wasserman, S., Iacobucci, D., 1986. Statistical analysis of discrete relational data. British Journal of Mathematical and Statistical Psychology 39 (1986) 41–64.]. However, measurement issues like reliability and validity, as discussed by Allen and Yen [Allen, M.J., Yen, W.M., 1979. Introduction to Measurement Theory. Brooks/Cole, Monterey, CA, 1979.], Nunnally [Nunnally, J., 1978. Psychometric Theory, 2nd edn. McGraw-Hill, New York, NY, 1978.] and Uebersax [Uebersax, J.S., 1988. Validity inferences from interobserver agreement. Psychological Bulletin 104 (1988) 405–416.], have not been considered in conjunction with these models, and little is known about the empirical performance of the dyadic models under sub-optimal measurement quality conditions. We offer two essential approaches to ascertaining the level of measurement error in the observed indicators of social ties and relationships. The first approach combines latent class and social network models in one integrated framework and allows for the simultaneous study of measurement and dyadic structural issues. The second approach is an alternative that may be more useful to social science researchers, both because the method is more accessible and because researchers could apply the techniques to data they have already partially analyzed. This approach is a two-staged procedure whereby in the first stage, a probability model based on latent class analysis is estimated which provides an indication of the measurement quality in the data. In the second stage, traditional social network models are estimated. To investigate the implications of different levels of measurement error for interpreting the nature of the network ties and the dyadic parametric performance, we also designed a Monte Carlo experiment. Measurement error is simulated as the likelihood of a binary relational choice (for simplicity) being inaccurately classified, where incorrect diagnoses can result from poor interitem agreement (i.e., unreliability) or poor interrater agreement. The simulation can be used by researchers in combination with the two-stage approach. The results of the simulation provide guidelines for situations when social network models can withstand a reasonable degree of sub-optimal measurement quality and highlight adverse conditions which can significantly affect the performance of the modeling approach. Further, the simulation shows that sample size assists in reducing the chances of making Type II errors, but it does not compensate for biases in parameter estimates in the presence of increasing error. Finally, the measurement and dyadic analytical methods are applied to a real dataset describing interorganizational relational activity using multiple raters. Recommendations are offered to guide the researcher in making decisions about research design when using dyadic models.     

Acyclic triplets and social structure in complete signed digraphs

This report is a study of the relationship between certain systems of signed acyclic triplets representing relationships among three actors and the properties of the graphs which they generate. It is a method of investigating macro-structure based on micro-structural properties. The motivation stems from the work of Cartwright and Harary, Davis, Leinhardt and Holland on affective ties, which we generalize. After showing the connections between our approach and theirs, we develop some new models that go beyond affect and positive sentiment.     

Centrality and power revisited: actor success in group decision making

For many years, network analysts viewed positional centrality as a source of social power. More recently, laboratory studies of exchange networks have called the centrality–power link into question: under zero-sum exchange conditions, the ability of certain actors to directly exploit others has been found to account for power independent of actors' centrality. But most observers believe that in non-zero-sum communication networks, centrality should positively affect power. In this study we examine the effect of centrality on power in a communication network involving group voting on political issues. Using a model in which actors' votes are determined by the strength of their initial positions and the social pressures to which they are subjected, we conduct computer simulations to examine the extent to which actors in various network positions achieve favorable political outcomes. Our findings indicate that the link between centrality and power is highly contingent on the structure of the network. In networks with a central actor and an odd number of subgroups, central actors fail to dominate. In fact, in these networks, when peripheral actors are able to directly influence one another, the central actor becomes the least powerful in the network. In networks with a central actor and an even number of subgroups, however, the central actor dominates even in situations with connected peripherals. The highly contingent effect of centrality on power accords with the findings of exchange theorists who have studied power under zero-sum conditions. This raises questions about the nature of the distinction between communication and exchange networks.     

On the core of characteristic function games associated with exchange networks

An exchange network is a social system in which the actors gain valued resources from bilateral transactions, but an opportunity to negotiate a deal is given only to those pairs of actors whose positions are tied with each other in a fixed communication network. A transaction consists in a mutually agreed-on division of a resource pool assigned to a network line. An additional constraint imposed on such a network restricts the range of transaction sets which may happen in a single negotiation round to those consistent with a given “exchange regime.” Under the one-exchange regime every actor is permitted to make no more than one deal per round. Bienenstock and Bonacich [Bienenstock, E.J., Bonacich, P., 1992. The core as a solution to exclusionary networks. Social Networks 14, 231–243] proposed to represent a one-exchange network with an n-person game in characteristic function form. The aim of this paper is to develop a mathematical theory of games associated with homogenous one-exchange networks (network homogeneity means that all lines are assigned resource pools of the same size). The focus is on the core, the type of solution considered most important in game theory. In particular, all earlier results obtained by Bonacich are re-examined and there is given a new graph-theoretic necessary and sufficient condition for the existence of nonempty core for the game representing a homogenous one-exchange network.     

Structural holes and bridging in two-mode networks

Social networks are often structured in such a way that there are gaps, or “structural holes,” between regions. Some actors are in the position to bridge or span these gaps, giving rise to individual advantages relating to brokerage, gatekeeping, access to non-redundant contacts, and control over network flows. The most widely used measures of a given actor’s bridging potential gauge the extent to which that actor is directly connected to others who are otherwise not well connected to each other. Unfortunately, the measures that have been developed to identify structural holes cannot be adapted directly to two-mode networks, like individual-to-organization networks. In two-mode networks, direct contacts cannot be directly connected to each other by definition, making the calculation of redundancy, effective size, and constraint impossible with conventional one-mode methods. We therefore describe a new framework for the measurement of bridging in two-mode networks that hinges on the mathematical concept of the intersection of sets. An actor in a given node class (“ego”) has bridging potential to the extent that s/he is connected to actors in the opposite node class that have unique profiles of connections to actors in ego’s own node class. We review the relevant literature pertaining to structural holes in two-mode networks, and we compare our primary bridging measure (effective size) to measures of bridging that result when using one-mode projections of two-mode data. We demonstrate the results of applying our approach to empirical data on the organizational affiliations of elites in a large U.S. city.     

Evaluating heterogeneous brokerage: New conceptual and methodological approaches and their application to multi-level environmental governance networks

We present two new approaches for assessing the relative contributions of different types of actors to heterogeneous brokerage in networks. These approaches distinguish between the tendency of certain types of actors to (1) mediate between dissimilar actors (heterogeneous brokerage “activity”), and (2) be the sole mediators between dissimilar actors (“exclusivity”). We present methods for implementing these approaches, using baseline models of tie formation and node removal, respectively. To illustrate the value of both approaches, independently and in combination, we apply them to evaluate horizontal and vertical heterogeneous brokerage in two environmental governance networks. Our analysis reveals certain types of actors with high heterogeneous brokerage activity but low exclusivity (and vice versa), which has important implications for governance processes and outcomes. Likewise, results show many similarities across the evaluated networks, but also some notable differences, suggesting that the incentives and constraints for heterogeneous brokerage vary not only by actor type, but also by network-level contextual differences.     

Does Actor Perspective Matter? A Case Study of Designing Intervention for Small‐Scale Palm Oil Production Enterprises in Kwaebibirem District of Ghana

Despite the fact that the government of Ghana imports the bulk of its industrial palm oil needs, it still fails to give assistance to about 80 percent of small‐scale producers to enhance development in the industry. To design interventions that will be sustainable for and beneficial to these producers, it is important to understand their perspectives first, so as not to “fix development” for them. This case study in the Kwaebibirem District of Ghana uses an actor‐oriented approach to understand the dynamics in the palm oil enterprise (kramer). Improvements in the kramer evidently evolve from the actors’ own agency. Any intervention for development should therefore first understand the dynamics of the kramer as a social field, and take this perspective as a bottom‐up starting point. This article is divided into six sections; the first section is an introduction, while the second describes our methodology. We next outline our conceptual approach, followed by an analysis of experiences of actors and their interactions. We then describe the resource flows and their interrelationships, including the power relations at play in the kramer networks. Finally, we conclude by drawing lessons on the relevance of an actor perspective in designing a learning intervention for processors, scientists, and extensionists.     

Missing data in networks: exponential random graph (p1) models for networks with non-respondents

Survey studies of complete social networks often involve non-respondents, whereby certain people within the “boundary” of a network do not complete a sociometric questionnaire—either by their own choice or by the design of the study—yet are still nominated by other respondents as network partners. We develop exponential random graph (p¹) models for network data with non-respondents. We model respondents and non-respondents as two different types of nodes, distinguishing ties between respondents from ties that link respondents to non-respondents. Moreover, if we assume that the non-respondents are missing at random, we invoke homogeneity across certain network configurations to infer effects as applicable to the entire set of network actors. Using an example from a well-known network dataset, we show that treating a sizeable proportion of nodes as non-respondents may still result in estimates, and inferences about structural effects, consistent with those for the entire network.If, on the other hand, the principal research focus is on the respondent-only structure, with non-respondents clearly not missing at random, we incorporate the information about ties to non-respondents as exogenous. We illustrate this model with an example of a network within and between organizational departments. Because in this second class of models the number of non-respondents may be large, values of parameter estimates may not be directly comparable to those for models that exclude non-respondents. In the context of discussing recent technical developments in exponential random graph models, we present a heuristic method based on pseudo-likelihood estimation to infer whether certain structural effects may contribute substantially to the predictive capacity of a model, thereby enabling comparisons of important effects between models with differently sized node sets.     

Assessing the Effectiveness of Faith-Based Programs

Abstract

The policy debate over faidibased initiatives has prompted calls for comparative effectiveness research. Drawing examples from an evaluation of California's Community and Faith-based Initiative (CFBI), we illustrate a research strategy that takes local networks as the primary unit of analysis. This approach focuses on understanding the roles different organizations play within local service delivery networks, and on analyzing how local actors coordinate services to affect participant, organization, and system outcomes. The network perspective casts new light on policy options, and suggests that caution is necessary when using administrative data to interpret program effectiveness.     

Local mobilisations and the formation of environmental networks in a democratizing Tunisia

ABSTRACT

This study examines the environmental protests that occurred in Tunisia after the 2011 uprisings. It analyses the factors underpinning the rise of the environmental networks during the period of transition (2011–2014). It details the mobilising strategies that were crucial for the networks’ growth or survival during this period of institutional instability. The study shows how networks leaders were able to bring together social and political actors from different backgrounds and ideological orientations. It is argued that the ability of networks to develop new distinctive collective identities was crucial for network sustainability. Those networks and actors who did not develop new clearly defined environmental identities and continued to rely importantly on pre-existing (authoritarian) structures and practices were more negatively impacted by ideological cleavages and political calculations. Empirically, the contribution builds on interviews and observations, as well as documents collected from Tunisian municipalities between 2013 and 2015. Conceptually, the research proposes a bottom-up perspective that highlights the interplay between micro- and macro-dynamics and strategies during a political transition. The analysis details the actors’ capacity to build alliances via interpersonal relations at the micro level, and their strategies to engage with institutional actors and processes.     

Centrality in affiliation networks

This paper discusses the conceptualization, measurement, and interpretation of centrality in affiliation networks. Although centrality is a well-studied topic in social network analysis, and is one of the most widely used properties for studying affiliation networks, virtually all discussions of centrality and centralization have concerned themselves with one-mode networks. Bonacich's work on simultaneous group and individual centralities is a notable exception (Social Networks, 1991, 13, 155–168). I begin by outlining the distinctive features of affiliation networks and describe four motivations for centrality indices in affiliation networks. I then consider properties of some existing centrality indices for affiliation networks, including the relationship between centralities for actors and events in these networks, and present a new conceptualization of centrality that builds on the formal properties of affiliation networks and captures important theoretical insights about the positions of actors and events in these networks. These centralities are then illustrated on Galaskiewicz's data on club and board memberships of a sample of corporate executive officers (Social Organization of an Urban Grants Economy. New York: Academic Press, 1985). The conclusion to this paper discusses strengths and weaknesses of centrality indices when applied to affiliation networks.     

Does the β-measure make empirical sense? A vignette experiment on humans’ judgment of social dominance

Dominance hierarchies play an important role in governing the social interactions of humans and other species of social animals. In a social group, dominance relations can be inferred from the directed network of matchups between actors. Methodologists have proposed different ways to measure social dominance in directed networks. One such measure, the “β-measure” (van den Brink and Gilles, 2000), emphasizes the quality of defeated opponents in a way that an actor is seen as being more dominant when s/he defeats opponents who are more rarely defeated. While insightful in theory, the validity of the measure in people’s perception remains questionable, considering the cognitive complexity imposed by this measure, compared to a simpler measure that merely counts the number of defeated opponents. We conducted a vignette experiment with human subjects (professional athletes) to test their judgments of the dominance relation in a hypothetical tournament. Fitting our parametric model to peoples’ evaluations in the experiment, we found strong evidence in support of the β-measure: Although, in general, contestants who win more in the tournament are regarded as being more dominant, the contents of the winning records matter, such that those who beat more victorious opponents are further regarded as more dominant than those who defeat less victorious opponents. We also found a gender difference, in that men have a stronger propensity than women to adopt the β-measure when judging social dominance.     

Commodities in action: measuring embeddedness and imposing values

Recent approaches in political economy look at the effects of technology and social values on economic action. Combining these approaches with those of economic anthropologists, this article poses that the way the economy is instituted can be understood by looking at reasons actors have for participating in actor‐networks of production, distribution and consumption. Using the author's research on American recycling, this article first shows that much of the‘making’or instituting of the economy happens outside the market, through political machinations, contracts and standards. Second, it suggests that these relationships impose value upon goods differently than do market relations. The details of the recycling‘chain’show the ways actors shape the network and demonstrate that the social values that add‘economic value’to goods are not uniform, but are highly contextual. Starting from Mark Granovetter's notion of 'social embeddedness', the article explains that the measure of social embeddedness is not as important as the values imposed upon other actors through social structure in the economy. It calls for a close observation of economic action in the locales within which production takes place to understand better the‘actions‐at‐a‐distance’where the politics of technology, social movements and power create the empirical, instituted economy.     

Sin Coyote Ni Patrón: Why the “Migrant Network” Fails to Explain International Migration

The “migrant network” concept cannot explain large‐scale international migratory flows. This article goes beyond a critique of its a historical and post factum nature. First, I argue that restrictions on its composition and functions also render the migrant network unable to explain why such migratory flows continue or expand even further. Second, a review of five studies illustrates why this concept, the propositions on which it rests, the methods it employs, and the conclusions that it imparts must be reconsidered. Third, the network analysis literature, along with my research data from the Mexico‐U.S. case, suggest an alternative approach. “International migration networks” include those from the labor‐sending hometowns who are emphasized in migrant network studies, as well as a variety of other actors based in the militarized border zone and the labor‐receiving regions. I conclude that accurate studies of migration must include the employers that demand new immigrant workers, as well as the labor smugglers and all other actors that respond to this demand. Immigration studies that fail to do so provide erroneous analyses which camouflage the activities of many network actors, and furnish an academic fig leaf behind which unintended, counterproductive, and even lethal public policies have been implemented.     

A New Model for Information Diffusion in Heterogeneous Social Networks

This paper discusses a new model for the diffusion of information through heterogeneous social networks. In earlier models, when information was given by one actor to another the transmitter did not retain the information. The new model is an improvement on earlier ones because it allows a transmitter of information to retain that information after telling it to somebody else. Consequently, the new model allows more actors to have information during the information diffusion process. The model provides predictions of diffusion times in a given network at the global, dyadic, and individual levels. This leads to straightforward generalizations of network measures, such as closeness centrality and betweenness centrality, for research problems that focus on the efficiency of information transfer in a network. We analyze in detail how information diffusion times and centrality measures depend on a series of network measures, such as degrees and bridges. One important finding is that predictions about the time actors need to spread information in the network differ considerably between the new and old models, while the predictions about the time needed to receive information hardly differ. Finally, some cautionary remarks are made about using the model in empirical research.     

Analysis of contested reports in exchange networks based on actors’ credibility

Exchanges of information, goods, and services are an essential part of human relations. However, a significant number of reported exchange ties tend to be contested: the reports of the sender and the receiver in an exchange do not concur with each other. To accurately understand the exchange ties between actors and the properties of the associated exchange networks, it is important to address such disagreement. Common practices either eliminate the contested reports or symmetrize them. Neither of them is ideal, as both underuse valuable information in the reports. In this paper, we propose new methods for handling contested exchange ties. The key idea is to measure actors’ credibility based on their asymmetric connections. For example, an actor is less credible the more contested ties she or he has. Using the credibility scores thus calculated, we develop two methods for handling contested ties. The first method is deterministic: it takes the report of the more credible actor as a reflection of the true exchange status between two actors. The second method is stochastic: it assumes the true exchange status between two actors is a random draw from their reports with probabilities proportional to their credibility. We illustrate the above methods by analyzing contested reports in cigarette exchange networks among middle school students in China and social and economic exchange networks among rural households in South Africa. The results show that our methods provide more reasonable corrections to contested reports than previous methods.     

The duality of firms and directors in board interlock networks: A relational event modeling approach

The long tradition of scholarly work on corporate interlocks has left us with competing theoretical frameworks on the causes of interlock networks. Board interlocks are studied either as means to overcome the resource dependence of corporations or as a group cohesion mechanism of business elites. This contrast is due to an empirical divide of the literature where either the firms or the individuals are considered as decision-making bodies. In systematically ignoring the agency of the other group of actors, these literatures suffer from both theoretical and empirical biases in understanding the drivers of new interlocks. In this paper, we employ a relational event modeling technique that allows us to overcome this problem. The analysis of board appointments in Denmark demonstrates how in fact both personal and corporate considerations simultaneously drive the evolution of the corporate networks. The study of the duality of actors is essential for understanding the causes and consequences of corporate networks across time and space.