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Exponential Random Graph Models for Social Networks Theory, Methods, and Applications

Intent of This Book Software and Data Structure of the Book Section I: Rationale Section II: Methods Section III: Applications Section IV: Future How To Read This Book Assumed Knowledge of Social Network Analysis Section I Rationale What Are Exponential Random Graph Models?Exponential Random Graph Models: A Short Definition ERGM Theory Brief History of ERGMs Network Data Amenable to ERGMs Formation of Social Network Structure Tie Formation: Emergence of Structure Formation of Social Ties Network Configurations: Consequential Network. Patterns and Related Processes Local Network Processes Dependency (and Theories of Network Dependence)Complex Combination of Multiple and Nested Social Processes Framework for Explanations of Tie Formation Network Self-Organization Individual Attributes Exogenous Contextual Factors: Dyadic Covariates Simplified Account of an Exponential Random Graph Model as a Statistical Model Random Graphs Distributions of Graphs Some Basic Ideas about Statistical Modeling Homogeneity Example Exponential Random Graph Model Analysis Applied ERGM Example: Communication in “The Corporation”ERGM Model and Interpretation Multiple Explanations for Network Structure Section II Methods Exponential Random Graph Model Fundamentals Outline Network Tie-Variables Notion of Independence ERGMs from Generalized Linear Model Perspective Possible Forms of Dependence Bernoulli Assumption Dyad-Independent Assumption Markov Dependence Assumption Realization-Dependent Models Different Classes of Model Specifications Bernoulli Model Dyadic Independence Models Markov Model Social Circuit Models Other Model Specifications Conclusion Dependence Graphs and Sufficient Statistics Outline Dependence Graph Hammersley-Clifford Theorem and Sufficient Statistics Sufficient Subgraphs for Nondirected Graphs Dependence Graphs Involving Attributes Conclusion Social Selection, Dyadic Covariates, and Geospatial Effects Individual, Dyadic, and Other Attributes ERGM Social Selection Models Models for Undirected Networks Models for Directed Networks Conditional Odds Ratios Dyadic Covariates Geospatial Effects Conclusion Autologistic Actor Attribute Models Social Influence Models Possible Forms of Dependence Independent Attribute Assumption Network-Dependent Assumptions Network-Attribute-Dependent Assumptions Covariate-Dependent Assumptions Different Model Specifications and Their Interpretation Independence Models Network Position Effects Models Network-Attribute Effects Models Covariate Effects Models Conclusion Exponential Random Graph Model Extensions: Models for Multiple Networks and Bipartite Networks Multiple Networks ERGMs for Analyzing Two Networks ERGM Specifications for Two Networks Bipartite Networks Bipartite Network Representation and Special Features ERGM Specifications for Bipartite Networks Additional Issues for Bipartite Networks Longitudinal Models Network Dynamics Data Structure Model Continuous-Time Markov Chain Tie-Oriented Dynamics Definition of Dynamic Process Stationary Distribution Estimation Based on Changes Configurations for Networks Relations to Other Models Reciprocity Model as Precursor Stochastic Actor-Oriented Models as Alternatives Conclusion Simulation, Estimation, and Goodness of Fit Exploring and Relating Model to Data in Practice Simulation: Obtaining Distribution of Graphs for a Given ERGM Sampling Graphs Using Markov Chain Monte Carlo Metropolis Algorithm Estimation Maximum Likelihood Principle Curved ERGMs Bayesian Inference Solving the Likelihood Equation Importance Sampling: Geyer-Thompson Approach Stochastic Approximation: Robbins-Monro Algorithm Modifications for Longitudinal Model Testing Effects Approximate Wald Test Alternative Tests Evaluating Log-Likelihood Degeneracy and Near-Degeneracy Missing or Partially Observed Data Conditional Estimation from Snowball Samples Goodness of Fit Approximate Bayesian GOF Illustrations: Simulation, Estimation, and Goodness of Fit Simulation Triangulation Degrees Stars and Triangles Together Estimation and Model Specification Some Example Model Specifications GOF How Do You Know Whether You Have a Good Model?What If Your Model Does Not Fit a Graph Feature?Should a Model Explain Everything?Section III Applications Personal Attitudes, Perceived Attitudes, and Social Structures: A Social Selection Model Perceptions of Others and Social Behavior Data and Measures Social Network Questions Attribute Measures Analyses Goodness of Fit Model Specification Purely Structural Effects Actor-Relation Effects Covariate Network Effects Results Example 1: Schoolboys Example 2: Football Team Discussion How To Close a Hole: Exploring Alternative Closure Mechanisms in Interorganizational Networks Mechanisms of Network Closure Data and Measures Setting and Data Model Specification Results Discussion Interdependencies between Working Relations: Multivariate ERGMs for Advice and Satisfaction Multirelational Networks in Organizations Data, Measures, and Analyses Descriptive Results Multivariate ERGM Results Low-AS Bank High-AS Bank Discussion Brain, Brawn, or Optimism? Structure and Correlates of Emergent Military Leadership Emergent Leadership in Military Context Antecedents to Emergent Leadership Structure of Emergent Leadership Setting and Participants Model Specification Modeling Issues Purely Structural Effects Actor-Relation Effects Results Results for Purely Structural Effects Results for Actor-Relation Effects Discussion Autologistic Actor Attribute Model Analysis of Unemployment: Dual Importance of Who You Know and Where You Live Unemployment: Location and Connections Data, Analysis, and Estimation Data Analysis Estimation Results Discussion Longitudinal Changes in Face-to-Face and Text Message-Mediated Friendship Networks Evolution of Friendship Networks, Communication Media, and Psychological Dispositions Data and Measures Social Network Questions Actor-Relation Measures Analyses Model Specification Results Results for Face-to-Face Superficial Networks Results for Face-to-Face Self-Disclosing Networks Results for Text Message-Mediated Superficial Networks Results for Text Message-Mediated Self-Disclosing Networks Discussion Differential Impact of Directors’ Social and Financial Capital on Corporate Interlock Formation Bipartite Society: The Individual and the Group Director Capital and Interlock Formation Data and Measures Social Network Data Actor-Relation Measures Analyses Model Specification Independent Bivariate Attribute Analysis Purely Structural Effects Models with Attributes: Actor-Relation Effects Results Results for Independent Bivariate Analysis Results for Purely Structural Effects Results for Models Including Purely Structural and Actor-Relation Effects Discussion Comparing Networks: Structural Correspondence between Behavioral and Recall Networks Relationship between Behavior and Recall Data and Measures Description of Networks Data Transformations Model Specification Results Visualization Preliminary Statistical Analysis Univariate Models Models of Recall Networks with Behavioral Networks as Covariates Multivariate Models Discussion Section IV Future Modeling Social Networks: Next Steps Distinctive Features of ERGMs Model Specification Dependence Hierarchy Building Model Specifications Models with Latent Variables: Hybrid Forms Assessing Homogeneity Assumptions General Issues for ERGMs

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Exponential Random Graph Model Extensions: Models for Multiple Networks and Bipartite Networks
Peng Wang In previous chapters, we presented details of models for univariate onemode network data. Exponential random graph models (ERGMs), however, can also be applied to other relational data types. In this chapter, we extend ERGM specifications to (1) multivariate analysis of two networks and (2)...
(Exponential Random Graph Models for Social Networks Theory, Methods, and Applications)
What Are Exponential Random Graph Models?
Garry Robins and Dean Lusher Exponential Random Graph Models: A Short Definition Exponential random graph models (ERGMs) are statistical models for network structure, permitting inferences about how network ties are patterned. Put another way, ERGMs are tie-based models for understanding how and...
(Exponential Random Graph Models for Social Networks Theory, Methods, and Applications)
Exponential Random Graph Models: A Short Definition
Exponential random graph models (ERGMs) are statistical models for network structure, permitting inferences about how network ties are patterned. Put another way, ERGMs are tie-based models for understanding how and why social network ties arise. This focus aligns ERGMs with a principal goal of much...
(Exponential Random Graph Models for Social Networks Theory, Methods, and Applications)
Simplified Account of an Exponential Random Graph Model as a Statistical Model
Garry Robins and Dean Lusher This chapter provides a simplified overview of some methodological aspects of exponential random graph models (ERGMs), with the technical detail presented in Section II, specifically in Chapters 6 and 7. To begin, it is worthwhile to consider the value of a statistical model...
(Exponential Random Graph Models for Social Networks Theory, Methods, and Applications)
Example Exponential Random Graph Model Analysis
Dean Lusher and Garry Robins Exponential random graph models (ERGMs) permit us to examine competing theories regarding the formation of network ties, all within a single analysis. This means that a researcher can test one network theoretical concept for tie formation against another (e.g., Does homophily...
(Exponential Random Graph Models for Social Networks Theory, Methods, and Applications)
Exponential Random Graph Model Fundamentals
Johan Koskinen and Galina Daraganova Outline This chapter provides a more detailed description of exponential random graph models and aims at answering the following questions: • What do the different notions of independence and interdependence imply for the modeling of tie-variables? • What...
(Exponential Random Graph Models for Social Networks Theory, Methods, and Applications)
Labeling Actors in Social Networks Using a Heterogeneous Graph Kernel
Abstract. We consider the problem of labeling actors in social networks where the labels correspond to membership in specific interest groups, or other attributes of the actors. Actors in a social network are linked to not only other actors but also items (e.g., video and photo) which in turn can be...
(Social Computing, Behavioral-Cultural Modeling and Prediction)
Complex adaptive systems, social networks and agent-based models
“Complex Adaptive Systems” is the term which has been coined to refer to systems, whether social, biological, or of another kind, whose aggregate behavior is the result of actions performed by different individuals who continuously adapt to an environment, which itself is constituted by others individuals...
(Sociologies of Formality and Informality)
Modeling Social Networks: Next Steps
Pip Pattison and Tom Snijders In this final chapter, we review the progress made in modeling social networks using exponential random graph models (ERGMs) and identify some important questions that remain to be addressed, along with possible ways of approaching them. We also consider the development...
(Exponential Random Graph Models for Social Networks Theory, Methods, and Applications)
Social Network and Social Capital Theories
Social network studies have been a staple of the social sciences since Emile Durkheim in the 1890s. Bourdieu (1983/2001) reframed network as social capital, consisting of linkages, responsibilities, and connections which could be converted into economic or cultural capital. Stanton-Salazar (2001) explored...
(Family Engagement in Black Students’ Academic Success: Achievement and Resistance in an American Suburban School)