Social Network Analysis
How do we get from here.... to here?
These networks are from the Fall and Spring semesters of 6th grade for one cohort of students in the Middle School Transitions Project. In these illustrations, blue circles indicate boys, pink circles indicate girls, and the arrows indicate friendship nominations from one student to another (double-headed arrows indicate mutual relationships). The size of each circle indicates how aggressive each student is (larger circles indicate more aggressive students). The challenge for peer relationships researchers is to explain how children's friendships and behavior change co-evolve over time.
Peer networks are inherently relational and thus violate statistical assumptions of independence. Studies often make simplifying assumptions to satisfy this requirement, but this can produce misleading results. Fortunately, new models have been formulated to account for these dependencies (Hanneman & Riddle, 2005; Scott, 2000).
Individual Level: Children's position in the social network can be identified, either on a continuous scale by describing their network centrality (Borgatti, 2005; Bonacich, 1987; Hanneman & Riddle, 2005; Wasserman & Faust, 1994) or categorically by identifying youth as isolates, clique members or liaisons or by classifying youth by sociometric status (e.g., rejected, controversial). Alternatively, links between one’s ties (egocentric density) can be assessed. One limitation of studying peer relationships at the individual level, however, is that the identity and characteristics of youths’ peers are ignored. For example, does it matter who rejects a child or whether youth are popular or central members of delinquent groups?
Some of the most promising new methods for studying peer relationships are social network analytic models that focus on identifying cohesive peer groups and modeling entire networks and how they change over time. Two of these approaches are described below.
Exponential Random Graph Models (ERGMs): ERGM or “p*” models describe relationships at the entire network level (Hunter, Goodreau, & Handcock, under review; Robins, Pattison, Kalish, & Lusher, in press) by modeling the probability that a tie (or “edge”) is observed between any two individuals (“nodes”) conditional on the rest of the network (“graph”). The essential modeling task is to estimate a vector of network statistics that capture features of the network structure, including the dependencies between ties and the characteristics of the individuals who form those ties (e.g., each person’s aggression; differences in delinquency between people; each person's position in the network). These models are most useful for cross-sectional analyses.
Actor-oriented models: Actor-oriented models assume that observations of friendships and behavior are snapshots of a continuous, unobserved (or latent) process. In between observations, youth initiate changes in their friendship ties and behavior. The goal is to develop a model that describes how often students have an opportunity to change a friendship tie or their behavior (rate effects) and which changes they are more likely to initiate (network and behavioral dynamics). Because the models are so complex, model estimation is accomplished via simulations. The software program SIENA is typically used to estimate these programs. SIENA can be run through the program Stochnet and will soon be fully functional in R through the package RSiena.
Individual Level: Children's position in the social network can be identified, either on a continuous scale by describing their network centrality (Borgatti, 2005; Bonacich, 1987; Hanneman & Riddle, 2005; Wasserman & Faust, 1994) or categorically by identifying youth as isolates, clique members or liaisons or by classifying youth by sociometric status (e.g., rejected, controversial). Alternatively, links between one’s ties (egocentric density) can be assessed. One limitation of studying peer relationships at the individual level, however, is that the identity and characteristics of youths’ peers are ignored. For example, does it matter who rejects a child or whether youth are popular or central members of delinquent groups?
Some of the most promising new methods for studying peer relationships are social network analytic models that focus on identifying cohesive peer groups and modeling entire networks and how they change over time. Two of these approaches are described below.
Exponential Random Graph Models (ERGMs): ERGM or “p*” models describe relationships at the entire network level (Hunter, Goodreau, & Handcock, under review; Robins, Pattison, Kalish, & Lusher, in press) by modeling the probability that a tie (or “edge”) is observed between any two individuals (“nodes”) conditional on the rest of the network (“graph”). The essential modeling task is to estimate a vector of network statistics that capture features of the network structure, including the dependencies between ties and the characteristics of the individuals who form those ties (e.g., each person’s aggression; differences in delinquency between people; each person's position in the network). These models are most useful for cross-sectional analyses.
Actor-oriented models: Actor-oriented models assume that observations of friendships and behavior are snapshots of a continuous, unobserved (or latent) process. In between observations, youth initiate changes in their friendship ties and behavior. The goal is to develop a model that describes how often students have an opportunity to change a friendship tie or their behavior (rate effects) and which changes they are more likely to initiate (network and behavioral dynamics). Because the models are so complex, model estimation is accomplished via simulations. The software program SIENA is typically used to estimate these programs. SIENA can be run through the program Stochnet and will soon be fully functional in R through the package RSiena.
Introductory resources for those interested in social network analysis (SNA)
Introductory Texts:
Hanneman, R. A., & Riddle, M. (2005). Introduction to social network methods. Riverside, CA.
Click on the link to visit Robert Hanneman's website, which provides access to a free introductory textbook on SNA
Scott, J. (2000). Social Network Analysis: A Handbook. Thousand Oaks, CA: Sage Publications, Inc.
This volume provides a good introduction of social network analysis, including a brief history of social network analysis, a
description of how to handle relational data, and an overview of basic concepts and terms
Snijders, T.A.B., Steglich, C.E.G., & van de Bunt, G.G. (2009). Introduction to actor-based models for network dynamics.
(preprint). Social Networks, in press.
A fairly non-technical overview of actor-based modeling
Steglich, C.E.G., Snijders, T.A.B. & Pearson, M. (2009). Dynamic networks and behavior: Separating selection from
influence. Submitted for publication.
Another fairly non-technical introduction to actor-based modeling
Websites:
International Network on Social Network Analysis
Tom Snijders' Social Network Analysis homepage
This website provides links to the SIENA and Stochnet homepages, as well as links to additional SNA resources