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Social Network Analysis
 

Social Network Analysis

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Social Network Analysis Social Network Analysis Presentation Transcript

  • Dynamic Social Network Analysis
    • René Veenstra
    • Department of Sociology
    • http://www.gmw.rug.nl/~veenstra
  • The basics
    • What is a network?
      • A graph in which…
      • we have a set of nodes (children, companies, web pages)…
      • connected by ties ( friendship relations, product exchanges, citations)
    • Why do we look at networks?
      • to study relational data, considering simultaneously both individuals connected by a tie
      • to see how ties combine: individuals are connected to others, who themselves are also connected to others
      • to find and highlight statistical properties that characterize structure and behavior of networked systems
      • to make predictions based on measured structural properties
  • Network data
    • We commonly use matrices containing the ties
    • Example:
      • a 1 has a tie to a2 and a5
    0 1 1 1 1 1 a6 1 0 0 0 0 0 a5 0 0 0 0 1 1 a4 1 0 0 0 1 0 a3 0 0 0 0 0 1 a2 0 1 0 0 1 0 a1 a6 a5 a4 a3 a2 a1
  • Non-directed and directed graphs
    • Non-directed
      • e.g., romantic relationship, marriage ties
    • Directed
      • e.g., friendship nominations, bullying
  • Network parameters: Degree
    • In-degree:
      • number of ties directed at the node
      • popularity of an actor
      • number of received nominations
    • Out-degree:
      • number of ties going from the node
      • activity of an actor
      • number of given nominations
    • Isolate:
      • Node without lines attached to it
  • Network parameters
    • Number of possible lines
      • non-directed: n (n-1)/2
      • directed: n (n-1)
    • Density (ranges from 0 to 1)
      • the proportion of possible lines that are actually present in the graph
    • Outdegree (density = 0.5  outdegree = 0)
      • models the density of the network
    • Reciprocity (with friendship data usually positive)
      • a mutual tie: i chooses j and j chooses i.
  • Network parameters: closure
    • Transitivity (usually positive)
      • measure of triads
      • ‘ a friend of a friend is a friend’
  • Evolution of social networks
    • Single observations are snapshots
      • Result of untraceable history
      • Explaining them has limited importance
    • Longitudinal modeling offers promise for understanding network structure
    • Structures of relations between actors that evolve
    • Dynamics of social networks
  • SIENA: Actor oriented approach
    • Analyzing longitudinal changes in networks
    • At certain moments in time actors can make choices, based on the evaluation of their position in the network:
      • actors can change ties (selection processes)
      • actors can change their behavior (socialization or influence processes)
    • See also:
      • Steglich, C.E.G., Snijders, T.A.B., & West, P. (2006). Applying SIENA. Methodology, 48-56.
      • Burk, W. J., Steglich, C. E. G., & Snijders, T. A. B. (2007). Beyond dyadic interdependence. International Journal of Behavioral Development, 31, 397-404.
  • Purpose of statistical modeling
    • Investigate network evolution as function of:
      • Structural network effects (e.g., reciprocity, transitivity)
      • Explanatory actor variables (e.g., gender, aggression, victimization)
      • Explanatory dyadic variables (e.g., same-gender, bullying relationship)
    • All effects control for each other
    • Without structural network effects, tests of other effects would be unreliable
  • Example data of Ernest Hodges
    • 167 male actors (predominantly Hispanic and low SES background)
    • Tie = friendship
    • Actor covariates: gender, aggression, victimization, weapon carrying
    • 2 measurements: one year apart
    • Dijkstra, J.K., Lindenberg, S., Veenstra, R., & Hodges, E.V.E. Selection and influence processes in weapon carrying in early adolescence. The role of status, aggression, and vulnerability.
  • Tie Changes Between Wave 1 and 2
    • Period 0=>0 0=>1 1=>0 1=>1 Missing
    • 1 ==> 2 22842 847 896 1610 1527 ( 6%)
    • Average degree
    • T1: 0.109
    • T2: 0.095
    • Proportion of Reciprocated Ties: 2M/(2M+A)
    • T1: 75% (2262 / 3020)
    • T2: 70% (1718 / 2458)
  • Prevalence of Weapon Carrying
    • T1 T2
    • ( N =164) ( N =138)
    • 0 times 72.6% 69.6%
    • 1 time 4.9% 5.8%
    • 2-5 times 10.4% 8.7%
    • 6-10 times 2.4% 2.2%
    • > 10 times 9.8% 13.8%
    • Period down up constant Missing
    • 1 ==> 2 17 ( 29 steps ) 24 ( 49 steps ) 94 32
  • SIENA Estimates and Standard Errors
    • Network Effects: Est. SE
    • 1. Outdegree -1.411 (0.065) ***
    • 2. Reciprocity 1.434 (0.133) ***
    • 3. Transitivity 0.024 (0.001) ***
    • Network Dynamics:
    • 4. Weapon carrying similarity (selection) 0.087 (0.117)
    • Effect of weapon carrying on
    • 5. Friendship nominations received 0.117 (0.033) ***
    • 6. Friendship nominations given -0.065 (0.029) *
  • SIENA Estimates and Standard Errors
    • Behavioral tendencies: Est. SE
    • 7. Weapon Carrying Linear -1.100 (0.173) ***
    • 8. Weapon Carrying Quadratic 0.582 (0.090) ***
    • Behavior Dynamics:
    • 9. Weapon carrying similarity (influence) 3.316 (1.864) ~
    • 10. Effect of Aggression T1 2.270 (1.370) ~
    • 11. Effect of Victimization T1 -0.246 (1.187)
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  • One-week Summer Course in Kansas
    • Kansas University Summer Institute in Statistics
    • one-week course (June 15-19, 2009) "Social Network Dynamics“
    • taught by Tom Snijders
    • This will be the first workshop where the new version of SIENA implemented as an R package will be taught
    • Topics:
    • statistical analysis of network dynamics for complete networks
    • networks co-evolving with dependent actor variables
  • SNA Community
    • Handbooks
    • Wasserman, S. & Faust, K. (1994). Social Network Analysis: Methods and Applications . New York: Cambridge University Press.
    • Carrington, P.J., Scott, J., & Wasserman, S. (2005) (eds.) Models and methods in Social Network Analysis. New York: Cambridge University Press.
    • Journal: Social Networks
    • Conference: Sunbelt
  • Thank you for your attention Software and manual: http://stat.gamma.rug.nl/siena/