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The Structure of Consensus: Cohesion and Hierarchy in Peer Networks G. Robin Gauthier Duke University. Partial support for this project thanks to NSF/HSD: 0624158 ( Moody, McFarland & Gest , PIs), W. T. Grant Foundation 8316 & NIDA 1R01DA018225-01 (Osgood , Moody, Feinberg, Gest , PIs ).

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Main Question

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  1. The Structure of Consensus: Cohesion and Hierarchy in Peer NetworksG. Robin GauthierDuke University Partial support for this project thanks to NSF/HSD: 0624158 (Moody, McFarland & Gest, PIs), W. T. Grant Foundation 8316 & NIDA 1R01DA018225-01 (Osgood, Moody, Feinberg, Gest, PIs)

  2. Main Question • What accounts for variation in peer group consensus? • What do I mean by consensus? • Group level agreement • What has past literature shown broadly? • Shortened path lengths increases diffusion (Friedkin 1986)

  3. Outline • Background Theory • Theoretical Model and Expectations • Data • Simulation results • Empirical Results

  4. Network Theory I Dependent Variable Consensus (on what?) Attitudinal Agreement Friedkin, 1986; Martin, 2002 Correlation between Attitudes Martin, 1997 Peer Group Behaviors (especially delinquency) Anderson, 1964; Cohen, 1977

  5. Theory II Independent Variables • Network Transitivity • Cohesive Subgroups (Haynie, Anderson) • Communication and sanctioning power • Hierarchy • Friedkin’s Model of Social Influence • How are the network structures Friedkin (1986) analyzed empirically distributed?

  6. Theoretical Model and Expectations Do Hierarchy and Cohesion each have a linear effect on consensus, or do their effects depend on the combination of the two? Low Hierarchy ? Low Cohesion High Cohesion ? High Hierarchy

  7. Data • National Longitudinal Study of Adolescent Health (Add Health) • 125 Schools • 4019 Peer Groups • Fast and Greedy • Clauset, Newman and Moore, 2004 • Label Propagation • Raghavan, Albert and Kumara, 2007

  8. Consensus • Index of Qualitative Variation (Heterogeneity) • K is the number of groups • P is the number of people in each group • Ranges from 0 to 1 • 0 if all people take on values in the same category • 1 if the values people take on are divided equally across the categories

  9. Dependent Variables • TV Watching • None, 1-4 hours per week, over 4 hours • College Aspirations • No chance, Some chance, Likely • Drinking Behavior • More than a few times • Smoking Behavior • More than a few times

  10. Transitivity

  11. Centralization

  12. Peer Group Quadrants

  13. Why Simulation • Generate hypotheses for the off-diagonal cases • Isolate social process • Clarify underlying assumptions • Equilibrium model • Edges carry equal weight

  14. Directed paths were modeled for each actor with a probability of 5% for transmission at each stepAll uninfected adjacent actors remained susceptible through all steps until the network was saturated or 100 steps had been reached The proportion of the network infected at each step was recorded Simulation Process Step 1 Step 2 Step 3 Step 4

  15. Diffusion Curves

  16. Expectations • Networks in the Low Transitivity/Low Centralization group will have the lowest consensus • Networks in the High Transitivity/Low Centralization group will have slightly more consensus • Networks in the Low Transitivity/High Centralization group will have slightly more consensus • Networks in the High Transitivity/High Centralization group will have the highest rate of consensus of all

  17. Empirical Results(Categorical Model)

  18. Linear Models

  19. Linear Model

  20. Conclusion • Both transitivity and centralization contribute to reducing heterogeneity (increasing consensus) • Centralization is the weaker force • The effect of centralization depends of the level of transitivity in the group

  21. Thank You

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