Transcript The Structure of Consensus: Cohesion and Hierarchy in Peer

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)
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)
Outline
•Background Theory
•Theoretical Model and Expectations
•Data
•Simulation results
•Empirical Results
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
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?
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
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
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
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
Transitivity
Centralization
Peer Group Quadrants
Why Simulation
• Generate hypotheses for the off-diagonal
cases
• Isolate social process
• Clarify underlying assumptions
• Equilibrium model
• Edges carry equal weight
Simulation Process
Directed paths were modeled for each actor with a probability of
5% for transmission at each step
All 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
Step 1
Step 2
Step 3
Step 4
Diffusion Curves
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
Empirical Results
(Categorical Model)
Linear Models
Linear Model
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
Thank You