Agent-Based Methods for Dynamic Social Networks
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Agent-Based Methods for Dynamic Social Networks Eric Vance ISDS Duke University Graduate Student Research Day April 5, 2006
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Agent-Based Methods for Dynamic Social Networks. Eric Vance ISDS Duke University. Graduate Student Research Day April 5, 2006. Social Networks. Social Network analysis models relationships between actors. 1 signifies a friendship, 0 indicates the absence of a friendship. F AB =1 - PowerPoint PPT Presentation
Transcript of Agent-Based Methods for Dynamic Social Networks
Agent-Based Methods for Dynamic Social Networks
Agent-Based Methods for Dynamic Social Networks
Eric Vance
ISDS
Duke University
Eric Vance
ISDS
Duke University
Graduate Student Research DayApril 5, 2006
Social NetworksSocial Networks
Social Network analysis models relationships between actors.
1 signifies a friendship, 0 indicates the absence of a friendship
Social Network analysis models relationships between actors.
1 signifies a friendship, 0 indicates the absence of a friendship
FAB=1FAC=1FBA=1FBC=0FCA=0FCB=1
Dynamic Social NetworksDynamic Social Networks
How do networks change over time?
How do we identify patterns?
How do we make predictions?
How do networks change over time?
How do we identify patterns?
How do we make predictions?
Agent-based modelsAgent-based models
Program simple rules for agents in a computer simulation.
Complex phenomena can be generated by individual agents acting according to the simple rules.
Evaluate each new rule.
Program simple rules for agents in a computer simulation.
Complex phenomena can be generated by individual agents acting according to the simple rules.
Evaluate each new rule.
Static Social Network ModelStatic Social Network Model
logit(pij)=0+s(si+rj)+ Xij-|zi-zj| Intercept 0 is a baseline probability for friendship Sender si random effect Receiver rj random effect Vector of dyad-specific (observable) covariates Xij
Positions (zi) in latent (unobservable) Social Space
The distance between zi and zj in Social Space affects the probability of a friendship from i j. Actors close together in social space are more likely to be
friends.
logit(pij)=0+s(si+rj)+ Xij-|zi-zj| Intercept 0 is a baseline probability for friendship Sender si random effect Receiver rj random effect Vector of dyad-specific (observable) covariates Xij
Positions (zi) in latent (unobservable) Social Space
The distance between zi and zj in Social Space affects the probability of a friendship from i j. Actors close together in social space are more likely to be
friends.
Our Approach--MotivationOur Approach--Motivation
Students arrive at a boarding school having no friends.
Each student occupies a position in Social Space.
Students make friends at each time according to simple rules which mimic the static social network model.
Students arrive at a boarding school having no friends.
Each student occupies a position in Social Space.
Students make friends at each time according to simple rules which mimic the static social network model.
Student Social SpaceStudent Social Space
Social Space is a useful proxy for that which we cannot measure.
Students move towards their friends in Social Space.
Students change their habits and interests to be more similar to their friends’.
Social Space is a useful proxy for that which we cannot measure.
Students move towards their friends in Social Space.
Students change their habits and interests to be more similar to their friends’.
Student Social SpaceStudent Social Space
Students close together have similar characteristics Students close together have similar characteristics
Sports
Fashion
3 Rules for Agent Model3 Rules for Agent Model
Students are endowed with a position (zi), Sexi=M or F, Charisma ci N(0,1).
Make friends according to probability pij: logit(pij)=0+s(ci+cj)+ Xij-|zi-zj|
Move 1/3 distance towards the average of friends’ positions.
What happens when 0, s, and vary?
Students are endowed with a position (zi), Sexi=M or F, Charisma ci N(0,1).
Make friends according to probability pij: logit(pij)=0+s(ci+cj)+ Xij-|zi-zj|
Move 1/3 distance towards the average of friends’ positions.
What happens when 0, s, and vary?
SimulationSimulation
SimulationSimulation
Simulation ResultsSimulation Results
Analysis of Results--ANOVA TableAnalysis of Results--ANOVA Table Approximate as a linear model:
Avg # friends = coef 0+ coef s+ coef || +
Approximate as a linear model:
Avg # friends = coef 0+ coef s+ coef || +
Deg. f Sum Squares p-value
0 1 122148 <2e-16
s 1 4138 <2e-16
|| 1 172 1.2e-06
Residuals 4455 32504
The intercept 0 has a very large effect. The
coefficient has a small effect.
The intercept 0 has a very large effect. The coefficient has a small effect.
Future DirectionsFuture Directions
Use the model to estimate parameters for a dynamic network with real data.
How to summarize a social network?
Add rules to better reflect reality.
Use the model to estimate parameters for a dynamic network with real data.
How to summarize a social network?
Add rules to better reflect reality.
