Exploring Network Effects and Tobacco Use with IENA David R. chaefer chool of Human Evolution & ocial Change Arizona tate University upported by the National Institutes of Health (R21-HD060927, R21HD071885)
Overview Why model networks? The IENA approach Application of IENA to adolescent smoking IENA as an agent-based model April 17, 2014 Institute of Medicine 2
efferson High (Add Health, 1995) 30-day smoking None 1-11 days 12+ days 3
tatistical Network Models Recognize that actors are interdependent Reciprocity, homophily, transitivity, degree differentials (e.g., Matthew effect), local hierarchies Goal is to identify main network features through parameter estimates (and quantify uncertainty surrounding estimates) Helpful to think of dyad as the unit of analysis and some dyad quality (e.g., presence/absence of a tie) as the outcome April 17, 2014 Institute of Medicine 4
Modeling Approaches Relational Event Model equences of dyadic events (e.g., emails, exchange) Exponential-family Random Graph Model (ERGM) Predict cross-sectional ties based on local structure tochastic Actor-Based Model (ABM, IENA ) Predict change in ties over time over time Ties assumed to be states that can persist Actor-driven model (not tie-based, as in ERGM) Natural extension to include behavior change April 17, 2014 Institute of Medicine 5
Modeling Behavior Change Recognition that networks and behavior are interdependent Behavior shapes network structure Network processes shape behavior Complicates attempts to answer important theoretical questions (e.g., peer influence) Examples April 17, 2014 Institute of Medicine 6
Network Homogeneity on moking time t-1 Peer Influence A C B D A time t B or C D Friend election A C B D April 17, 2014 Institute of Medicine 7
moking-related Popularity time t-1 Popularity leads to smoking A C B D A time t B or moking enhances popularity A C B D C D April 17, 2014 Institute of Medicine 8
Inferring Network Behavior Requires controlling for selection on: 1. Behavior 2. Correlates of the behavior (e.g., attributes, shared context) 3. Network processes (e.g., triad closure) Can amplify network-behavior patterns April 17, 2014 Institute of Medicine 9
IENA Approach Endogenous Network Effects ocial Influence on Behavior Network Individual/ Contextual Attributes Behavior Network election based on Behavior April 17, 2014 Institute of Medicine 10
Model Components Actors control their outgoing ties and behavior Functions specify when/how they change Decision Timing Decision Rules Network Evolution Network rate function* Network objective function Behavior Evolution Behavior rate function* Behavior objective function * Waiting time is usually distributed uniformly across actors, but can specify differences based on actor attributes April 17, 2014 Institute of Medicine 11
ABM pecification Objective functions operationalize decision rules The network function models tie change based on: Behavior/attributes of self & others (ego & alters) Dyadic attributes (similarity, context) Network processes (e.g., triad closure) The behavior function models change based upon: Individual attributes Friends behavior Network position (e.g., popularity) April 17, 2014 Institute of Medicine 12
Decision Process Data from discrete time points Assume ties and behavior change on a continuoustime scale (between observation waves) through series of micro steps ( smallest possible change ) Network: change in one tie (add or drop) Behavior: step up or down on behavior score Choice probabilities take the form of a multinomial logit model instantiated by the objective function Actors evaluate all possible changes Option with highest evaluation most likely (small amount of error added to each evaluation) April 17, 2014 Institute of Medicine 13
Micro tep Example: election on moking Given the chance to change a tie, what does A do? A moke=1?? B moke=1 C moke=0 Evaluate the contribution to the network function of each tie choice (-.5 * moke ego ) + (-.25 * moke alter ) + (2.25 * moke similarity ) A B (-.5 * 1) + (-.25 * 1) + (2.25 * [1 -.6]) -.5 -.25 +.9 =.15 A C (-.5 * 1) + (-.25 * 0) + (2.25 * [0 -.6]) -.5 + 0-1.35 = -1.85 April 17, 2014 Institute of Medicine 14
Condition on wave 1 ABM Fitting Iterative process to estimate parameters that reproduce observed changes Convergence achieved when model is able to reproduce observed network & behavior at time 2+ (as represented by summary statistics) April 17, 2014 Institute of Medicine 15
IENA Data Requirements At least 2 panels of complete network data Ties measured for all actors w/in bounded setting Little turnover in set of actors Observations of actor behavior at corresponding time points To model change, coded as ordinal measure Controls: settings, anything correlated with network and behavior N = 30 - ~2,000 April 17, 2014 Institute of Medicine 16
Application to Adolescent moking National Longitudinal tudy of Adolescent Health (Add Health) In-home surveys conducted 1994-1995 (2 waves) tudents nominated up to 5 male and 5 female friends (directed network) Friendships coded as present (1) or absent (0) for each dyad April 17, 2014 Institute of Medicine 17
Network function b E Rate 10.26 ***.49 Outdegree -3.91 ***.08 Reciprocity 1.91 ***.09 Transitive triplets.52 ***.04 Popularity.29 ***.04 Extracurric. act. overlap.28 ***.06 moke similarity.68 ***.12 moke alter.14 **.05 moke ego -.04.05 Female similarity.24 ***.04 Female alter -.11 *.05 Female ego -.04.05 Age similarity 1.00 ***.13 Age alter -.01.03 Age ego -.04.03 Delinquency similarity.15.08 Delinquency alter -.04.04 Delinquency ego.02.04 Alcohol similarity.27 **.10 Alcohol alter -.03.03 Alcohol ego -.03.04 GPA similarity.70 ***.13 GPA alter -.05.04 GPA ego -.02.04 Low tie probability Reciprocated ties more likely Tendency toward closed triads Higher indegree students attract more future ties Tendency toward friendship among activity co-participants Ties driven by similarity on: Gender Age Alcohol use GPA Females less attractive as friends than males. From chaefer, Haas and Bishop (2012, American ournal of Public Health) April 17, 2014 Institute of Medicine 18
Network function b E Rate 10.26 ***.49 Outdegree -3.91 ***.08 Reciprocity 1.91 ***.09 Transitive triplets.52 ***.04 Popularity.29 ***.04 Extracurric. act. overlap.28 ***.06 moke similarity.68 ***.12 moke alter.14 **.05 moke ego -.04.05 Female similarity.24 ***.04 Female alter -.11 *.05 Female ego -.04.05 Age similarity 1.00 ***.13 Age alter -.01.03 Age ego -.04.03 Delinquency similarity.15.08 Delinquency alter -.04.04 Delinquency ego.02.04 Alcohol similarity.27 **.10 Alcohol alter -.03.03 Alcohol ego -.03.04 GPA similarity.70 ***.13 GPA alter -.05.04 GPA ego -.02.04 Ties driven by similarity on smoking behavior. mokers more attractive as friends than non-smokers. Contributions to objective function by dyad type Ego Alter Nonsmoker moker Nonsmoker.25 -.19 moker -.51.41 From chaefer, Haas and Bishop (2012, American ournal of Public Health) April 17, 2014 Institute of Medicine 19
moking function b E Rate 2.06 ***.26 Linear shape -.11.22 Quadratic shape 1.17 ***.16 Female.16.19 Age -.00.10 Parent moking.01.23 Delinquency.44 **.16 Alcohol -.10.14 GPA -.09.13 Average similarity 2.89 ***.91 In-degree -.04.11 In-degree squared.00.01 U-shaped smoking distribution Delinquency leads to higher levels of smoking tudents adopt smoking levels that bring them closer to the average of their friends Average similarity x x ( sim sim 1 z z i j ij ij ) sim ij z i z j max ij z z i j From chaefer, Haas and Bishop (2012, American ournal of Public Health) April 17, 2014 Institute of Medicine 20
Asymmetric Peer Influence Implicit assumption that parameters equal for: Tie formation vs. maintenance Behavior increase vs. decrease Unrealistic for smoking Physical/psychological dependence, social learning Easy to relax this assumption eparate behavior objective function into: Creation function: only considers increasing behavior Maintenance function: only considers decreasing behavior Could make similar distinction in network function April 17, 2014 Institute of Medicine 21
Contribution Contribution Contributions to the moking Function Util. -3-1 1 3 Util. -3-1 1 3 Util. -3-1 1 3 moking level with greatest contribution most likely to be A adopted (with caveat that actors can only move behavior one level during a given micro step) Util. -3-1 1 3 Util. -3-1 Util. 1 3 0 1 2 Current moking Nonsmoking B GAlters -3-1 1 3 Util. -3-1 Util. 1 3 0 1 2 Ego is currently a moderate smoker (1) Current moking moking C H Alters -3-1 1 3 Util. -3-1 1 3 0 1 2 = efferson High chool = unshine High chool D 0 01 12 2 Prospective Current moking moking E 0 01 1 2 2 Prospective moking F Util. -3-1 1 3 From Haas & chaefer (2014, ournal of Health and ocial Behavior) Util. -3-1 1 3 April 17, 2014 Institute of Medicine 22 Util. -3-1 1 3
IENA as an ABM Useful to evaluate goodness-of-fit, decompose network-behavior associations, evaluate interventions Uses the same algorithm as model fitting 1. Fit model to empirical data 2. imulate network evolution using estimated parameters or manipulations of them Can also manipulate initial conditions (e.g., network structure, behavior distribution, etc.) 3. Measure network/behavior properties of interest April 17, 2014 Institute of Medicine 23
Indegree Distribution Goodness of Fit of IndegreeDistribution 483 491 459 437 401 343 tatistic 282 193 139 0 1 2 3 4 5 6 7 8 p: 0 April 17, 2014 Institute of Medicine 24
Geodesic Distribution Goodness of Fit of GeodesicDistribution tatistic 12081 11892 10598 7772 5014 2795 1381 1 2 3 4 5 6 7 p: 0.001 April 17, 2014 Institute of Medicine 25
Decomposing Network Homogeneity How much network homogeneity on smoking is due to selection vs. influence? ystematically set selection and influence parameters to zero and simulate networkbehavior co-evolution ource election (%) Influence (%) ample chaefer et al. 2012 40 34 U.. Mercken et al. 2009 17-47 6-23 Europe (6 countries) Mercken et al. 2010 31-46 15-22 Finland teglich et al. 2010 25-34 20-37 cotland April 17, 2014 Institute of Medicine 26
Evaluating Interventions How do smoking/friendship dynamics affect smoking prevalence? Manipulate parameters related to key intervention levers Peer influence (absent strong) moker popularity (unpopular absent popular) Remaining parameters from fitted model Initial conditions = observed wave 1 data April 17, 2014 Institute of Medicine 27
Results of Independent Manipulations From chaefer, adams & Haas (2013, Health Education & Behavior) April 17, 2014 Institute of Medicine 28
Results of oint Manipulation From chaefer, adams & Haas (2013, Health Education & Behavior) April 17, 2014 Institute of Medicine 29
Context Effects How do these effects depend upon context? Randomly manipulate initial smoking prevalence 25% initial smokers up to 75% Randomly distribute smokers and nonsmokers across the network imilar results with empirical and model-based manipulations April 17, 2014 Institute of Medicine 30
Results of Manipulating Initial Prevalence 75% Initial mokers 25% Initial mokers April 17, 2014 Institute of Medicine 31
Next teps Develop more realistic intervention scenarios Targeted to subset of actors (e.g., opinion leaders) Asymmetric effects (e.g., refusal skills) election into interventions Identify additional contextual factors Clustering based on smoking April 17, 2014 Institute of Medicine 32
Advantages of IENA ABM Can model very complex selection behavior Changes to network and behavior are both endogenous Parameters derived from real world April 17, 2014 Institute of Medicine 33
Disadvantages of IENA ABM Markov assumption: changes dependent only upon current state of network/behavior Ignores dependence on past events No coordinated or simultaneous change Limited actor behavior: change ties and/or behaviors Assumes ties are states (e.g., friendship, trust); no events (e.g., exchange, communication) April 17, 2014 Institute of Medicine 34