exploring network effects and tobacco use with …/media/files/activity files... · exploring...

Exploring Network Effects and Tobacco Use with SIENA

David R. Schaefer

School of Human Evolution & Social Change

Arizona State University

Supported by the National Institutes of Health (R21-HD060927, R21HD071885)

Overview

• Why model networks?

• The SIENA approach

• Application of SIENA to adolescent smoking

• SIENA as an agent-based model

April 17, 2014 Institute of Medicine 2

30-day smoking

None

1-11 days

12+ days

Jefferson High (Add Health, 1995)

3

Statistical 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


Modeling Approaches

Relational Event Model

• Sequences of dyadic events (e.g., emails, exchange)

Exponential-family Random Graph Model (ERGM)

• Predict cross-sectional ties based on local structure

Stochastic Actor-Based Model (SABM, “SIENA”)

• 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


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…


Network Homogeneity on Smoking

Peer

Influence

or

Friend

Selection

time t

time t-1

A

C D

B

A

C D

B

A

C D

B


Smoking-Related Popularity

Popularity

leads to

smoking

or

Smoking

enhances

popularity

time t

time t-1

C D

B A

C D

B A

C D

B A


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


SIENA Approach

Network

Individual/

Contextual

Attributes

Social Influence on Behavior

Network Selection based on Behavior

Behavior

Endogenous

Network

Effects


Model Components

• Actors control their outgoing ties and behavior

• Functions specify when/how they change

* Waiting time is usually distributed uniformly across actors, but can specify differences based on actor attributes

Decision Timing Decision Rules

Network Evolution Network rate

function* Network objective

function

Behavior Evolution Behavior rate

function* Behavior objective

function


SABM Specification

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)


Decision Process

• Data from discrete time points

• Assume ties and behavior change on a continuous-time 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)


Micro Step Example: Selection on Smoking

Evaluate the contribution to the network function of each tie choice

… (-.5 * Smokeego) + (-.25 * Smokealter) + (2.25 * Smokesimilarity) …

A B

(-.5 * 1) + (-.25 * 1) + (2.25 * [1 - .6])

-.5 - .25 + .9 = .15

A

Smoke=1

B

Smoke=1

C

Smoke=0

? ?

A C

(-.5 * 1) + (-.25 * 0) + (2.25 * [0 - .6])

-.5 + 0 - 1.35 = -1.85

Given the chance to change a tie, what does A do?


SABM Fitting

• Condition on wave 1

• 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)


SIENA 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


Application to Adolescent Smoking

• National Longitudinal Study of Adolescent Health

(Add Health)

• In-home surveys conducted 1994-1995 (2 waves)

• Students nominated up to 5 male and 5 female friends (directed network)

– Friendships coded as present (1) or absent (0) for each dyad


Network function b SE

Rate 10.26 *** .49

Outdegree -3.91 *** .08

Reciprocity 1.91 *** .09

Transitive triplets .52 *** .04

Popularity .29 *** .04

Extracurric. act. overlap .28 *** .06

Smoke similarity .68 *** .12

Smoke alter .14 ** .05

Smoke 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

From Schaefer, Haas and Bishop (2012, American Journal of Public Health)

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.


Network function b SE

Rate 10.26 *** .49

Outdegree -3.91 *** .08

Reciprocity 1.91 *** .09

Transitive triplets .52 *** .04

Popularity .29 *** .04

Extracurric. act. overlap .28 *** .06

Smoke similarity .68 *** .12

Smoke alter .14 ** .05

Smoke 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. Smokers more attractive as friends than non-smokers.

Alter

Nonsmoker Smoker

Ego Nonsmoker .25 -.19

Smoker -.51 .41

Contributions to objective function by dyad type



U-shaped smoking distribution

Smoking function b SE

Rate 2.06 *** .26

Linear shape -.11 .22

Quadratic shape 1.17 *** .16

Female .16 .19

Age -.00 .10

Parent Smoking .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

Delinquency leads to higher levels of smoking

Students adopt smoking levels that bring them closer to the average of their friends

)(1 zz

ijj iji simsimxx

ji

ij

zzsim

jiij zz max

Average similarity


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 – Separate behavior objective function into:

• Creation function: only considers increasing behavior

• Maintenance function: only considers decreasing behavior

– Could make similar distinction in network function


Contributions to the Smoking Function

Co

ntr

ibu

tio

n

Prospective Smoking

Nonsmoking Alters

J = Jefferson High School S = Sunshine High School

From Haas & Schaefer (2014, Journal of Health and Social Behavior)


Smoking level with greatest contribution most likely to be adopted (with caveat that actors can only move behavior one level during a given micro step)

-3-1

13

Current Smoking

Util.

0 1 2

J

J

J

S

SS

A

-3-1

13

Current Smoking

Util.

0 1 2

J

J

J

S

SS

B

-3-1

13

Current Smoking

Util.

0 1 2

J

J

J

S

S

S

C

-3-1

13

Current Smoking

Util.

0 1 2

J

J

J

SS

S

D

-3-1

13

Current Smoking

Util.

0 1 2

J

J

JS

SS

E

-3-1

13

Current Smoking

Util.

0 1 2

J

J

JS

SS

F

-3-1

13

Util.

0 1 2

J

J

J

SS

S

G

-3-1

13

Util.

0 1 2

J

J

J

S

S

S

H

-3-1

13

Util.

0 1 2

J

J

J

S

S

S

I

Co

ntr

ibu

tio

n

Prospective Smoking

Smoking Alters

-3-1

13

Current Smoking

Util.

0 1 2

J

J

J

S

SS

A

-3-1

13

Current Smoking

Util.

0 1 2

J

J

J

S

SS

B

-3-1

13

Current Smoking

Util.

0 1 2

J

J

J

S

S

S

C

-3-1

13

Current Smoking

Util.

0 1 2

J

J

J

SS

S

D

-3-1

13

Current Smoking

Util.

0 1 2

J

J

JS

SS

E

-3-1

13

Current Smoking

Util.

0 1 2

J

J

JS

SS

F

-3-1

13

Util.

0 1 2

J

J

J

SS

S

G

-3-1

13

Util.

0 1 2

J

J

J

S

S

S

H

-3-1

13

Util.

0 1 2

J

J

J

S

S

S

I

Ego is currently a moderate smoker (1)

SIENA 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. Simulate 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


Indegree Distribution Goodness of Fit of IndegreeDistribution

p: 0

Sta

tistic

0 1 2 3 4 5 6 7 8

139

193

282

343

401

437

459

483491


Geodesic Distribution Goodness of Fit of GeodesicDistribution

p: 0.001

Sta

tistic

1 2 3 4 5 6 7

1381

2795

5014

7772

10598

12081 11892


Decomposing Network Homogeneity

Source Selection (%) Influence (%) Sample

Schaefer et al. 2012 40 34 U.S.

Mercken et al. 2009 17-47 6-23 Europe (6 countries)

Mercken et al. 2010 31-46 15-22 Finland

Steglich et al. 2010 25-34 20-37 Scotland

• How much network homogeneity on smoking is due to selection vs. influence?

– Systematically set selection and influence parameters to zero and simulate network-behavior co-evolution


Evaluating Interventions

How do smoking/friendship dynamics affect smoking prevalence?

• Manipulate parameters related to key “intervention levers”

– Peer influence (absent…strong)

– Smoker popularity (unpopular…absent…popular)

• Remaining parameters from fitted model

• Initial conditions = observed wave 1 data


Results of Independent Manipulations

From Schaefer, adams & Haas (2013, Health Education & Behavior)


Results of Joint Manipulation

From Schaefer, adams & Haas (2013, Health Education & Behavior)


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

– Similar results with empirical and model-based manipulations


25% Initial Smokers

Results of Manipulating Initial Prevalence


75% Initial Smokers

Next Steps

• Develop more realistic intervention scenarios

– Targeted to subset of actors (e.g., opinion leaders)

– Asymmetric effects (e.g., refusal skills)

– Selection into interventions

• Identify additional contextual factors

– Clustering based on smoking


Advantages of SIENA ABM

• Can model very complex selection behavior

• Changes to network and behavior are both endogenous

• Parameters derived from real world


Disadvantages of SIENA 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)


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