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AnIntroduc+ontoStochas+cActor-OrientedModels
(akaSIENA)
Dr.DavidR.SchaeferArizonaStateUniversity
SocialNetworks&HealthTrainingWorkshopDukeUniversityJune20,2016
1Dyadindependentmodels2R(sna)=lnam
Outcome
Figureadaptedfromjimiadams
ModeledInterdependenciesNone w/inDyad1 Dyad+
A;ribute GeneralLinearModel
Actor-PartnerInterdependence
(APIM)
NetworkAutoregressive2 Stochas+c
Actor-OrientedModel(SAOM)Network Erdös-Renyi (MR)QAP
Exponen+alRandomGraph(ERGM/TERGM),Rela+onalEvent
May20,2016 DukeSocialNetworks&HealthWorkshop 2
Sta?s?calModeling&SNA
WhentouseaSAOM
May20,2016 DukeSocialNetworks&HealthWorkshop 3
• Ques+onsaboutchangesinnetworkstructureover+me– Includingmul+plenetworks– Includingtwo-modenetworks(selec+ngintofoci)
• Ques+onsabouthownetworksaffectindividual“behaviors,”suchasthroughpeerinfluence– Includingmul+plebehaviorsandpossiblereciprocaleffects
• Ques+onsabouttheendogenousassocia+onbetweennetworksandbehavior
Stochas?cActor-OrientedModel
• AlsocalledStochas+cActor-BasedModel(SABM),or“SIENA”basedonthesobwareusedtoes+matethemodel– Simula'onInves'ga'onforEmpiricalNetworkAnalysis– Currentlyes+mableinR(RSiena)
• Recogni+onthatnetworksandbehaviorareinterdependent– Behaviorscanaffectnetworkstructure– Networkstructurecanaffectbehavior– Thus,both“outcomes”areendogenous– Complicatesademptstoanswerimportanttheore+calques+ons(e.g.,peerinfluence)
May20,2016 DukeSocialNetworks&HealthWorkshop 4
NetworkHomogeneityonSmoking
Peer Influence
or
Friend Selection
time t
time t-1
A
C D
B
A
C D
B
A
C D
B
May20,2016 DukeSocialNetworks&HealthWorkshop 5
Smoking-RelatedPopularity
Popularity leads to smoking
or
Smoking enhances popularity
time t
time t-1
C D
B AC D
B A
C D
B A
May20,2016 DukeSocialNetworks&HealthWorkshop 6
InferringNetwork→Behavior
Requirescontrollingfornetworkselec?onbasedon:1. Pre-exis+ngsimilarityinthebehavior2. Similarityonadributescorrelatedwiththebehavior3. Networkprocesses,suchastriadclosure
• Canamplifynetwork-behaviorpaderns(seebelow)
May20,2016 DukeSocialNetworks&HealthWorkshop 7
C D
B A
I♥Homophily!
C D
B A
C D
B A
Homophilythrough
Reciprocity
Homophilythrough
Transi?vity
OverviewofModelPresenta?on
1. Thegeneralformofthemodel– Networkfunc+onforrela+onshipchange– Behaviorfunc+onfor“behavior”change– Ratefunc+ons
2. Modeles+ma+onprocedure– Modelassump+ons– MCMCes+ma+onalgorithm– GoodnessofFit
3. Empiricalexample4. Extensions&Miscellany
May20,2016 DukeSocialNetworks&HealthWorkshop 8
1.GeneralSAOMForm
May20,2016 DukeSocialNetworks&HealthWorkshop 9
• Discretechangeismodeledasoccurringincon+nuous+me(betweenobserva+ons)throughasequenceofmicrosteps
• Actorscontroltheiroutgoing+esandbehavior– Func+onsspecifywhenandhowtheychange
SAOMComponents
DecisionTiming(whenchangesoccur)
DecisionRules(howchangesoccur)
NetworkEvolu+on Networkratefunc+on
Networkobjec+vefunc+on
BehaviorEvolu+on Behaviorratefunc+on
Behaviorobjec+vefunc+on
May20,2016 DukeSocialNetworks&HealthWorkshop 10
NetworkObjec?veFunc?on
• Networkchangeismodeledbyallowingactorstoselect+es(byaddingordroppingthem)basedupon:
fi(β,x)isthevalueofthenetworkobjec+vefunc+onforactori,given:• thecurrentsetofparameteres+mates(β)• stateofthenetwork(x)• Forkeffects,representedasski,whichmaybebasedon
– thenetwork(x),orindividualadributes(z)• Es+matedwithrandomdisturbance(ε)associatedwithx, z, t andj
• Goalofmodelfimngistoes+mateeachβk
May20,2016 DukeSocialNetworks&HealthWorkshop 11
fi (β, x) = βkskik∑ (x)+ε(x, z, t, j)
j3
ego
j4
j2
j1
NetworkDecision
€
fego(β,x) = -2
€
xijj∑ + 1.8
€
xij x jij∑
outdegree reciprocity
€
fego(β,x) = -2
€
xijj∑ + 1.8
€
xij x jij∑
€
fego(β,x) = -2
€
xijj∑ + 1.8
€
xij x jij∑
Duringamicrostep,anactorevaluateshowchangingitsoutgoing+eineachdyadwouldaffectthevalueoftheobjec+vefunc+on(goalistomaximizethevalueofthefunc+on)
ego j1 j2 j3 j4
ego - 1 1 0 0
j1 1 - 0 0 0
j2 0 0 - 0 0
j3 1 0 0 - 0
j4 0 0 0 0 -
May20,2016 DukeSocialNetworks&HealthWorkshop 12
If… outdegree reciprocity sum
Nochange -2*2=-4 1.8*1=1.8 -2.2
Dropj1 -2*1=-2 1.8*0=0 -2
Dropj2 -2*1=-2 1.8*1=1.8 -.2
Addj3 -2*3=-6 1.8*3=3.6 -2.4
Addj4 -2*3=-6 1.8*1=1.8 -4.2
Giventhecurrentstateofthenetwork,egoismostlikelytodropthe?etoj2,becausethatdecisionmaximizestheobjec+vefunc+on
• Outdegreealwayspresent• Networkprocesses(e.g.,reciprocity,transi+vity)• Adributebased:
– Sociality:effectofadributeonoutgoing+es– Popularity:effectofbehavioronincoming+es– Homophily:ego-altersimilarity– Note:adributesmaybestableor+me-changing(exogenousorendogenouslymodeled)
• Dyadicadributes(e.g.,co-membership)
May20,2016 DukeSocialNetworks&HealthWorkshop 13
NetworkObjec?veFunc?onEffects
• Predictchangein“behavior,”whichisthegenerictermforanindividualadribute– Referstoanyamtude,belief,healthfactor,etc.
• Op+onal:SAOMsdon’trequireoneandthey’renotrelevantformanyques+ons
• Ordinalmeasurementrequired(~2-10levelsbest)• Goalistoes+mateeffectofnetworkonbehaviorchange
May20,2016 DukeSocialNetworks&HealthWorkshop 14
BehaviorObjec?veFunc?on
BehaviorObjec?veFunc?on
• Choiceprobabili+estaketheformofamul+nomiallogitmodelinstan+atedbytheobjec+vefunc+on
wherezrepresentsthebehavior• Thefunc+ondictateswhichlevelofthebehavioractorsadopt
– Actorsevaluateallpossiblechanges• Increase/decreasebyoneunit,ornochange
– Op+onwithhighestevalua+onmostlikely
May20,2016 DukeSocialNetworks&HealthWorkshop 15
fiz (β, x, z) = βk
zskiz
k∑ (x, z)+ε(x, z, t,δ)
FigureadaptedfromC.Steglich
• Lineartermtocontrolfordistribu+on(quadra+ctermifthebehaviorhas3+levels)
• Predictorsofpeerinfluence– Alters’valueonthebehavior,oranotheradributeorbehavior
• Mul+plespecifica+ons,includingmean,minimum,maximum…
• Ego’sotherbehaviorsoradributes(e.g.,gender,age)– Ego’snetworkposi+on(e.g.,degree)– Interac+onswithreciprocity
May20,2016 DukeSocialNetworks&HealthWorkshop 16
BehaviorObjec?veFunc?onEffects
BehaviorDecision
May20,2016 DukeSocialNetworks&HealthWorkshop 17
Lineareffect
Quadra+ceffect
Adributeeffect(e.g.age)
Similarityeffect
Howadrac+veiseachlevelofthebehaviorbasedontheseeffects?
Ego,j1 1-|1-1|/2=.5 1(.5-.05)=.45
Ego,j2 1-|1-1|/2=.5 1(.5-.05)=.45
Ego,j3 1-|1-0|/2=0 1(0-.05)=.05
Ego,j4 1-|1-2|/2=0 0(0-.05)=0
Similaritysta?s?c=.95
BehaviorDecision*
May20,2016 DukeSocialNetworks&HealthWorkshop 18
J3(0)
Ego(1)
J4(2)
J1(1)€
xij (simijZ − simZ )
j∑
€
simijZ =1−|
€
z i−z j |
€
/ΔZ
€
ΔZ =maxij |
€
z i−z j| = 2 where=
€
simZ = similarity expected by chance
= similarity expected by chance = .05
simijZ xij (simij
Z − simZ )j2(1)Maintainz=1
First,calculatesimilarityforeachofego’spossibledecisions
*Assumecovariatesuncentered
Ego,j1 1-|0-1|/2=0 1(0-.05)=-.05
Ego,j2 1-|0-1|/2=0 1(0-.05)=-.05
Ego,j3 1-|0-0|/2=.5 1(.5-.05)=.45
Ego,j4 1-|0-2|/2=-.5 0(-.5-.05)=0
Similaritysta?s?c=.35
BehaviorDecision*
May20,2016 DukeSocialNetworks&HealthWorkshop 19
J3(0)
Ego(1)
J4(2)
J1(1)
First,calculatesimilarityforeachofego’spossibledecisions
€
xij (simijZ − simZ )
j∑
€
simijZ =1−|
€
z i−z j |
€
/ΔZ
€
ΔZ =maxij |
€
z i−z j| = 2 =
€
simZ = similarity expected by chance
= similarity expected by chance = .05
simijZ xij (simij
Z − simZ )j2(1)Decreasetoz=0
*Assumecovariatesuncentered
where
Ego,j1 1-|2-1|/2=0 1(0-.05)=-.05
Ego,j2 1-|2-1|/2=0 1(0-.05)=-.05
Ego,j3 1-|2-0|/2=-.5 1(-.5-.05)=-.45
Ego,j4 1-|2-2|/2=.5 0(.5-.05)=0
Similaritysta?s?c=-.55
BehaviorDecision*
May20,2016 DukeSocialNetworks&HealthWorkshop 20
J3(0)
Ego(1)
J4(2)
J1(1)€
xij (simijZ − simZ )
j∑
€
simijZ =1−|
€
z i−z j |
€
/ΔZ
€
ΔZ =maxij |
€
z i−z j| = 2 =
€
simZ = similarity expected by chance
= similarity expected by chance = .05
simijZ xij (simij
Z − simZ )j2(1)Increasetoz=2
First,calculatesimilarityforeachofego’spossibledecisions
*Assumecovariatesuncentered
where
BehaviorDecision*
May20,2016 DukeSocialNetworks&HealthWorkshop 21
If… linear quad age similarity sum
Dropto0 -.5*0=0 .25*0=0 .1*10*0=0 1*.35=.35 .35
Stayat1 -.5*1=-.5 .25*1=.25 .1*10*1=1 1*.95=.95 1.7
Upto2 -.5*2=-1 .25*4=1 .1*10*2=2 1*-.55=-.55 1.45
*Assumecovariatesuncentered
Second,calculatethecontribu+onsforeachoftheothereffects
BehaviorDecision*
May20,2016 DukeSocialNetworks&HealthWorkshop 22
If… linear quad age similarity sum
Dropto0 -.5*0=0 .25*0=0 .1*10*0=0 1*.35=.35 .35
Stayat1 -.5*1=-.5 .25*1=.25 .1*10*1=1 1*.95=.95 1.7
Upto2 -.5*2=-1 .25*4=1 .1*10*2=2 1*-.55=-.55 1.45
*Assumecovariatesuncentered
Theseeffectspullegotowardthe
extremes
Theposi+veagebpushesego’s
behaviorupward
Similaritypushesegotostaythe
same
Altogether,thegreatestcontribu+ontothebehaviorfunc+oncomesfromegochoosingtomaintainthesamebehaviorlevel
• Necessaryforbothnetworkandbehavior• Determinethewai+ng+meun+lactor’schancetomakedecisions• Func+onofobservedchanges
– Butnotthesameasthenumberofchangesobserved– Separaterateparameterforeachperiodbetweenobserva+ons
• Wai+ng+medistributeduniformlybydefault,butdifferencescanbemodeledbasedon:• Actoradributes:dosometypesofactorsexperiencemoreor
lesschange• Degree:doactorswithmore/fewer+esexperienceadifferent
volumeofchange
May20,2016 DukeSocialNetworks&HealthWorkshop 23
RateFunc?ons
2.SAOMEs+ma+on
May20,2016 DukeSocialNetworks&HealthWorkshop 24
SAOMEs?ma?on
• Goalduringes+ma+onistoiden+fyparametervalues(i.e.,amodel)thatproducenetworkswhosesta+s+csarecenteredontargetsta+s+cs– Sameasmodeledeffectsmeasuredatt1+
• Robbins-Monroalgorithminthreephases1. Ini+alizeparameterstar+ngvalues2. Usesimula+onstorefineparameteres+mates(nextslide)
• Alargenumberofsimula+onitera+ons,nestedin4+subphases• Actordecisionsand+mingbasedonobjec+veandratefunc+ons• Updateparameteres+matesabereachsimula+onitera+on
– Adempttominimizedevia+onofendingstatefromtarget3. Addi+onalsimula+ons(2,000+)tocalculatestandarderrorsbasedon
parameteres+matesfromphase2
May20,2016 DukeSocialNetworks&HealthWorkshop 25
MarkovChainAlgorithm
May20,2016 DukeSocialNetworks&HealthWorkshop 26
Ini+alizeatfirstobserva+on
Actorsdraw:1) Wai+ng+mefornetwork2) Wai+ng+meforbehaviorDeterminedbyratefunc+ons
Shortestwai+ng+me/typeiden+fied
Timeup?Actorchanges+e|behavior
Determinedbyobjec+vefunc+ons
Update+me(nextmicrostep)
“STOP”
YesNo
ForeachstepinaMarkovchain:
Maxitera+ons?
No
Yes
IfPhase2,updateparameters
Storeendingnetwork&behavior
Post-Es?ma?on1
• CheckforConvergence• Convergenceachievedwhenmodelisabletoreproduce
observednetwork&behaviorat+me2+– Foreacheffect,t-ra+otocomparetargetsta+s+cswithdistribu+on(tshouldbe<.10)
– Maximumt-ra+oforconvergence(tconv.max)shouldbelessthan.25
– Ifconvergencenotreached,rerunwithusinges+matesasnewstar+ngvalues;mayneedtorespecifymodel
May20,2016 DukeSocialNetworks&HealthWorkshop 27
Post-Es?ma?on2
• GoodnessofFit• Usesimula+onstocomparenetworksgeneratedbymodelto
sta+s+csNOTexplicitlyinthemodel– Typicalcandidates:
• In-&Out-degreedistribu+ons• TriadCensus• Geodesicdistribu+on• Behaviordistribu+on• Behaviornetworkassocia+ons
May20,2016 DukeSocialNetworks&HealthWorkshop 28
3.SAOMExample
May20,2016 DukeSocialNetworks&HealthWorkshop 29
AnEmpiricalExamplewithAdolescentSmoking
• Na+onalLongitudinalStudyofAdolescentHealth(AddHealth)• In-homesurveysconducted1994-1995(2waves)
– Earlierin-schoolsurveyhasnetworkdatabutlimitedbehaviordata
• Studentsnominatedupto5maleand5femalefriends(directednetwork)– Friendshipscodedpresent(1)orabsent(0)foreachdyad
May20,2016 DukeSocialNetworks&HealthWorkshop 30
30-daysmoking
None(0)
1-11days(1)
12+days(2)
JeffersonHigh(AddHealth,1995)
May20,2016 DukeSocialNetworks&HealthWorkshop 31
• Helpfultoimaginethenetworkfunc+onasalogis+cregression– Unitofanalysis:dyad– Outcome:+epresence(keepingoradding)vs.absence(dissolvingorfailingtoadd)
– Eacheffectrepresentshowaone-unitchangeintheeffectsta+s+caffectsthelog-oddsofa+e,allelsebeingequal
• Someeffectsinterpretableusingoddsra+os,but– One-unitchangesmaynotbemeaningful– Allelseisneverequal(anychangealsoaffectstheoutdegreecount,ataminimum)
• Behaviorfunc+onspecifieshowaone-unitchangeintheeffectsta+s+caffectstheoddsofincreasingbehavioroneunit
May20,2016 DukeSocialNetworks&HealthWorkshop 32
Interpre?ngResults
Networkfunc?on b SERate 10.26*** .49Outdegree -3.91*** .08Reciprocity 1.91*** .09Transi+vetriplets .52*** .04Popularity .29*** .04Extracurric.act.overlap .28*** .06Smokesimilarity .68*** .12Smokealter .14** .05Smokeego -.04 .05Femalesimilarity .24*** .04Femalealter -.11* .05Femaleego -.04 .05Agesimilarity 1.00*** .13Agealter -.01 .03Ageego -.04 .03Delinquencysimilarity .15 .08Delinquencyalter -.04 .04Delinquencyego .02 .04Alcoholsimilarity .27** .10Alcoholalter -.03 .03Alcoholego -.03 .04GPAsimilarity .70*** .13GPAalter -.05 .04GPAego -.02 .04
FromSchaefer,D.R.S.A.Haas,andN.Bishop.2012.“ADynamicModelofUSAdolescents’SmokingandFriendshipNetworks.”AmericanJournalofPublicHealth,102:e12-e18.
May20,2016 DukeSocialNetworks&HealthWorkshop 33
Rate:Eachactorisgiven~10microstepsinwhichtomakeachangetoitsnetwork• Adda+e,dropa+e,ormake
nochange
Rate
Networkfunc?on b SERate 10.26*** .49Outdegree -3.91*** .08Reciprocity 1.91*** .09Transi+vetriplets .52*** .04Popularity .29*** .04Extracurric.act.overlap .28*** .06Smokesimilarity .68*** .12Smokealter .14** .05Smokeego -.04 .05Femalesimilarity .24*** .04Femalealter -.11* .05Femaleego -.04 .05Agesimilarity 1.00*** .13Agealter -.01 .03Ageego -.04 .03Delinquencysimilarity .15 .08Delinquencyalter -.04 .04Delinquencyego .02 .04Alcoholsimilarity .27** .10Alcoholalter -.03 .03Alcoholego -.03 .04GPAsimilarity .70*** .13GPAalter -.05 .04GPAego -.02 .04
FromSchaefer,D.R.S.A.Haas,andN.Bishop.2012.“ADynamicModelofUSAdolescents’SmokingandFriendshipNetworks.”AmericanJournalofPublicHealth,102:e12-e18.
May20,2016 DukeSocialNetworks&HealthWorkshop 34
Outdegree:Thenega+vesignistypical.Itmeansthat+esareunlikely,unlessothereffectsinthemodelmakeaposi+vecontribu+ontothenetworkfunc+on.
density
Networkfunc?on b SERate 10.26*** .49Outdegree -3.91*** .08Reciprocity 1.91*** .09Transi+vetriplets .52*** .04Popularity .29*** .04Extracurric.act.overlap .28*** .06Smokesimilarity .68*** .12Smokealter .14** .05Smokeego -.04 .05Femalesimilarity .24*** .04Femalealter -.11* .05Femaleego -.04 .05Agesimilarity 1.00*** .13Agealter -.01 .03Ageego -.04 .03Delinquencysimilarity .15 .08Delinquencyalter -.04 .04Delinquencyego .02 .04Alcoholsimilarity .27** .10Alcoholalter -.03 .03Alcoholego -.03 .04GPAsimilarity .70*** .13GPAalter -.05 .04GPAego -.02 .04
FromSchaefer,D.R.S.A.Haas,andN.Bishop.2012.“ADynamicModelofUSAdolescents’SmokingandFriendshipNetworks.”AmericanJournalofPublicHealth,102:e12-e18.
May20,2016 DukeSocialNetworks&HealthWorkshop 35
Reciprocity:Tiesthatcreateareciprocated+earemorelikelytobeaddedormaintained.Thiseffecthoversaround2infriendship-typenetwork.
recip
Networkfunc?on b SERate 10.26*** .49Outdegree -3.91*** .08Reciprocity 1.91*** .09Transi+vetriplets .52*** .04Popularity .29*** .04Extracurric.act.overlap .28*** .06Smokesimilarity .68*** .12Smokealter .14** .05Smokeego -.04 .05Femalesimilarity .24*** .04Femalealter -.11* .05Femaleego -.04 .05Agesimilarity 1.00*** .13Agealter -.01 .03Ageego -.04 .03Delinquencysimilarity .15 .08Delinquencyalter -.04 .04Delinquencyego .02 .04Alcoholsimilarity .27** .10Alcoholalter -.03 .03Alcoholego -.03 .04GPAsimilarity .70*** .13GPAalter -.05 .04GPAego -.02 .04
FromSchaefer,D.R.S.A.Haas,andN.Bishop.2012.“ADynamicModelofUSAdolescents’SmokingandFriendshipNetworks.”AmericanJournalofPublicHealth,102:e12-e18.
May20,2016 DukeSocialNetworks&HealthWorkshop 36
Transi?vetriplets:Tiesthatcreatemoretransi+vetriadshaveagreaterlikelihood.• Shouldalsotestinterac+on
withReciprocity(usuallynega+ve)
transTrip
Networkfunc?on b SERate 10.26*** .49Outdegree -3.91*** .08Reciprocity 1.91*** .09Transi+vetriplets .52*** .04Popularity .29*** .04Extracurric.act.overlap .28*** .06Smokesimilarity .68*** .12Smokealter .14** .05Smokeego -.04 .05Femalesimilarity .24*** .04Femalealter -.11* .05Femaleego -.04 .05Agesimilarity 1.00*** .13Agealter -.01 .03Ageego -.04 .03Delinquencysimilarity .15 .08Delinquencyalter -.04 .04Delinquencyego .02 .04Alcoholsimilarity .27** .10Alcoholalter -.03 .03Alcoholego -.03 .04GPAsimilarity .70*** .13GPAalter -.05 .04GPAego -.02 .04
FromSchaefer,D.R.S.A.Haas,andN.Bishop.2012.“ADynamicModelofUSAdolescents’SmokingandFriendshipNetworks.”AmericanJournalofPublicHealth,102:e12-e18.
May20,2016 DukeSocialNetworks&HealthWorkshop 37
IndegreePopularity:Actorswithmoreincoming+eshaveagreaterlikelihoodofreceivingfuture+es
inPop
Networkfunc?on b SERate 10.26*** .49Outdegree -3.91*** .08Reciprocity 1.91*** .09Transi+vetriplets .52*** .04Popularity .29*** .04Extracurric.act.overlap .28*** .06Smokesimilarity .68*** .12Smokealter .14** .05Smokeego -.04 .05Femalesimilarity .24*** .04Femalealter -.11* .05Femaleego -.04 .05Agesimilarity 1.00*** .13Agealter -.01 .03Ageego -.04 .03Delinquencysimilarity .15 .08Delinquencyalter -.04 .04Delinquencyego .02 .04Alcoholsimilarity .27** .10Alcoholalter -.03 .03Alcoholego -.03 .04GPAsimilarity .70*** .13GPAalter -.05 .04GPAego -.02 .04
FromSchaefer,D.R.S.A.Haas,andN.Bishop.2012.“ADynamicModelofUSAdolescents’SmokingandFriendshipNetworks.”AmericanJournalofPublicHealth,102:e12-e18.
May20,2016 DukeSocialNetworks&HealthWorkshop 38
DyadicCovariate:Actorswhoshareanextracurricularac+vity(coded1)aremorelikelytohaveafriendship+e
X
Networkfunc?on b SERate 10.26*** .49Outdegree -3.91*** .08Reciprocity 1.91*** .09Transi+vetriplets .52*** .04Popularity .29*** .04Extracurric.act.overlap .28*** .06Smokesimilarity .68*** .12Smokealter .14** .05Smokeego -.04 .05Femalesimilarity .24*** .04Femalealter -.11* .05Femaleego -.04 .05Agesimilarity 1.00*** .13Agealter -.01 .03Ageego -.04 .03Delinquencysimilarity .15 .08Delinquencyalter -.04 .04Delinquencyego .02 .04Alcoholsimilarity .27** .10Alcoholalter -.03 .03Alcoholego -.03 .04GPAsimilarity .70*** .13GPAalter -.05 .04GPAego -.02 .04
Tiesdrivenbysimilarityon:Gender(coulduse“same”effect)AgeAlcoholuseGPAFemaleslessadrac+veasfriendsthanmales.
FromSchaefer,D.R.S.A.Haas,andN.Bishop.2012.“ADynamicModelofUSAdolescents’SmokingandFriendshipNetworks.”AmericanJournalofPublicHealth,102:e12-e18.
altX
egoX
simX
May20,2016 DukeSocialNetworks&HealthWorkshop 39
Networkfunc?on b SERate 10.26*** .49Outdegree -3.91*** .08Reciprocity 1.91*** .09Transi+vetriplets .52*** .04Popularity .29*** .04Extracurric.act.overlap .28*** .06Smokesimilarity .68*** .12Smokealter .14** .05Smokeego -.04 .05Femalesimilarity .24*** .04Femalealter -.11* .05Femaleego -.04 .05Agesimilarity 1.00*** .13Agealter -.01 .03Ageego -.04 .03Delinquencysimilarity .15 .08Delinquencyalter -.04 .04Delinquencyego .02 .04Alcoholsimilarity .27** .10Alcoholalter -.03 .03Alcoholego -.03 .04GPAsimilarity .70*** .13GPAalter -.05 .04GPAego -.02 .04
FromSchaefer,D.R.S.A.Haas,andN.Bishop.2012.“ADynamicModelofUSAdolescents’SmokingandFriendshipNetworks.”AmericanJournalofPublicHealth,102:e12-e18.
Tiesdrivenbysimilarityonsmokingbehavior.Smokersmoreadrac+veasfriendsthannon-smokers.
Alter Nonsmoker Smoker
Ego Nonsmoker .25 -.19 Smoker -.51 .41
Similarityisan“interac+on”betweenegoandalter,thusinterpreta+onrequiresconsideringthemaineffectsEgo-alterselec+on:Contribu+onstonetworkobjec+vefunc+onbydyadtype
May20,2016 DukeSocialNetworks&HealthWorkshop 40
FromSchaefer,D.R.S.A.Haas,andN.Bishop.2012.“ADynamicModelofUSAdolescents’SmokingandFriendshipNetworks.”AmericanJournalofPublicHealth,102:e12-e18.
Smokingfunc?on b SERate 2.06*** .26Linearshape -.11 .22Quadra+cshape 1.17*** .16Female .16 .19Age -.00 .10ParentSmoking .01 .23Delinquency .44** .16Alcohol -.10 .14GPA -.09 .13Averagesimilarity 2.89*** .91In-degree -.04 .11In-degreesquared .00 .01
May20,2016 DukeSocialNetworks&HealthWorkshop 41
Rate:Studentshavearound2chancesonaverage(microsteps)tochangetheirsmokingbehavior
Rate
FromSchaefer,D.R.S.A.Haas,andN.Bishop.2012.“ADynamicModelofUSAdolescents’SmokingandFriendshipNetworks.”AmericanJournalofPublicHealth,102:e12-e18.
Smokingfunc?on b SERate 2.06*** .26Linearshape -.11 .22Quadra+cshape 1.17*** .16Female .16 .19Age -.00 .10ParentSmoking .01 .23Delinquency .44** .16Alcohol -.10 .14GPA -.09 .13Averagesimilarity 2.89*** .91In-degree -.04 .11In-degreesquared .00 .01
May20,2016 DukeSocialNetworks&HealthWorkshop 42
linear
quad
FromSchaefer,D.R.S.A.Haas,andN.Bishop.2012.“ADynamicModelofUSAdolescents’SmokingandFriendshipNetworks.”AmericanJournalofPublicHealth,102:e12-e18.
Smokingfunc?on b SERate 2.06*** .26Linearshape -.11 .22Quadra+cshape 1.17*** .16Female .16 .19Age -.00 .10ParentSmoking .01 .23Delinquency .44** .16Alcohol -.10 .14GPA -.09 .13Averagesimilarity 2.89*** .91In-degree -.04 .11In-degreesquared .00 .01
May20,2016 DukeSocialNetworks&HealthWorkshop 43
Smoking(z,M=.9) Linear Quad
Raw Centered b=-.11 b=1.17 Sum
0 -.90 .099 .948 1.047
1 .10 -.011 .012 .001
2 1.10 -.121 1.416 1.295
SmokingLevel
Summed
Effe
cts
Incombina+on,thelinearandquadeffectsrepresenttheU-shapedsmokingdistribu+on.• Kidseitherdon’tsmokeor
smoke12+days/month.
.0
.2
.4
.6
.8
1.0
1.2
1.4
0 1 2
Contribu?ontoBehaviorFunc?on
+ =
+ =
+ =
FromSchaefer,D.R.S.A.Haas,andN.Bishop.2012.“ADynamicModelofUSAdolescents’SmokingandFriendshipNetworks.”AmericanJournalofPublicHealth,102:e12-e18.
Smokingfunc?on b SERate 2.06*** .26Linearshape -.11 .22Quadra+cshape 1.17*** .16Female .16 .19Age -.00 .10ParentSmoking .01 .23Delinquency .44** .16Alcohol -.10 .14GPA -.09 .13Averagesimilarity 2.89*** .91In-degree -.04 .11In-degreesquared .00 .01
EgoCovariate:Delinquencyleadstohigherlevelsofsmoking
May20,2016 DukeSocialNetworks&HealthWorkshop 44
effFrom
FromSchaefer,D.R.S.A.Haas,andN.Bishop.2012.“ADynamicModelofUSAdolescents’SmokingandFriendshipNetworks.”AmericanJournalofPublicHealth,102:e12-e18.
Smokingfunc?on b SERate 2.06*** .26Linearshape -.11 .22Quadra+cshape 1.17*** .16Female .16 .19Age -.00 .10ParentSmoking .01 .23Delinquency .44** .16Alcohol -.10 .14GPA -.09 .13Averagesimilarity 2.89*** .91In-degree -.04 .11In-degreesquared .00 .01
AverageSimilarity:Studentsadoptsmokinglevelsthatbringthemclosertotheaverageoftheirfriends
xi+−1 xijj∑ (simij
z − simz )
Δ
−−Δ=
jiij
zzsim
jiij zz −=Δ max
May20,2016 DukeSocialNetworks&HealthWorkshop 45
avSim
• Howwellisthees+matedmodelabletoreproducefeaturesoftheobserveddatathatwerenotexplicitlymodeled?– Network
• Degreedistribu+on• Geodesicdistribu+on• Triadcensus
– Behaviordistribu?on
LotsofroomtoimproveGOFmeasures,especiallybehavior
May20,2016 DukeSocialNetworks&HealthWorkshop 46
GoodnessofFit(GOF)
Cumula?veIndegreeDistribu?onGoodness of Fit of IndegreeDistribution
p: 0
Statistic
0 1 2 3 4 5 6 7 8
139
193
282
343
401
437
459
483491
May20,2016 DukeSocialNetworks&HealthWorkshop 47
GeodesicDistribu?onGoodness of Fit of GeodesicDistribution
p: 0.001
Statistic
1 2 3 4 5 6 7
1381
2795
5014
7772
10598
12081 11892
May20,2016 DukeSocialNetworks&HealthWorkshop 48
TriadCensusGoodness of Fit of TriadCensus
p: 0.114
Sta
tistic
(cen
tere
d an
d sc
aled
)
003 012 102 021D 021U 021C 111D 111U 030T 030C 201 120D 120U 120C 210 300
21286492428358 129429
693
11411052
923
625
108
4 171114
5839
91
36
May20,2016 DukeSocialNetworks&HealthWorkshop 49
SmokingDistribu?onGoodness of Fit of BehaviorDistribution
p: 1
Statistic
0 1 2
222
98
182
May20,2016 DukeSocialNetworks&HealthWorkshop 50
4.Extensions&Miscellany
May20,2016 DukeSocialNetworks&HealthWorkshop 51
ExtensionstoBasicModel
May20,2016 DukeSocialNetworks&HealthWorkshop 52
• interac+ons• eventhistoryoutcomes• mul+plebehaviors• mul+plenetworkop+ons• valued+es• mul+levelnetworks• twomodenetworks• increasevs.decreasein+esand/orbehavior• +meheterogeneity• simula+ons(testinterven+ons)• ML,Bayeses+ma+on
AsymmetricPeerInfluence
• Implicitassump+onthateffectsworkthesamefor:– Tieforma+onvs.dissolu+on– Behaviorincreasevs.decrease
• Unrealis+cforsmoking– Physical/psychologicaldependence,sociallearning
• Easytorelaxthisassump+on– Separatebehaviorobjec+vefunc+oninto:
• Crea?onfunc?on:onlyconsidersincreases• Maintenancefunc?on:onlyconsidersdecreases
– Couldmakesimilardis+nc+oninthenetworkfunc+on
May20,2016 DukeSocialNetworks&HealthWorkshop 53
Contribu?onstotheSmokingFunc?on
Contrib
u+on
Prospec+veSmoking
NonsmokingAlters
J=JeffersonHighSchoolS=SunshineHighSchool
FromHaas,StevenA.andDavidR.Schaefer.2014.“WithaLidleHelpfromMyFriends?AsymmetricalSocialInfluenceonAdolescentSmokingIni+a+onandCessa+on.”JournalofHealthandSocialBehavior,55:126-143.
Smokinglevelwithgreatestcontribu+onmostlikelytobeadopted(withcaveatthatactorscanonlymovebehavioronelevelduringagivenmicrostep)
-3-1
13
Current Smoking
Util
.
0 1 2
J
JJ
S
SS
A
-3-1
13
Current Smoking
Util
.
0 1 2
J
JJ
S
SS
B
-3-1
13
Current Smoking
Util
.
0 1 2
JJ
J
S
S
S
C
-3-1
13
Current Smoking
Util
.
0 1 2
J
JJ
SS
S
D
-3-1
13
Current Smoking
Util
.
0 1 2
JJ
JS
SS
E
-3-1
13
Current Smoking
Util
.
0 1 2
J
J
JS
S S
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
Contrib
u+on
Prospec+veSmoking
SmokingAlters
-3-1
13
Current Smoking
Util
.
0 1 2
J
JJ
S
SS
A
-3-1
13
Current Smoking
Util
.
0 1 2
J
JJ
S
SS
B
-3-1
13
Current Smoking
Util
.
0 1 2
JJ
J
S
S
S
C
-3-1
13
Current Smoking
Util
.
0 1 2
J
JJ
SS
S
D
-3-1
13
Current Smoking
Util
.
0 1 2
JJ
JS
SS
E
-3-1
13
Current Smoking
Util
.
0 1 2
J
J
JS
S S
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
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S
S
S
I
Egoiscurrentlyamoderatesmoker(1)
May20,2016 DukeSocialNetworks&HealthWorkshop 54
SIENAasanABM
• Usefultoevaluategoodness-of-fit,decomposenetwork-behaviorassocia+ons,evaluateinterven+ons
• Usesthesamealgorithmasmodelfimng1. Fitmodeltoempiricaldata(op+onal)2. Simulatenetworkevolu+onusinges+matedparametersor
manipula+onsofthem• Canalsomanipulateini+alcondi+ons(e.g.,networkstructure,behaviordistribu+on,etc.)
3. Measuresimulatednetwork/behaviorproper+esofinterest
May20,2016 DukeSocialNetworks&HealthWorkshop 55
DecomposingNetworkHomogeneity
Source Selec?on(%) Influence(%) Sample
Schaeferetal.2012 40 34 U.S.
Merckenetal.2009 17-47 6-23 Europe(6countries)
Merckenetal.2010 31-46 15-22 Finland
Steglichetal.2010 25-34 20-37 Scotland
• Howmuchnetworkhomogeneityonsmokingisduetoselec?onvs.influence?– Systema+callysetselec+onandinfluenceparameterstozeroandsimulatenetwork-behaviorco-evolu+on(seeSteglichetal.2010)
May20,2016 DukeSocialNetworks&HealthWorkshop 56
Evalua?ngInterven?ons
Howdosmoking/friendshipdynamicsaffectsmokingprevalence?• Manipulatemodelparametersrelatedtokey“interven+on
levers”– Peerinfluence(absent…strong)– Smokerpopularity(unpopular…absent…popular)
• Remainingmodelparametersfromfidedmodel• Ini+alcondi+ons=observedwave1data
May20,2016 DukeSocialNetworks&HealthWorkshop 57
ResultsofManipula?ngPeerInfluence(PI)andSmoking-basedPopularity(smokealter)
SchaeferDR,adamsj,HaasSA.2013.SocialNetworksandSmoking:ExploringtheEffectsofPeerInfluence
andSmokerPopularitythroughSimula+ons.HealthEduca'on&Behavior,40(S1):24-32.
May20,2016 DukeSocialNetworks&HealthWorkshop 58
IndependentManipula+onsJointManipula+on
Strongerpeerinfluenceincreasessmokingprevalence,butonlywhensmokersarepopular(nega+veeffectswhensmokersunpopular)
ContextEffects
Howdotheseeffectsdependuponcontext?• Randomlymanipulateini+alsmokingprevalence
– 25%ini+alsmokersupto75%• Randomlydistributesmokersandnonsmokersacrossthe
network– Similarresultswithempiricalandmodel-basedmanipula+ons
• Fullresultsinadams,jimi&DavidR.Schaefer.2016.“HowIni+alPrevalenceModeratesNetwork-BasedSmokingChange:Es+ma+ngContextualEffectswithStochas+cActorBasedModels.”JournalofHealth&SocialBehavior57(1):22-38.
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May20,2016 DukeSocialNetworks&HealthWorkshop 60
SmokingDistribu+on:Empirically-Based,Model-Based,Random
May20,2016 DukeSocialNetworks&HealthWorkshop 61
PI Parameter01
23
45
6
Smoke Alter Param
eter
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
Change in S
mokers
-0.2
-0.1
0.0
0.1
0.2
25%Ini+alSmokers 75%Ini+alSmokers
PI Parameter01
23
45
6
Smoke Alter Param
eter
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
Change in S
mokers
-0.2
-0.1
0.0
0.1
0.2
Contras?ngContexts
• Tiesaremoreorlessenduringstates– Plausibleforfriendshiporcollabora+ons– Notusefulfor“event”data(e.g.phonecalls)
• Changeoccursincon+nuous+me• Markovprocess:futurestateonlyafunc+onofcurrentstate
– Nolaggedeffects,“grudges”• Actorscontroloutgoing+esandbehavior• Onechangeata+me
– Nocoordinatedorsimultaneouschanges
May20,2016 DukeSocialNetworks&HealthWorkshop 62
Assump?ons
• Upto10%probablyok,morethan20%likelyaproblem• Endogenousnetwork&behaviorimputa+on
– Missingvaluesatt0setto0(network)ormode(behavior)– Missingvaluesatt1+imputedwithlastvalidvalueifpossible,otherwise0
• Covariatesimputedwiththemean– Othervaluescanbespecified
• Imputedvaluesaretreatedasnon-informa+ve,thusnotusedincalcula+ngtargetsta+s+cs– Convergenceandfitaredeterminedbasedonlyuponobservedcases
May20,2016 DukeSocialNetworks&HealthWorkshop 63
MissingData
GoodSourcesofInforma?on
May20,2016 DukeSocialNetworks&HealthWorkshop 64
• RSienamanual• Snijders,vandeBunt&Steglich,2010• Steglich,Snijders&Pearson,2010
• TomSnijders’SIENAwebsitewww.stats.ox.ac.uk/siena/– Workshops– Scripts– Applica+onsintheliterature– LatestversionofRSiena– Linktostocnetlistserv–importantupdatesannouncedhere– “Siena_algorithms.pdf”
EndofLecture
May20,2016 DukeSocialNetworks&HealthWorkshop 65
SAOMLab
Ifyouhaven’tdonesoalready:• Downloadthe“RSienalab.R”scriptfromdropbox• InstalltheRSienalibrary
– See“RSienalab.R”sec+on1 or– Type:install.packages("RSiena”)
May20,2016 DukeSocialNetworks&HealthWorkshop 66
• Onemodeortwomodenetworkwithatleasttwoobserva+ons,eachrepresentedasamatrix– Tiescoded0,1,10(structural0),11(structural1),orNA
• Foreach“period”betweenadjacentwaves,stabilitymeasuredbytheJaccardcoefficientshouldbeatleast.25– Tiespersisted/(+esformed++esdissolved++espersisted)
• “Completenetworkdata”allactorsw/inboundedsemng– Someturnoverinsetofactorsallowedbutsameactorsinthedataforeachwave(evenifnotobservedduringwave)
– Seemanualforhowtodealwithcomposi+onchange• RecommendedN:30-2000
May20,2016 DukeSocialNetworks&HealthWorkshop 67
DataStructure:Network
• Dependentbehaviors– Time-varyingadributesusedasdependentvariable(s)– Codedasinteger(e.g.,1-10)– Last+mepointisused
• Changingactorcovariates– Time-varyingadributesusedasindependentvariables– Last+mepointnotused(onlyapplicablefor3+waves)
• Constantcovariates– Ex:age,sex,race/ethnicity,behavior
• Dyadiccovariates– Ex:semngsthatdrivecontact NOTE:Covariatesarecenteredbydefault
May20,2016 DukeSocialNetworks&HealthWorkshop 68
Addi?onalDataStructures