13 an introduction to stochastic actor-oriented models (aka siena)

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


•  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)


NetworkHomogeneityonSmoking

Peer Influence

or

Friend Selection

time t

time t-1

A

C D

B

A

C D

B

A

C D

B


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


InferringNetwork→Behavior

Requirescontrollingfornetworkselec?onbasedon:1.  Pre-exis+ngsimilarityinthebehavior2.  Similarityonadributescorrelatedwiththebehavior3.  Networkprocesses,suchastriadclosure

•  Canamplifynetwork-behaviorpaderns(seebelow)


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


1.GeneralSAOMForm


•  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


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


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 -


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)


NetworkObjec?veFunc?onEffects

•  Predictchangein“behavior,”whichisthegenerictermforanindividualadribute–  Referstoanyamtude,belief,healthfactor,etc.

•  Op+onal:SAOMsdon’trequireoneandthey’renotrelevantformanyques+ons

•  Ordinalmeasurementrequired(~2-10levelsbest)•  Goalistoes+mateeffectofnetworkonbehaviorchange


BehaviorObjec?veFunc?on

BehaviorObjec?veFunc?on

•  Choiceprobabili+estaketheformofamul+nomiallogitmodelinstan+atedbytheobjec+vefunc+on

wherezrepresentsthebehavior•  Thefunc+ondictateswhichlevelofthebehavioractorsadopt

–  Actorsevaluateallpossiblechanges•  Increase/decreasebyoneunit,ornochange

–  Op+onwithhighestevalua+onmostlikely


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


BehaviorObjec?veFunc?onEffects

BehaviorDecision


Lineareffect

Quadra+ceffect

Adributeeffect(e.g.age)

Similarityeffect

Howadrac+veiseachlevelofthebehaviorbasedontheseeffects?

BehaviorDecision*


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


Second,calculatethecontribu+onsforeachoftheothereffects

BehaviorDecision*


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


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


RateFunc?ons

2.SAOMEs+ma+on


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


MarkovChainAlgorithm


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


Post-Es?ma?on2

•  GoodnessofFit•  Usesimula+onstocomparenetworksgeneratedbymodelto

sta+s+csNOTexplicitlyinthemodel–  Typicalcandidates:

•  In-&Out-degreedistribu+ons•  TriadCensus•  Geodesicdistribu+on•  Behaviordistribu+on•  Behaviornetworkassocia+ons


3.SAOMExample


AnEmpiricalExamplewithAdolescentSmoking

•  Na+onalLongitudinalStudyofAdolescentHealth(AddHealth)•  In-homesurveysconducted1994-1995(2waves)

–  Earlierin-schoolsurveyhasnetworkdatabutlimitedbehaviordata

•  Studentsnominatedupto5maleand5femalefriends(directednetwork)–  Friendshipscodedpresent(1)orabsent(0)foreachdyad


30-daysmoking

None(0)

1-11days(1)

12+days(2)

JeffersonHigh(AddHealth,1995)


•  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


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.


Rate:Eachactorisgiven~10microstepsinwhichtomakeachangetoitsnetwork•  Adda+e,dropa+e,ormake

nochange

Rate




Outdegree:Thenega+vesignistypical.Itmeansthat+esareunlikely,unlessothereffectsinthemodelmakeaposi+vecontribu+ontothenetworkfunc+on.

density




Reciprocity:Tiesthatcreateareciprocated+earemorelikelytobeaddedormaintained.Thiseffecthoversaround2infriendship-typenetwork.

recip




Transi?vetriplets:Tiesthatcreatemoretransi+vetriadshaveagreaterlikelihood.•  Shouldalsotestinterac+on

withReciprocity(usuallynega+ve)

transTrip




IndegreePopularity:Actorswithmoreincoming+eshaveagreaterlikelihoodofreceivingfuture+es

inPop




DyadicCovariate:Actorswhoshareanextracurricularac+vity(coded1)aremorelikelytohaveafriendship+e

X


Tiesdrivenbysimilarityon:Gender(coulduse“same”effect)AgeAlcoholuseGPAFemaleslessadrac+veasfriendsthanmales.


altX

egoX

simX




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



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


Rate:Studentshavearound2chancesonaverage(microsteps)tochangetheirsmokingbehavior

Rate




linear

quad




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

+ =

+ =

+ =



EgoCovariate:Delinquencyleadstohigherlevelsofsmoking


effFrom



AverageSimilarity:Studentsadoptsmokinglevelsthatbringthemclosertotheaverageoftheirfriends

xi+−1 xijj∑ (simij

z − simz )

Δ

−−Δ=

jiij

zzsim

jiij zz −=Δ max


avSim

•  Howwellisthees+matedmodelabletoreproducefeaturesoftheobserveddatathatwerenotexplicitlymodeled?–  Network

•  Degreedistribu+on•  Geodesicdistribu+on•  Triadcensus

–  Behaviordistribu?on

LotsofroomtoimproveGOFmeasures,especiallybehavior


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


GeodesicDistribu?onGoodness of Fit of GeodesicDistribution

p: 0.001

Statistic

1 2 3 4 5 6 7

1381

2795

5014

7772

10598

12081 11892


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


SmokingDistribu?onGoodness of Fit of BehaviorDistribution

p: 1

Statistic

0 1 2

222

98

182


4.Extensions&Miscellany


ExtensionstoBasicModel


•  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


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

J

S

S

S

I

Egoiscurrentlyamoderatesmoker(1)


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


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)


Evalua?ngInterven?ons

Howdosmoking/friendshipdynamicsaffectsmokingprevalence?•  Manipulatemodelparametersrelatedtokey“interven+on

levers”–  Peerinfluence(absent…strong)–  Smokerpopularity(unpopular…absent…popular)

•  Remainingmodelparametersfromfidedmodel•  Ini+alcondi+ons=observedwave1data


ResultsofManipula?ngPeerInfluence(PI)andSmoking-basedPopularity(smokealter)

SchaeferDR,adamsj,HaasSA.2013.SocialNetworksandSmoking:ExploringtheEffectsofPeerInfluence

andSmokerPopularitythroughSimula+ons.HealthEduca'on&Behavior,40(S1):24-32.


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.



SmokingDistribu+on:Empirically-Based,Model-Based,Random


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


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


MissingData

GoodSourcesofInforma?on


•  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


SAOMLab

Ifyouhaven’tdonesoalready:•  Downloadthe“RSienalab.R”scriptfromdropbox•  InstalltheRSienalibrary

– See“RSienalab.R”sec+on1 or– Type:install.packages("RSiena”)


•  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


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


Addi?onalDataStructures

13 an introduction to stochastic actor-oriented models (aka siena)

Science