【复旦大学首批FIST项目传播学研究方法讲义】9-时间序列数据

9、时间序列数据分析LongitudinalDataAnalysisJonathanZhu祝建华复旦大学新闻学院2013年FIST课程·传播研究方法OutlineWHATisandWHYuselongitudinaldataanalysisHOWtodootrendanalysis*ocohortanalysis*otimeseriesanalysisopaneldataanalysisObjectives:learningtoodistinguishcross-sectionalandlongitudinaldataoanalyzelaggedandcross-laggedmodelsounderstandautocorrelationounderstand2SLSmodels29.1IntroductiontoLongitudinalAnalysisCross-sectionalmodel:Yi=bXiwhereireferstothei-thindividual(i=1ton).Cross-sectionaldata:Cross-sectionalrelationship:Longitudinalmodel:Yt=bXtwheretreferstothei-thtimepoint(t=1toT).Longitudinaldata:Longitudinalrelationship:3IDYX…1304…2121……………n806…YXTimeYX…1304…2121……………T806…YtXWhyUseLongitudinalAnalysis?Conditionsrequiredtoestablishacausalrelationship:1.XandYarecorrelated;2.XoccursbeforeYdoes;3.OthereffectsonYarecontrolledfor/removed.Cross-sectionalanalysiscansatisfyconditions1and3,butdoesn’tsatisfycondition2.Longitudinalanalysissatisfiesallthreeconditions,bytestingifX1affectsY2.4YtXAClassificationofLongitudinalAnalysis(for9.2-9.5)TimePointsUnitofAnalysisRepeatedMeasures(2-29)TimeSeries(30+)PopulationTrendAnalysis(KZSCh15.2)TSA(KZSCh15.5)GroupCohortAnalysis(KZSCh15.3)PooledTSAIndividualPanelDataAnalysis(KZSCh15.4)MultilevelTSASource:modifiedfromKe,Zhu&Sun(2003),p.39259.2HowtoDoTrendAnalysis(brief)6Example:ChangesinMediaExposurefromT1toT27Example:ChangesinSocialIdentityduringT1-T389.3CohortAnalysis(brief)Cohort:aspecificagegroup(or“generation”)whosemembersshareuniqueexperienceduringtheirformative(youth)periodsothattheyconsistentlydifferfromothercohorts.Cohorteffectunderscoresthreesourcesofchangeovertime:oAge:theimpactofbiologicalprocess(e.g.,thesameindividualsbecomemoreconservativeastheygrowolder)oTime:theimpactofcriticaleventstoeveryoneinasociety(e.g.,911intheU.S.,512WenchuanearthquakeinChina,etc.)oCohort:theimpactofcriticaleventstoaparticulargeneration(e.g.,differentgenresofmusic)9Cohort-Age-Time(CAT)Table10Example:CohortAnalysisofAdversarialAttitudesofAmericanJournalists,1983-19881112Source:Peng&Zhu(2008).CohorttrendsinperceivedInternetinfluence.Cyberpsychology&Behavior,11,75-79.F4,4112=25.74,p0.001LongitudinalDataFormat(for9.4-9.5)Timeseriesdata:Yt=f(Xt)+etTimeYtXt…1y1x1…2y2x2……………TyTxT…“Fat”paneldata:Yit=f(Yit-1)+f(Xit)+eitIDYitYit-1XitXit-1…1y1ty1t-1x1tx1t-1…2y2ty2t-1x2tx2t-1…………………nyNtyNt-1xNtxNt-1…“Tall”paneldata*:Yit=f(Xit)+eitIDTimeYitXit…11y11x11…12y12x12…....………1Ty1Tx1T21y21x21………………nTyNTxNT…Cross-sectionaldata:Yi=f(Xi)+eiIDYiXi…1y1x1…2y2x2……………nyNxN…*Alsoknownas“pooled”datastructure,usedinmultilevelanalysis139.4PanelDataAnalysisi.Researchquestionsaskedforpaneldataanalysisii.Cross-laggedmodelofpaneldataiii.Specificationofpanelmodela)SpecifytheDVb)Specifythetimelagiv.Regressionanalysisofcross-laggedmodela)OLSregressionapproachb)2SLSregressionapproachv.Advancedtopics:otherapproachestopaneldata*14i.TypicalQuestionsforPanelDataAnalysis1.TotestcausaleffectsofXonY:DoesXattime1affectYattime2?2.TotestreciprocaleffectsbetweenXandY:DoXandYmutuallyaffecteachother?3.Toidentifytimelagofcausaleffects:HowlongdoesittakeforXtoaffectY?4.Toteststabilityofcausaleffects:DotheeffectsofXonYchangeovertime?15X1Y2X1X2Y1Y2X1Y2b0?bXbYbX=bY0?t2-t1=howlong?X1X2Y2b1b2b1=b2?X2Y2TerminologyofPanelDataAnalysis……Wave1Wave2…WavetSynchronousCorrelationSynchronous/InstantEffectAutoregression/StabilityEffectX1,…,XtandY1,…,Yt:Time-varyingvariables;Z1:Time-constantvariable16X1X2XtY1Y2YtDelayed/LaggedEffectii.Cross-laggedModelofPanelData17X1X2X3Y1Y2Y3Z1Z2Z3.........bx1x2bx2x3bx3xtby1y2by2y3by3ytby1x2by2x3by3xtbx1y2bx2y3bx3ytbz1y2bz2y3bz3ytrx1y1ry1z1rx1z1Cross-laggedCorrelationinAgenda-settingMediaAgendaatTime1MediaAgendaatTime2PublicAgendaatTime1PublicAgendaatTime2.51.19Source:ShawandMcCombs(1977)18iii.aSpecifytheFormofDV1.Changescore:∆Y=Y2–Y1AlthoughintuitiveformodelingofchangeinDV,thechangescoreisflawedintwoways:oItisnegativelycorrelatedwithY1(seenextpage)oItovercorrectsautocorrelationintheerrors2.Static(raw)score:Y2Although“static”,theimpactofY1canbemodeledasanIVofY2:Y2=b0+b1Y1NotethatY2–b1Y1≠∆Yaslongasb11,whichisusuallythecase.Conclusion:ingeneral,don’tusechangescores(∆Y)astheDV;instead,usestaticscores(i.e.,Y2).19wherethesubscripts“1”and“2”areequivalentto“t-1”and“t”,respectively.Sincesdy1andsdy2areusuallyverysimilarorevenidenticalandrY1Y2ispositivebutsmallerthan1.0,thenumeratorisusuallynegativeand,hence,theresultingcorrelationbetweenthechangescore∆YandY1isnegativeaswell.ChangeScoreandRegressiontotheMean*Eq.15.2.1Correlationbetweenthechangescore(Y2-Y1)andtheinitial/laggedscore(Y1)isgivenby:20iii.bSpecifytheTimeLagfromT1toT2TimeLagbetweent1andt2RelationshipShort-lag(totestdelayedeffects)Long-lag(totestinstanteffects)UnidirectionalYt2=b0+b1Xt1+b2Yt1Yt2=b0+b1Xt2+b2Yt1BidirectionalYt2=b0+b1Xt1+b2Yt1Xt2=b0+b3Yt1+b4Xt1Yt2=b0+b1Xt2+b2Yt1Xt2=b0+b3Yt2+b4Xt121iv.RegressionAnalysisofCross-laggedModel22Forbeginners,ordinaryleastsquare(OLS)regressionisrecommendedfortheanalysisofcross-laggedmodels,fortheeaseofcalculationandsimplicityofinterpretation.OLSRe