(cid:2) STATISTICS AND CAUSALITY (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) WILEYSERIESINPROBABILITYANDSTATISTICS EstablishedbyWALTERA.SHEWHARTandSAMUELS.WILKS Editors:DavidJ.Balding,NoelA.C.Cressie,GarrettM.Fitzmaurice, GeofH.Givens,HarveyGoldstein,GeertMolenberghs,DavidW.Scott, AdrianF.M.Smith,RueyS.Tsay,SanfordWeisberg EditorsEmeriti:J.StuartHunter,IainM.Johnstone,JosephB.Kadane, JozefL.Teugels Acompletelistofthetitlesinthisseriesappearsattheendofthisvolume. (cid:2) (cid:2) STATISTICS AND CAUSALITY Methods for Applied Empirical Research Editedby WOLFGANGWIEDERMANN ALEXANDERVONEYE (cid:2) (cid:2) (cid:2) (cid:2) Copyright©2016byJohnWiley&Sons,Inc.Allrightsreserved PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey PublishedsimultaneouslyinCanada Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformor byanymeans,electronic,mechanical,photocopying,recording,scanning,orotherwise,exceptas permittedunderSection107or108ofthe1976UnitedStatesCopyrightAct,withouteithertheprior writtenpermissionofthePublisher,orauthorizationthroughpaymentoftheappropriateper-copyfeeto theCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,(978)750-8400,fax (978)750-4470,oronthewebatwww.copyright.com.RequeststothePublisherforpermissionshould beaddressedtothePermissionsDepartment,JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ 07030,(201)748-6011,fax(201)748-6008,oronlineathttp://www.wiley.com/go/permissions. LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsin preparingthisbook,theymakenorepresentationsorwarrantieswithrespecttotheaccuracyor completenessofthecontentsofthisbookandspecificallydisclaimanyimpliedwarrantiesof merchantabilityorfitnessforaparticularpurpose.Nowarrantymaybecreatedorextendedbysales representativesorwrittensalesmaterials.Theadviceandstrategiescontainedhereinmaynotbesuitable foryoursituation.Youshouldconsultwithaprofessionalwhereappropriate.Neitherthepublishernor authorshallbeliableforanylossofprofitoranyothercommercialdamages,includingbutnotlimitedto special,incidental,consequential,orotherdamages. Forgeneralinformationonourotherproductsandservicesorfortechnicalsupport,pleasecontactour CustomerCareDepartmentwithintheUnitedStatesat(800)762-2974,outsidetheUnitedStatesat (cid:2) (317)572-3993orfax(317)572-4002. (cid:2) Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmay notbeavailableinelectronicformats.FormoreinformationaboutWileyproducts,visitourwebsiteat www.wiley.com. LibraryofCongressCataloging-in-PublicationData: Names:Wiedermann,Wolfgang,1981-editorofcompilation.|Eye,Alexander von,editorofcompilation. Title:Statisticsandcausality:methodsforappliedempiricalresearch/ editedbyWolfgangWiedermann,AlexandervonEye. Othertitles:Wileyseriesinprobabilityandstatistics. Description:Hoboken,NewJersey:JohnWiley&Sons,2016.|Series:Wiley seriesinprobabilityandstatistics|Includesbibliographicalreferences andindex. Identifiers:LCCN2015047424(print)|LCCN2015050865(ebook)|ISBN 9781118947043(cloth)|ISBN9781118947050(pdf)|ISBN9781118947067 (epub) Subjects:LCSH:Statistics–Methodology.|Causation.|Quantitative research–Methodology. Classification:LCCQA276.A2S732016(print)|LCCQA276.A2(ebook)|DDC 001.4/22–dc23 LCrecordavailableathttp://lccn.loc.gov/2015047424 Typesetin10/12ptTimesLTStdbySPiGlobal,Chennai,India PrintedintheUnitedStatesofAmerica 10987654321 (cid:2) (cid:2) CONTENTS LISTOFCONTRIBUTORS xiii PREFACE xvii (cid:2) (cid:2) ACKNOWLEDGMENTS xxv PARTI BASESOFCAUSALITY 1 1 CausationandtheAimsofInquiry 3 NedHall 1.1 Introduction, 3 1.2 TheAimofanAccountofCausation, 4 1.2.1 ThePossibleUtilityofaFalseAccount, 4 1.2.2 Inquiry’sAim, 5 1.2.3 Roleof“Intuitions”, 6 1.3 TheGoodNews, 7 1.3.1 TheCoreIdea, 7 1.3.2 Taxonomizing“Conditions”, 9 1.3.3 Unpacking“Dependence”, 10 1.3.4 TheGoodNews,Amplified, 12 1.4 TheChallengingNews, 17 1.4.1 MultipleRealizability, 17 1.4.2 ProtractedCauses, 18 1.4.3 HigherLevelTaxonomiesand“Normal”Conditions, 25 (cid:2) (cid:2) vi CONTENTS 1.5 ThePerplexingNews, 26 1.5.1 TheCentralityof“CausalProcess”, 26 1.5.2 ASpeculativeProposal, 28 2 EvidenceandEpistemicCausality 31 MichaelWilde&JonWilliamson 2.1 CausalityandEvidence, 31 2.2 TheEpistemicTheoryofCausality, 35 2.3 TheNatureofEvidence, 38 2.4 Conclusion, 40 PARTII DIRECTIONALITYOFEFFECTS 43 3 StatisticalInferenceforDirectionofDependenceinLinearModels 45 YadolahDodge&ValentinRousson 3.1 Introduction, 45 3.2 ChoosingtheDirectionofaRegressionLine, 46 3.3 SignificanceTestingfortheDirectionofaRegressionLine, 48 3.4 LurkingVariablesandCausality, 54 (cid:2) 3.4.1 TwoIndependentPredictors, 55 (cid:2) 3.4.2 ConfoundingVariable, 55 3.4.3 SelectionofaSubpopulation, 56 3.5 BrainandBodyDataRevisited, 57 3.6 Conclusions, 60 4 DirectionalityofEffectsinCausalMediationAnalysis 63 WolfgangWiedermann&AlexandervonEye 4.1 Introduction, 63 4.2 ElementsofCausalMediationAnalysis, 66 4.3 DirectionalityofEffectsinMediationModels, 68 4.4 TestingDirectionalityUsingIndependencePropertiesofCompeting MediationModels, 71 4.4.1 IndependencePropertiesofBivariateRelations, 72 4.4.2 IndependencePropertiesoftheMultipleVariableModel, 74 4.4.3 MeasuringandTestingIndependence, 74 4.5 SimulatingthePerformanceofDirectionalityTests, 82 4.5.1 Results, 83 4.6 EmpiricalDataExample:DevelopmentofNumericalCognition, 85 4.7 Discussion, 92 (cid:2) (cid:2) CONTENTS vii 5 DirectionofEffectsinCategoricalVariables:AStructural Perspective 107 AlexandervonEye&WolfgangWiedermann 5.1 Introduction, 107 5.2 ConceptsofIndependenceinCategoricalDataAnalysis, 108 5.3 DirectionDependenceinBivariateSettings:MetricandCategorical Variables, 110 5.3.1 SimulatingthePerformanceofNonhierarchicalLog-Linear Models, 114 5.4 ExplainingtheStructureofCross-Classifications, 117 5.5 DataExample, 123 5.6 Discussion, 126 6 DirectionalDependenceAnalysisUsingSkew–NormalCopula-Based Regression 131 SeongyongKim&DaeyoungKim 6.1 Introduction, 131 6.2 Copula-BasedRegression, 133 6.2.1 Copula, 133 6.2.2 Copula-BasedRegression, 134 (cid:2) 6.3 DirectionalDependenceintheCopula-BasedRegression, 136 (cid:2) 6.4 Skew–NormalCopula, 138 6.5 InferenceofDirectionalDependenceUsingSkew–Normal Copula-BasedRegression, 144 6.5.1 EstimationofCopula-BasedRegression, 144 6.5.2 DetectionofDirectionalDependenceandComputationofthe DirectionalDependenceMeasures, 146 6.6 Application, 147 6.7 Conclusion, 150 7 Non-GaussianStructuralEquationModelsforCausalDiscovery 153 ShoheiShimizu 7.1 Introduction, 153 7.2 IndependentComponentAnalysis, 156 7.2.1 Model, 157 7.2.2 Identifiability, 157 7.2.3 Estimation, 158 7.3 BasicLinearNon-GaussianAcyclicModel, 158 7.3.1 Model, 158 7.3.2 Identifiability, 160 7.3.3 Estimation, 162 7.4 LINGAMforTimeSeries, 167 7.4.1 Model, 167 (cid:2) (cid:2) viii CONTENTS 7.4.2 Identifiability, 168 7.4.3 Estimation, 168 7.5 LINGAMwithLatentCommonCauses, 169 7.5.1 Model, 169 7.5.2 Identifiability, 171 7.5.3 Estimation, 174 7.6 ConclusionandFutureDirections, 177 8 NonlinearFunctionalCausalModelsforDistinguishingCausefrom Effect 185 KunZhang&AapoHyvärinen 8.1 Introduction, 185 8.2 NonlinearAdditiveNoiseModel, 188 8.2.1 DefinitionofModel, 188 8.2.2 LikelihoodRatioforNonlinearAdditiveModels, 188 8.2.3 Information-TheoreticInterpretation, 189 8.2.4 LikelihoodRatioandIndependence-BasedMethods, 191 8.3 Post-NonlinearCausalModel, 192 8.3.1 TheModel, 192 8.3.2 IdentifiabilityofCausalDirection, 193 8.3.3 DeterminationofCausalDirectionBasedonthePNLCausal (cid:2) Model, 193 (cid:2) 8.4 OntheRelationshipsBetweenDifferentPrinciplesforModel Estimation, 194 8.5 RemarkonGeneralNonlinearCausalModels, 196 8.6 SomeEmpiricalResults, 197 8.7 DiscussionandConclusion, 198 PARTIII GRANGERCAUSALITYANDLONGITUDINALDATA MODELING 203 9 AlternativeFormsofGrangerCausality,Heterogeneity,and Nonstationarity 205 PeterC.M.Molenaar&LawrenceL.Lo 9.1 Introduction, 205 9.2 SomeInitialRemarksontheLogicofGrangerCausalityTesting, 206 9.3 PreliminaryIntroductiontoTimeSeriesAnalysis, 207 9.4 OverviewofGrangerCausalityTestingintheTimeDomain, 210 9.5 GrangerCausalityTestingintheFrequencyDomain, 212 9.5.1 TwoEquivalentRepresentationsofaVAR(a), 212 9.5.2 PartialDirectedCoherence(PDC)asaFrequency-Domain IndexofGrangerCausality, 213 9.5.3 SomePreliminaryComments, 214 (cid:2)