Statistics and Causality: Methods for Applied Empirical Research

467 Pages·2016·7.06 MB·English

by  Wolfgang Wiedermann

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STATISTICS AND
CAUSALITY
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WILEYSERIESINPROBABILITYANDSTATISTICS
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STATISTICS AND
CAUSALITY
Methods for Applied Empirical
Research
Editedby
WOLFGANGWIEDERMANN
ALEXANDERVONEYE
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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
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CONTENTS
LISTOFCONTRIBUTORS xiii
PREFACE xvii
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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
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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
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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
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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
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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
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