Table Of Content(cid:2)
DirectionDependenceinStatisticalModeling
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Direction Dependence in Statistical
Modeling
Methods of Analysis
Edited by
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Wolfgang Wiedermann
Daeyoung Kim
Engin A. Sungur
Alexander von Eye
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Thiseditionfirstpublished2021
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LibraryofCongressCataloging-in-PublicationData
Names:Wiedermann,Wolfgang,1981-editor.|Kim,Daeyoung,editor.|
Sungur,Engin,editor.|Eye,Alexandervon,editor.
Title:Directiondependenceinstatisticalmodeling:methodsofanalysis/
editedbyWolfgangWiedermann,DaeyoungKim,EnginSungur,Alexandervon
Eye.
Description:Hoboken,NJ:Wiley,2021.|Includesbibliographical
referencesandindex.
Identifiers:LCCN2020015364(print)|LCCN2020015365(ebook)|ISBN
9781119523079(cloth)|ISBN9781119523130(adobepdf)|ISBN
9781119523147(epub)
Subjects:LCSH:Dependence(Statistics)
Classification:LCCQA273.18.D572020(print)|LCCQA273.18(ebook)|
DDC519.5–dc23
LCrecordavailableathttps://lccn.loc.gov/2020015364
LCebookrecordavailableathttps://lccn.loc.gov/2020015365
CoverdesignbyWiley
Coverimage:©zhengshuntang/GettyImages
Setin9.5/12.5ptSTIXTwoTextbySPiGlobal,Chennai,India
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
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ToAnnaandLinus
—W.W
TomywifeShu-MinandmysonMinjun
—D.K
TomywifeLamiaSungur
—E.S
ToDonata,theoriginofdirection
—A.vE
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vii
Contents
AbouttheEditors xv
NotesonContributors xvii
Acknowledgments xxi
Preface xxiii
PartI FundamentalConceptsofDirectionDependence 1
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1 FromCorrelationtoDirectionDependenceAnalysis
1888–2018 3
YadolahDodgeandValentinRousson
1.1 Introduction 3
1.2 CorrelationasaSymmetricalConceptofXandY 4
1.3 CorrelationasanAsymmetricalConceptofXandY 5
1.4 OutlookandConclusions 6
References 6
2 DirectionDependenceAnalysis:StatisticalFoundationsand
Applications 9
WolfgangWiedermann,XintongLi,andAlexandervonEye
2.1 SomeOriginsofDirectionDependenceResearch 11
2.2 CausationandAsymmetryofDependence 13
2.3 FoundationsofDirectionDependence 14
2.3.1 DataRequirements 15
2.3.2 DDAComponentI:DistributionalPropertiesofObserved
Variables 16
2.3.3 DDAComponentII:DistributionalPropertiesofErrors 19
2.3.4 DDAComponentIII:IndependenceProperties 20
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viii Contents
2.3.5 PresenceofConfounding 21
2.3.6 AnIntegratedFramework 24
2.4 DirectionDependenceinMediation 29
2.5 DirectionDependenceinModeration 32
2.6 SomeApplicationsandSoftwareImplementations 34
2.7 ConclusionsandFutureDirections 36
References 38
3 TheUseofCopulasforDirectionalDependence
Modeling 47
EnginA.Sungur
3.1 IntroductionandDefinitions 47
3.1.1 WhyCopulas? 48
3.1.2 DefiningDirectionalDependence 48
3.2 DirectionalDependenceBetweenTwoNumericalVariables 51
3.2.1 AsymmetricCopulas 52
3.2.2 RegressionSetting 59
3.2.3 AnAlternativeApproachtoDirectionalDependence 62
3.3 DirectionalAssociationBetweenTwoCategoricalVariables 70
3.4 ConcludingRemarksandFutureDirections 74
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References 75
PartII DirectionDependenceinContinuousVariables 79
4 AsymmetryPropertiesofthePartialCorrelationCoefficient:
FoundationsforCovariateAdjustmentinDistribution-Based
DirectionDependenceAnalysis 81
WolfgangWiedermann
4.1 AsymmetryPropertiesofthePartialCorrelationCoefficient 84
4.2 DirectionDependenceMeasureswhenErrorsAreNon-Normal 86
4.3 StatisticalInferenceonDirectionDependence 89
4.4 Monte-CarloSimulations 90
4.4.1 StudyI:ParameterRecovery 90
4.4.1.1 Results 91
4.4.2 StudyII:CICoverageandStatisticalPower 91
4.4.2.1 TypeIErrorCoverage 94
4.4.2.2 StatisticalPower 94
4.5 DataExample 98
4.6 Discussion 101
4.6.1 RelationtoCausalInferenceMethods 103
References 105
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Contents ix
5 RecentAdvancesinSemi-ParametricMethodsforCausal
Discovery 111
ShoheiShimizuandPatrickBlöbaum
5.1 Introduction 111
5.2 LinearNon-GaussianMethods 113
5.2.1 LiNGAM 113
5.2.2 HiddenCommonCauses 115
5.2.3 TimeSeries 118
5.2.4 MultipleDataSets 119
5.2.5 OtherMethodologicalIssues 119
5.3 NonlinearBivariateMethods 119
5.3.1 AdditiveNoiseModels 120
5.3.1.1 Post-NonlinearModels 121
5.3.1.2 DiscreteAdditiveNoiseModels 121
5.3.2 IndependenceofMechanismandInput 121
5.3.2.1 Information-GeometricApproachforCausalInference 122
5.3.2.2 CausalInferencewithUnsupervisedInverseRegression 123
5.3.2.3 ApproximationofKolmogorovComplexitiesviatheMinimum
DescriptionLengthPrinciple 123
5.3.2.4 RegressionErrorBasedCausalInference 124
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5.3.3 ApplicationstoMultivariateCases 125
5.4 Conclusion 125
References 126
6 AssumptionCheckingforDirectionalCausality
Analyses 131
PhillipK.Wood
6.1 EpistemicCausality 135
6.1.1 ExampleDataSet 136
6.2 AssessmentofFunctionalForm:LoessRegression 137
6.3 InfluentialandOutlyingObservations 140
6.4 DirectionalDependenceBasedonAllAvailableData 141
6.4.1 StudentizedDeletedResiduals 143
6.4.2 Lever 143
6.4.3 DFFITS 144
6.4.4 DFBETA 145
6.4.5 ResultsfromInfluenceDiagnostics 145
6.4.6 DirectionalDependenceBasedonFactorScores 148
6.5 DirectionalDependenceBasedonLatentDifferenceScores 149
6.6 DirectionDependenceBasedonState-TraitModels 153
6.7 Discussion 156
References 163
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7 CompleteDependence:ASurvey 167
SantiTasena
7.1 BasicProperties 168
7.2 MeasureofCompleteDependence 171
7.3 ExampleCalculation 177
7.4 FutureWorksandOpenProblems 180
References 181
PartIII DirectionDependenceinCategorical
Variables 183
8 LocatingDirectionDependenceUsingLog-LinearModeling,
ConfiguralFrequencyAnalysis,andPredictionAnalysis 185
AlexandervonEyeandWolfgangWiedermann
8.1 SpecifyingDirectionalHypothesesinCategoricalVariables 187
8.2 TypesofDirectionalHypotheses 192
8.2.1 MultiplePremisesandOutcomes 192
8.3 AnalyzingEvent-BasedDirectionalHypotheses 193
8.3.1 Log-LinearModelsofDirectionDependence 193
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8.3.1.1 IdentificationIssues 197
8.3.2 ConfirmatoryConfiguralFrequencyAnalysis(CFA)ofDirection
Dependence 198
8.3.3 PredictionAnalysisofCross-Classifications 200
8.3.3.1 DescriptiveMeasuresofPredictionSuccess 202
8.4 DataExample 203
8.4.1 Log-LinearAnalysis 205
8.4.2 ConfiguralAnalysis 206
8.4.3 PredictionAnalysis 208
8.5 ReversingDirectionofEffect 209
8.5.1 Log-LinearModelingoftheRe-SpecifiedHypotheses 209
8.5.2 CFAoftheRe-SpecifiedHypotheses 210
8.5.3 PAoftheRe-SpecifiedHypotheses 212
8.6 Discussion 212
References 215
9 RecentDevelopmentsonAsymmetricAssociationMeasures
forContingencyTables 219
XiaonanZhu,ZhengWei,andTonghuiWang
9.1 Introduction 219
9.2 MeasuresonTwo-WayContingencyTables 220
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Contents xi
9.2.1 FunctionalChi-SquareStatistic 220
9.2.2 MeasuresofCompleteDependence 222
9.2.3 AMeasureofAsymmetricAssociationUsingSubcopula-Based
Regression 223
9.3 AsymmetricMeasuresofThree-WayContingencyTables 225
9.3.1 MeasuresofCompleteDependenceforThreeWayContingency
Table 225
9.3.2 SubcopulaBasedMeasureforThreeWayContingencyTable 232
9.3.3 Estimation 235
9.4 SimulationofThree-WayContingencyTables 237
9.5 RealDataofThree-WayContingencyTables 239
References 240
10 AnalysisofAsymmetricDependenceforThree-Way
ContingencyTablesUsingtheSubcopulaApproach 243
DaeyoungKimandZhengWei
10.1 Introduction 243
10.2 ReviewonSubcopulaBasedAsymmetricAssociationMeasurefor
OrdinalTwo-WayContingencyTable 245
10.3 MeasureofAsymmetricAssociationforOrdinalThree-Way
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ContingencyTablesviaSubcopulaRegression 248
10.3.1 SubcopulaRegression-BasedAsymmetricAssociationMeasures 248
10.3.2 Estimation 251
10.4 NumericalExamples 253
10.4.1 SensitivityAnalysis 253
10.4.2 DataAnalysis 257
10.5 Conclusion 260
10.A Appendix 261
10.A.1 TheProofofProposition10.1 261
References 262
PartIV ApplicationsandSoftware 265
11 Distribution-BasedCausalInference:AReviewandPractical
GuidanceforEpidemiologists 267
TomRosenströmandReginaGarcía-Velázquez
11.1 Introduction 267
11.2 DirectionofDependenceinLinearRegression 268
11.3 PreviousEpidemiologicApplicationsofDistribution-BasedCausal
Inference 271
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11.4 ARunningExample:Re-VisitingtheCaseofSleepProblemsand
Depression 273
11.5 EvaluatingtheAssumptionsinPracticalWork 274
11.5.1 TestingLinearity 275
11.5.2 TestingNon-Normality 276
11.5.3 TestingIndependence 277
11.6 Distribution-BasedCausalityEstimatesfortheRunningExample 278
11.7 ConductingSensitivityAnalyses 279
11.7.1 ConvergentEvidencefromMultipleEstimators 279
11.7.2 Simulation-BasedAnalysisofRobustnesstoLatentConfounding 279
11.7.2.1 ObtainData-BasedParameters 281
11.7.2.2 DefiningParametersandSimulationConditions 281
11.7.2.3 DefiningtheSimulationModel 282
11.7.2.4 RunSimulationandInterpretResults 283
11.8 Simulation-BasedAnalysisofStatisticalPower 284
11.9 TriangulatingCausalInferences 288
11.10 Conclusion 291
References 292
12 DeterminingCausalityinRelationtoEarlyRiskFactorsfor
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ADHD:TheCaseofBreastfeedingDuration 295
JoelT.Nigg,DianeD.Stadler,AlexandervonEye,andWolfgang
Wiedermann
12.1 Method 298
12.1.1 Participants 298
12.1.1.1 RecruitmentandIdentification 298
12.1.1.2 ParentalPsychopathology 299
12.1.1.3 EthicalStandards 300
12.1.2 ExclusionCriteria 300
12.1.2.1 AssessmentofBreastfeedingDuration 300
12.1.3 Covariates 301
12.1.3.1 ParentalEducation 301
12.1.3.2 PrimaryResidenceandFamilyIncome 301
12.1.3.3 ParentalOccupationalStatus 301
12.1.4 DataReductionandDataAnalysis 301
12.1.4.1 ParentalADHD 301
12.1.4.2 DataReduction 301
12.1.4.3 DataAnalysis 302
12.2 Results 304
12.2.1 StudyParticipantDemographicandClinicalCharacteristics 304
12.3 Discussion 316
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