Table Of Content
Analysis of
Longitudinal Data
with Examples
Analysis of
Longitudinal Data
with Examples
You-Gan Wang
Liya Fu
Sudhir Paul
First edition published 2022
by CRC Press
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ISBN: 978-1-4987-6460-5 (hbk)
ISBN: 978-1-032-19652-7 (pbk)
ISBN: 978-1-315-15363-6 (ebk)
DOI: 10.1201/9781315153636
Publisher’s note: This book has been prepared from camera-ready copy provided by the authors.
To those who have passions in longitudinal data analysis
Contents
ListofFigures xiii
ListofTables xv
Preface xvii
AuthorBios xxi
Contributors xxiii
Acknowledgment xxv
1 Introduction 1
1.1 LongitudinalStudies 1
1.2 Notation 2
2 ExamplesandOrganizationofTheBook 5
2.1 ExamplesforLongitudinalStudies 5
2.1.1 HIVStudy 5
2.1.2 ProgabideStudy 5
2.1.3 HormoneStudy 7
2.1.4 TeratologyStudies 8
2.1.5 SchizophreniaStudy 11
2.1.6 LaborPainStudy 11
2.1.7 LaborMarketExperience 11
2.1.8 WaterQualityData 13
2.2 OrganizationoftheBook 14
3 ModelFrameworkandItsComponents 17
3.1 DistributionalTheory 17
3.1.1 LinearExponentialDistributionFamily 18
3.1.2 QuadraticExponentialDistributionFamily 20
3.1.3 TiltedExponentialFamily 20
3.2 Quasi-Likelihood 21
3.3 GaussianLikelihood 22
3.4 GLMandMeanFunctions 23
3.5 MarginalModels 27
3.6 ModelingtheVariance 28
vii
viii CONTENT
3.7 ModelingtheCorrelation 31
3.8 RandomEffectsModels 35
4 ParameterEstimation 37
4.1 LikelihoodApproach 38
4.2 Quasi-likelihoodApproach 39
4.3 GaussianApproach 41
4.4 GeneralizedEstimatingEquations(GEE) 44
4.4.1 EstimationofMeanParametersβ 45
4.4.2 EstimationofVarianceParametersτ 48
4.4.2.1 GaussianEstimation 48
4.4.2.2 ExtendedQuasi-likelihood 49
4.4.2.3 NonlinearRegression 50
4.4.2.4 EstimationofScaleParameterφ 50
4.4.3 EstimationofCorrelationParameters 51
4.4.3.1 StationaryCorrelationStructures 51
4.4.3.2 GeneralizedMarkovCorrelationStructure 54
4.4.3.3 SecondMomentMethod 55
4.4.3.4 GaussianEstimation 55
4.4.3.5 QuasiLeast-squares 57
4.4.3.6 ConditionalResidualMethod 58
4.4.3.7 CholeskyDecomposition 59
4.4.4 CovarianceMatrixofβˆ 63
4.4.5 Example:EpilepticData 66
4.4.6 Infeasibility 68
4.5 QuadraticInferenceFunction 72
5 ModelSelection 75
5.1 Introduction 75
5.2 SelectingCovariates 76
5.2.1 Quasi-likelihoodCriterion 76
5.2.2 GaussianLikelihoodCriterion 78
5.3 SelectingCorrelationStructure 79
5.3.1 CICCriterion 79
5.3.2 C(R)Criterion 79
5.3.3 EmpiricalLikelihoodCriteria 80
5.4 Examples 82
5.4.1 ExamplesforVariableSelection 82
5.4.2 ExamplesforCorrelationStructureSelection 82
6 RobustApproaches 89
6.1 Introduction 89
6.2 Rank-basedMethod 89
6.2.1 AnIndependenceWorkingModel 89
6.2.2 AWeightedMethod 90
CONTENT ix
6.2.3 CombinedMethod 92
6.2.4 AMethodBasedonGEE 93
6.2.5 PediatricPainToleranceStudy 94
6.3 QuantileRegression 97
6.3.1 AnIndependenceWorkingModel 98
6.3.2 AWeightedMethodBasedonGEE 99
6.3.3 ModelingCorrelationMatrixviaGaussianCopulas 99
6.3.3.1 ConstructingEstimatingFunctions 100
6.3.3.2 ParameterandCovarianceMatrixEstimation 101
6.3.4 WorkingCorrelationStructureSelection 103
6.3.5 AnalysisofDentalData 103
6.4 OtherRobustMethods 105
6.4.1 ScoreFunctionandWeightedFunction 106
6.4.2 MainAlgorithm 107
6.4.3 ChoiceofTuningParameters 108
7 ClusteredDataAnalysis 111
7.1 Introduction 111
7.1.1 ClusteredData 111
7.1.2 IntraclusterCorrelation 112
7.2 AnalysisofClusteredData:ContinuousResponses 113
7.2.1 InferenceforIntraclassCorrelationfromOne-wayAnalysis
ofVariance 113
7.2.2 Inference for Intracluster Correlation from More General
Settings 115
7.2.3 MaximumLikelihoodEstimationoftheParameters 117
7.2.4 AsymptoticVariance 120
7.2.5 InferenceforIntraclusterCorrelationCoefficient 121
7.2.6 AnalysisofClusteredorIntralitterData:DiscreteResponses 122
7.2.7 TheModels 122
7.2.8 Estimation 123
7.2.9 Inference 125
7.3 SomeExamples 125
7.4 RegressionModelsforMultilevelClusteredData 126
7.5 Two-LevelLinearModels 126
7.6 AnExample:DevelopmentalToxicityStudyofEthyleneGlycol 127
7.7 Two-LevelGeneralizedLinearModel 129
7.8 RankRegression 131
7.8.1 NationalCooperativeGallstoneStudy 132
7.8.2 ReproductiveStudy 133
8 MissingDataAnalysis 135
8.1 Introduction 135
8.2 MissingDataMechanism 135
8.3 MissingDataPatterns 137
