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E-raamat: Analysis of Longitudinal Data with Examples

(Queensland University of Technology, Brisbane, Australia), (Xi'an Jiaotong University, PR of China), (University of Windsor, Canada)
  • Formaat: 252 pages
  • Ilmumisaeg: 16-Feb-2022
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781498764629
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Analysis of Longitudinal Data with ExamplesSuurem pilt
  • Formaat: 252 pages
  • Ilmumisaeg: 16-Feb-2022
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781498764629
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Development in methodology on longitudinal data is fast. Currently, there are a lack of intermediate /advanced level textbooks which introduce students and practicing statisticians to the updated methods on correlated data inference. This book will present a discussion of the modern approaches to inference, including the links between the theories of estimators and various types of efficient statistical models including likelihood-based approaches. The theory will be supported with practical examples of R-codes and R-packages applied to interesting case-studies from a number of different areas.

Key Features:

Includes the most up-to-date methods

Use simple examples to demonstrate complex methods

Uses real data from a number of areas

Examples utilize R code
List of Figures
xiii
List of Tables
xv
Preface xvii
Author Bios xxi
Contributors xxiii
Acknowledgment xxv
1 Introduction
1(4)
1.1 Longitudinal Studies
1(1)
1.2 Notation
2(3)
2 Examples and Organization of The Book
5(12)
2.1 Examples for Longitudinal Studies
5(9)
2.1.1 HIV Study
5(1)
2.1.2 Progabide Study
5(2)
2.1.3 Hormone Study
7(1)
2.1.4 Teratology Studies
8(3)
2.1.5 Schizophrenia Study
11(1)
2.1.6 Labor Pain Study
11(1)
2.1.7 Labor Market Experience
11(2)
2.1.8 Water Quality Data
13(1)
2.2 Organization of the Book
14(3)
3 Model Framework and Its Components
17(20)
3.1 Distributional Theory
17(4)
3.1.1 Linear Exponential Distribution Family
18(2)
3.1.2 Quadratic Exponential Distribution Family
20(1)
3.1.3 Tilted Exponential Family
20(1)
3.2 Quasi-Likelihood
21(1)
3.3 Gaussian Likelihood
22(1)
3.4 GLM and Mean Functions
23(4)
3.5 Marginal Models
27(1)
3.6 Modeling the Variance
28(3)
3.7 Modeling the Correlation
31(4)
3.8 Random Effects Models
35(2)
4 Parameter Estimation
37(38)
4.1 Likelihood Approach
38(1)
4.2 Quasi-likelihood Approach
39(2)
4.3 Gaussian Approach
41(3)
4.4 Generalized Estimating Equations (GEE)
44(28)
4.4.1 Estimation of Mean Parameters β
45(3)
4.4.2 Estimation of Variance Parameters τ
48(1)
4.4.2.1 Gaussian Estimation
48(1)
4.4.2.2 Extended Quasi-likelihood
49(1)
4.4.2.3 Nonlinear Regression
50(1)
4.4.2.4 Estimation of Scale Parameter φ
50(1)
4.4.3 Estimation of Correlation Parameters
51(1)
4.4.3.1 Stationary Correlation Structures
51(3)
4.4.3.2 Generalized Markov Correlation Structure
54(1)
4.4.3.3 Second Moment Method
55(1)
4.4.3.4 Gaussian Estimation
55(2)
4.4.3.5 Quasi Least-squares
57(1)
4.4.3.6 Conditional Residual Method
58(1)
4.4.3.7 Cholesky Decomposition
59(4)
4.4.4 Covariance Matrix of β
63(3)
4.4.5 Example: Epileptic Data
66(2)
4.4.6 Infeasibility
68(4)
4.5 Quadratic Inference Function
72(3)
5 Model Selection
75(14)
5.1 Introduction
75(1)
5.2 Selecting Covariates
76(3)
5.2.1 Quasi-likelihood Criterion
76(2)
5.2.2 Gaussian Likelihood Criterion
78(1)
5.3 Selecting Correlation Structure
79(3)
5.3.1 CIC Criterion
79(1)
5.3.2 C(R) Criterion
79(1)
5.3.3 Empirical Likelihood Criteria
80(2)
5.4 Examples
82(7)
5.4.1 Examples for Variable Selection
82(1)
5.4.2 Examples for Correlation Structure Selection
82(7)
6 Robust Approaches
89(22)
6.1 Introduction
89(1)
6.2 Rank-based Method
89(8)
6.2.1 An Independence Working Model
89(1)
6.2.2 A Weighted Method
90(2)
6.2.3 Combined Method
92(1)
6.2.4 A Method Based on GEE
93(1)
6.2.5 Pediatric Pain Tolerance Study
94(3)
6.3 Quantile Regression
97(8)
6.3.1 An Independence Working Model
98(1)
6.3.2 A Weighted Method Based on GEE
99(1)
6.3.3 Modeling Correlation Matrix via Gaussian Copulas
99(1)
6.3.3.1 Constructing Estimating Functions
100(1)
6.3.3.2 Parameter and Covariance Matrix Estimation
101(2)
6.3.4 Working Correlation Structure Selection
103(1)
6.3.5 Analysis of Dental Data
103(2)
6.4 Other Robust Methods
105(6)
6.4.1 Score Function and Weighted Function
106(1)
6.4.2 Main Algorithm
107(1)
6.4.3 Choice of Tuning Parameters
108(3)
7 Clustered Data Analysis
111(24)
7.1 Introduction
111(2)
7.1.1 Clustered Data
111(1)
7.1.2 Intracluster Correlation
112(1)
7.2 Analysis of Clustered Data: Continuous Responses
113(12)
7.2.1 Inference for Intraclass Correlation from One-way Analysis of Variance
113(2)
7.2.2 Inference for Intracluster Correlation from More General Settings
115(2)
7.2.3 Maximum Likelihood Estimation of the Parameters
117(3)
7.2.4 Asymptotic Variance
120(1)
7.2.5 Inference for Intracluster Correlation Coefficient
121(1)
7.2.6 Analysis of Clustered or Intralitter Data: Discrete Responses
122(1)
7.2.7 The Models
122(1)
7.2.8 Estimation
123(2)
7.2.9 Inference
125(1)
7.3 Some Examples
125(1)
7.4 Regression Models for Multilevel Clustered Data
126(1)
7.5 Two-Level Linear Models
126(1)
7.6 An Example: Developmental Toxicity Study of Ethylene Glycol
127(2)
7.7 Two-Level Generalized Linear Model
129(2)
7.8 Rank Regression
131(4)
7.8.1 National Cooperative Gallstone Study
132(1)
7.8.2 Reproductive Study
133(2)
8 Missing Data Analysis
135(36)
8.1 Introduction
135(1)
8.2 Missing Data Mechanism
135(2)
8.3 Missing Data Patterns
137(2)
8.4 Missing Data Methodologies
139(8)
8.4.1 Missing Data Methodologies: The Methods of Imputation
140(1)
8.4.1.1 Last Value Carried Forward Imputation
140(1)
8.4.1.2 Imputation by Related Observation
140(1)
8.4.1.3 Imputation by Unconditional Mean
140(1)
8.4.1.4 Imputation by Conditional Mean
140(1)
8.4.1.5 Hot Deck Imputation
140(1)
8.4.1.6 Cold Deck Imputation
141(1)
8.4.1.7 Imputation by Substitution
141(1)
8.4.1.8 Regression Imputation
141(1)
8.4.2 Missing Data Methodologies: Likelihood Methods
141(6)
8.5 Analysis of Zero-inflated Count Data With Missing Values
147(8)
8.5.1 Estimation of the Parameters with No Missing Data
148(1)
8.5.2 Estimation of the Parameters with Missing Responses
149(1)
8.5.2.1 Estimation under MCAR
149(1)
8.5.2.2 Estimation under MAR
150(3)
8.5.2.3 Estimation under MNAR
153(2)
8.6 Analysis of Longitudinal Data With Missing Values
155(16)
8.6.1 Normally Distributed Data
155(2)
8.6.2 Complete-data Estimation via the EM
157(3)
8.6.3 Estimation with Nonignorable Missing Response Data (MAR and MNAR)
160(4)
8.6.4 Generalized Estimating Equations
164(1)
8.6.4.1 Introduction
164(1)
8.6.4.2 Weighted GEE for MAR Data
164(1)
8.6.5 Some Applications of the Weighted GEE
165(1)
8.6.5.1 Weighted GEE for Binary Data
165(1)
8.6.5.2 Two Modifications
166(5)
9 Random Effects and Transitional Models
171(18)
9.1 A General Discussion
171(1)
9.2 Random Intercept Models
172(1)
9.3 Linear Mixed Effects models
173(3)
9.4 Generalized Linear Mixed Effects Models
176(5)
9.4.1 The Logistic Random Effects Models
176(1)
9.4.2 The Binomial Random Effects Models
177(1)
9.4.3 The Poisson Random Effects Models
177(3)
9.4.4 Examples: Estimation for European Red Mites Data and the Ames Salmonella Assay Data
180(1)
9.5 Transition Models
181(3)
9.6 Fitting Transition Models
184(1)
9.7 Transition Model for Categorical Data
185(3)
9.8 Further reading
188(1)
10 Handing High Dimensional Longitudinal Data
189(12)
10.1 Introduction
189(1)
10.2 Penalized Methods
190(3)
10.2.1 Penalized GEE
190(2)
10.2.2 Penalized Robust GEE-type Methods
192(1)
10.3 Smooth-threshold Method
193(2)
10.4 Yeast Data Study
195(1)
10.5 Further Reading
196(5)
Bibliography 201(16)
Author Index 217(6)
Subject Index 223
Professor Wang obtained his Ph.D. on dynamic optimization in 1991 (University of Oxford) and worked for CSIRO (20052010). Before returning to Australia, Professor Wang worked for the National University of Singapore (20012005) and Harvard University as Assistant Professor and Associate Professor (19982000) in biostatistics. He joined the University of Queensland in April 2010 as Chair Professor of Applied Statistics to lead the Centre for Applications in Natural Resource Mathematics and to promote applied statistics and mathematics. Currently, he is Capacity Building Professor in Data Science at Queensland University of Technology, Australia. Professor Wang has developed a number of novel statistical methodologies in longitudinal data analysis published by top statistical journals (Biometrika, Biometrics, Statistics in Medicine, Journal of the American Statistician Association, Annals of Statistics). His recent interests and successes include (1) working likelihood approach for hyperparameter estimation and model selection, (2) integrating statistical learning and machine learning for dependent data analysis and (3) data-driven approach for robust estimation. More recently, he advocates working likelihood approaches to parameter estimation but recognizing possibly a different likelihood that generating the observed data in inferencing. This has been found very useful in finding datadependent tuning parameters in robust estimation and hyper-parameters in machine learning algorithms.

Liya Fu obtained her Ph.D. in 2010 from Northeast Normal University. Currently she is Associate Professor of Statistics at Xian Jiaotong University. She worked briefly as a Postdoctoral Fellow at the University of Queensland after after two-years visiting student at CSIRO (2008010), Australia. Dr. Fu mainly focuses on the methodologies for the analysis of longitudinal data and has published about 20 papers in international journals, including Biometrics, Statistics in Medicine, Journal of Multivariate Analysis. Professor Sudhir Paul obtained his PhD in 1976 (University of Wales). He worked as a Postdoctoral Fellow (University of Newcastle Upon Tyne, 1976- 1978) and a Lecturer (University of Kent at Canterbury, 1978-1982) before moving to Canada in 1982. He started as Assistant Professor at the University of Windsor and moved through all professorial ranks and finally in 2005 became distinguished University Professor. He became Fellow of the Royal Statistical Society in 1982 and Fellow of the American Statistical Association in 1986.

Professor Paul has developed many methodologies for the analyses of overdispersed and zero-inflated count data, longitudinal data, and familial data and published in most of the top-tier journals in statistics (Journal of the Royal Statistical Society, Biometrika, Biometrics, Journal of the American Statistician Association, Technometrics). Professor Paul supervised over 50 graduate students including 16 PhD students and has published over 100 papers.
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