
Correlated Data Analysis
Modeling, Analytics, and Applications
Hardcover | 27 July 2007
At a Glance
368 Pages
23.39 x 15.6 x 2.06
Hardcover
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Industry Reviews
From the reviews:
"The book presents recent developments in the field of correlated data analysis. Its aim is to give a systematic account of regression models and their application to the modelling and analysis of correlated data. ... Various real-world data examples, numerical illustrations and software usage tips are presented throughout the book, making it suitable for graduate courses on correlated data analysis. ... also serve as a reference for those that need theoretical explanations and a deeper understanding of the theory that underlies the related analyses." (Christina Diakaki, Zentralblatt MATH, Vol. 1132 (10), 2008)
"This is an ambitious book that covers an enormous amount of material in a relatively small number of pages. ... would be a good addition to the library of a statistician interested in both the theoretical and applied aspects of correlated data analysis. ... it would be a good choice for a graduate-level course focusing on the theoretical aspects of longitudinal and discrete time series data analysis. It also might serve as a good reference book for a more applied course on this subject." (Paul S. Albert, Journal of the American Statistical Association, Vol. 103 (484), December, 2008)
"This book is a highly recommended text for those armed with a strong computational background and ambitious enough to attack real world problems of high dimension, unknown complexity, and at most hazy knowledge of the causalities. Such problems abound. i:.g., in medicine, biology, meteorology, and climate change.... The results as presented are impressive. It is amazing what can be done if one uses available software. e.g., from SAS at several instances or of related software sources, e.g., WINBUGS or "R." Anyone doing similar empirical work should read this book. (Goetz Ube, AStA - Advances in Statistical Analysis. DOI 10.1007/s10182-008-9)
"This book focuses on correlated data analysis and is divided into three main parts. ...The structure of the content is quite helpful. There are clearly laid out SAS codes that are useful for researchers. ... the book is easy to read and comprehend and it can serve as a very good guide to correlated data analysis and a useful tool in the hands of researchers and graduate students. The book is well suited to professionals working in the medical, biomedical, and econometric fields." (Filia Vonta, Mathematical Reviews, Issue 2009 e)
"The book provides several advanced mathematical tools for correlated data analysis that are useful for research and instructional purposes . In my opinion, the title Correlated Data Analysis: Modeling, Analytics, and Applications reflects the book's content perfectly. The book is very pleasant to read, and I have no doubt that Technometrics readers will enjoy reading it. ... The book is intended for statisticians or biostatistician researchers whose research interests involve theory and approaches of correlated data analysis. It addresses advanced theoretical problems arising in analysis of correlated data sets and several mathematical results underlying generalized estimating equations and quadratic inference function. The mathematical results are derived with a balance between details and elegant technical tools The book also addresses several practical problems arising in the analysis of correlated data sets and describes some real data sets that are made available to the reader. It also can serve as a good reference for a graduate students in the areas of statistics, biostatistics, or other areas where correlated data analysis is needed. ... In general, this book is very well written, well organized, and clear. The derivations of mathematical results are given with a perfect blend of simplicity, rigor, technical tools. And details. ...I think that reader will thoroughly enjoy this book..." (Technometrics, May 2010, Vol. 52, No. 2)| Preface | p. vii |
| Introduction and Examples | p. 1 |
| Correlated Data | p. 1 |
| Longitudinal Data Analysis | p. 2 |
| Data Examples | p. 6 |
| Indonesian Children's Health Study | p. 6 |
| Epileptic Seizures Data | p. 7 |
| Retinal Surgery Data | p. 9 |
| Orientation of Sandhoppers | p. 10 |
| Schizophrenia Clinical Trial | p. 11 |
| Multiple Sclerosis Trial | p. 13 |
| Tretinoin Emollient Cream Trial | p. 13 |
| Polio Incidences in USA | p. 14 |
| Tokyo Rainfall Data | p. 15 |
| Prince George Air Pollution Study | p. 16 |
| Remarks | p. 19 |
| Outline of Subsequent Chapters | p. 20 |
| Dispersion Models | p. 23 |
| Introduction | p. 23 |
| Dispersion Models | p. 25 |
| Definitions | p. 26 |
| Properties | p. 28 |
| Exponential Dispersion Models | p. 30 |
| Residuals | p. 35 |
| Tweedie Class | p. 36 |
| Maximum Likelihood Estimation | p. 37 |
| General Theory | p. 38 |
| MLE in the ED Models | p. 41 |
| MLE in the Simplex GLM | p. 42 |
| MLE in the von Mises GLM | p. 49 |
| Inference Functions | p. 55 |
| Introduction | p. 55 |
| Quasi-Likelihood Inference in GLMs | p. 56 |
| Preliminaries | p. 58 |
| Optimal Inference Functions | p. 61 |
| Multi-Dimensional Inference Functions | p. 65 |
| Generalized Method of Moments | p. 68 |
| Modeling Correlated Data | p. 73 |
| Introduction | p. 73 |
| Quasi-Likelihood Approach | p. 76 |
| Conditional Modeling Approaches | p. 80 |
| Latent Variable Based Approach | p. 80 |
| Transitional Model Based Approach | p. 82 |
| Joint Modeling Approach | p. 84 |
| Marginal Generalized Linear Models | p. 87 |
| Model Formulation | p. 88 |
| GEE: Generalized Estimating Equations | p. 89 |
| General Theory | p. 90 |
| Some Special Cases | p. 93 |
| Wald Test for Nested Models | p. 95 |
| GEE2 | p. 95 |
| Constant Dispersion Parameter | p. 96 |
| Varying Dispersion Parameter | p. 100 |
| Residual Analysis | p. 101 |
| Checking Distributional Assumption | p. 102 |
| Checking Constant Dispersion Assumption | p. 102 |
| Checking Link Functions | p. 102 |
| Checking Working Correlation | p. 102 |
| Quadratic Inference Functions | p. 103 |
| Implementation and Softwares | p. 106 |
| Newton-Scoring Algorithm | p. 106 |
| SAS PROC GENMOD | p. 107 |
| SAS MACRO QIF | p. 108 |
| Examples | p. 109 |
| Longitudinal Binary Data | p. 110 |
| Longitudinal Count Data | p. 112 |
| Longitudinal Proportional Data | p. 116 |
| Vector Generalized Linear Models | p. 121 |
| Introduction | p. 121 |
| Log-Linear Model for Correlated Binary Data | p. 122 |
| Multivariate ED Family Distributions | p. 125 |
| Copulas | p. 126 |
| Construction | p. 127 |
| Interpretation of Association Parameter | p. 129 |
| Simultaneous Maximum Likelihood Inference | p. 136 |
| General Theory | p. 136 |
| VGLMs for Correlated Continuous Outcomes | p. 137 |
| VGLMs for Correlated Discrete Outcomes | p. 138 |
| Scores for Association Parameters | p. 139 |
| Algorithms | p. 141 |
| Algorithm I: Maximization by Parts | p. 142 |
| Algorithm II: Gauss-Newton Type | p. 146 |
| An Illustration: VGLMs for Trivariate Discrete Data | p. 146 |
| Trivariate VGLMs | p. 147 |
| Comparison of Asymptotic Efficiency | p. 148 |
| Data Examples | p. 150 |
| Analysis of Two-Period Cross-Over Trial Data | p. 150 |
| Analysis of Hospital Visit Data | p. 152 |
| Analysis of Burn Injury Data | p. 153 |
| Mixed-Effects Models: Likelihood-Based Inference | p. 157 |
| Introduction | p. 157 |
| Model Specification | p. 161 |
| Estimation | p. 165 |
| MLE Based on Numerical Integration | p. 167 |
| Simulated MLE | p. 174 |
| Conditional Likelihood Estimation | p. 176 |
| MLE Based on EM Algorithm | p. 178 |
| Approximate Inference: PQL and REML | p. 182 |
| SAS Software | p. 192 |
| PROC MIXED | p. 192 |
| PROC NLMIXED | p. 193 |
| PROC GLIMMIX | p. 194 |
| Mixed-Effects Models: Bayesian Inference | p. 195 |
| Bayesian Inference Using MCMC Algorithm | p. 195 |
| Gibbs Sampling: A Practical View | p. 195 |
| Diagnostics | p. 198 |
| Enhancing Burn-in | p. 201 |
| Model Selection | p. 202 |
| An Illustration: Multiple Sclerosis Trial Data | p. 203 |
| Multi-Level Correlated Data | p. 206 |
| WinBUGS Software | p. 212 |
| WinBUGS Code in Multiple Sclerosis Trial Data Analysis | p. 213 |
| WinBUGS Code for the TEC Drug Analysis | p. 214 |
| Linear Predictors | p. 217 |
| General Results | p. 217 |
| Estimation of Random Effects in GLMMs | p. 221 |
| Estimation in LMMs | p. 221 |
| Estimation in GLMMs | p. 221 |
| Kalman Filter and Smoother | p. 222 |
| General Forms | p. 222 |
| Generalized State Space Models | p. 227 |
| Introduction | p. 227 |
| Linear State Space Models | p. 231 |
| Shift-Mean Model | p. 232 |
| Monte Carlo Maximum Likelihood Estimation | p. 235 |
| Generalized State Space Models for Longitudinal Binomial Data | p. 239 |
| Introduction | p. 239 |
| Monte Carlo Kalman Filter and Smoother | p. 240 |
| Bayesian Inference Based on MCMC | p. 246 |
| Generalized State Space Models for Longitudinal Count Data | p. 261 |
| Introduction | p. 261 |
| Generalized Estimating Equation | p. 264 |
| Monte Carlo EM Algorithm | p. 265 |
| KEE in Stationary State Processes | p. 267 |
| Setup | p. 267 |
| Kalman Filter and Smoother | p. 269 |
| Godambe Information Matrix | p. 271 |
| Analysis of Polio Incidences Data | p. 272 |
| KEE in Non-Stationary State Processes | p. 275 |
| Model Formulation | p. 275 |
| Kalman Filter and Smoother | p. 278 |
| Parameter Estimation | p. 280 |
| Model Diagnosis | p. 281 |
| Analysis of Prince George Data | p. 283 |
| Missing Data in Longitudinal Studies | p. 291 |
| Introduction | p. 291 |
| Missing Data Patterns | p. 293 |
| Patterns of Missingness | p. 293 |
| Types of Missingness and Effects | p. 297 |
| Diagnosis of Missing Data Types | p. 300 |
| Graphic Approach | p. 301 |
| Testing for MCAR | p. 302 |
| Handling MAR Mechanism | p. 306 |
| Simple Solutions and Limitations | p. 307 |
| Multiple Imputation | p. 307 |
| EM Algorithm | p. 311 |
| Inverse Probability Weighting | p. 317 |
| Handling NM AR Mechanism | p. 320 |
| Parametric Modeling | p. 320 |
| A Semiparametric Pattern Mixture Model | p. 322 |
| References | p. 329 |
| Index | p. 343 |
| Table of Contents provided by Publisher. All Rights Reserved. |
ISBN: 9780387713922
ISBN-10: 0387713921
Series: Springer Series in Statistics
Published: 27th July 2007
Format: Hardcover
Language: English
Number of Pages: 368
Audience: Professional and Scholarly
Publisher: Springer Nature B.V.
Country of Publication: US
Dimensions (cm): 23.39 x 15.6 x 2.06
Weight (kg): 0.64
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