Correlated Data Analysis: Modeling, Analytics, and Applications

Thisbook,likemanyotherbooks,wasdeliveredundertremendousinspiration and encouragement from my teachers, research collaborators, and students. My interest in longitudinal data analysis began with a short course taught jointly by K. Y. Liang and S. L. Zeger at the Statistical Society of Canada Conference in Acadia University, Nova Scotia, in the spring of 1993. At that time, I was a ?rst-year PhD student in the Department of Statistics at the University of British Columbia, and was eagerly seeking potential topics for my PhD dissertation. It was my curiosity (driven largely by my terrible c- fusion) with the generalized estimating equations (GEEs) introduced in the short course that attracted me to the ?eld of correlated data analysis. I hope that my experience in learning about it has enabled me to make this book an enjoyable intellectual journey for new researchers entering the ?eld. Thus, the book aims at graduate students and methodology researchers in stat- tics or biostatistics who are interested in learning the theory and methods of correlated data analysis. I have attempted to give a systematic account of regression models and their applications to the modeling and analysis of correlated data. Longitu- nal data, as an important type of correlated data, has been used as a main venue for motivation, methodological development, and illustration throu- out the book. Given the many applied books on longitudinal data analysis - ready available, this book is inclined more towards technical details regarding the underlying theory and methodology used in software-based applications.

This book presents some recent developments in correlated data analysis. It utilizes the class of dispersion models as marginal components in the formulation of joint models for correlated data. This enables the book to handle a broader range of data types than those analyzed by traditional generalized linear models. One example is correlated angular data.

This book provides a systematic treatment for the topic of estimating functions. Under this framework, both generalized estimating equations (GEE) and quadratic inference functions (QIF) are studied as special cases. In addition to marginal models and mixed-effects models, this book covers topics on joint regression analysis based on Gaussian copulas and generalized state space models for longitudinal data from long time series.

Various real-world data examples, numerical illustrations and software usage tips are presented throughout the book. This book has evolved from lecture notes on longitudinal data analysis, and may be considered suitable as a textbook for a graduate course on correlated data analysis. This book is inclined more towards technical details regarding the underlying theory and methodology used in software-based applications. Therefore, the book will serve as a useful reference for those who want theoretical explanations to puzzles arising from data analyses or deeper understanding of underlying theory related to analyses.

Peter Song is Professor of Statistics in the Department of Statistics and Actuarial Science at the University of Waterloo. Professor Song has published various papers on the theory and modeling of correlated data analysis. He has held a visiting position at the University of Michigan School of Public Health (Ann Arbor, Michigan).