Growth Curve Models and Statistical Diagnostics

ISBN-13: 9781441928641 / Angielski / Miękka / 2011 / 388 str.

Jian-Xin Pan; Kai-Tai Fang

Opis

Growth-curve models are generalized multivariate analysis-of-variance models. The basic idea of the models is to use different polynomials to fit different treatment groups involved in the longitudinal study. It is not uncommon, however, to find outliers and influential observations in growth data that heavily affect statistical inference in growth curve models. This book provides a comprehensive introduction to the theory of growth curve models with an emphasis on statistical diagnostics. A variety of issues on model fittings and model diagnostics are addressed, and many criteria for outlier detection and influential observation identification are created within likelihood and Bayesian frameworks. This book is intended for postgraduates and statisticians whose research involves longitudinal study, multivariate analysis and statistical diagnostics, and also for scientists who analyze longitudinal data and repeated measures. The authors provide theoretical details on the model fittings and also emphasize the application of growth curve models to practical data analysis, which are reflected in the analysis of practical examples given in each chapter. The book assumes a basic knowledge of matrix algebra and linear regression. Jian-Xin Pan is a lecturer in Medical Statistics of Keele University in the U.K. He has published more than twenty papers on growth curve models, statistical diagnostics and linear/non-linear mixed models. He has a long-standing research interest in longitudinal data analysis and repeated measures in medicine and agriculture. Kai-Tai Fang is a chair professor in Statistics of Hong Kong Baptist University and a fellow of the Institute of Mathematical Statistics. He has published several books with Springer-Verlag, Chapman & Hall, and Science Press and is an author or co-author of over one hundred papers. His research interest includes generalized multivariate analysis, elliptically contoured distributions and uniform design.

Recenzje

From the reviews:

"The book is well written and contains a goodly number of real-data applications." ISI

Short Book Reviews, Vol.23/1, April 2003

"This book offers an extensive view of Growth Curve Models and a wide range of issues related with statistical diagnosis. ... Each chapter ends with some bibliographical notes that inform the reader about historical sources as well as about recent developments. The bibliographic list is impressive! ... the information given about Growth Curve Models and Statistical Diagnosis is excellent. The book is written very rigorously and precisely and I strongly recommend it for statisticians or for applied scientists with some mathematical and statistical background." (Prof. C. García-Olaverri, Kwantitatieve Methoden, Vol. 72B5, 2003)

"The authors have written a basic book on a well developed and important field in multivariate statistical analysis. It will undoubtedly serve as a reference in this field." (Arjun K. Gupta, Zentralblatt MATH, Vol. 1024, 2003)

"This book presents methods for analyzing repeated measures and longitudinal data using the growth curve models (GCMs), with specific focus on the generalized multivariate analysis of variance (GMANOVA) model. ... For researchers, the book's main strength is its level of detail. ... Theoreticians in multivariate analysis will find this book to be a good reference for this particular GCM and multivariate regression diagnosis." (Andrew M. Kuhn, Technometrics, Vol. 45 (3), 2003)

"Models are discussed for data variously described as growth curves, longitudinal data, or multilevel data. The text supplements the growing number of references on techniques for longitudinal data by focusing on diagnostics for outliers and influential observations. ... the book is well written and does contain a goodly number of real-data applications." (J. O. Ramsey, Short Book Reviews, Vol. 23 (1), 2003)

Spis treści

Introduction * Generalized Least Square Estimation * Maximum Likelihood Estimation * Discordant Outlier and Influential Observation * Likelihood-Based Local Influence * Bayesian Influence Assessment * Bayesian Local Influence

O autorze

Growth curve models are an active research area in multivariate analysis with applications to economics, biology, medical research, and epidemiology. This monograph by two of the leading researchers in the area discusses both theoretical and practical aspects.