Elements of Applied Stochastic Processes

This book presents methods for analyzing repeated measures and longitudinal data using the growth curve models (GCMs), with speci c focus on the generalized multivariate analysis of variance (GMANOVA) model. The Preface states that “this book is intended for researchers who are working in the area of theoretical studies related to the GCM” and “for applied statisticians working in application of the GCM to practical areas. ” The back cover copy states that “scientists engaged in analyzing longitudinal and repeated measures data will also  nd the book useful. ” The book comprises seven chapters. Chapter 1 provides motivation for the GCM model and reviews the concepts of in uential and outlying observations. There is a discussion of typical covariance matrix assumptions, including Rao’s simple covariance structure. This class of structures, which includes many common patterns (with the notable exception of the autoregressive structure), is used extensively throughout the text. A section of helpful matrix algebra results punctuates the chapter. This particular section, along with a similar section in the text of Vonesh and Chinchilli (1997), is a valuable resource for students and researchers studying the theoretical aspects of multivariate analysis. Chapter 2, “Generalized Least Squares Estimation,” focuses on estimating model parameters under various assumptions. This chapter also introduces several datasets used to illustrate the methods discussed in each chapter. The focus in this chapter and in Chapter 3, “Maximum Likelihood Estimation,” is on theoretical issues surrounding the estimates (e.g., unbiasedness, admissibility). Chapter 3 focuses a substantial amount of attention on estimation using restricted maximum likelihood. The next four chapters concentrate on methods for detecting in uential and outlying observations for the speci c GCM models detailed in previous chapters. Two chapters, “Discordant Outlier and In uential Observation” and “Likelihood-Based Local In uence,” derive several diagnostic procedures, including hypothesis tests for speci c outlier-generating models and extensions to familiar quantities like Cook’s distance. The  nal two chapters, “Bayesian In uence Assessment” and “Bayesian Local In uence,” focus on Kullback– Leibler divergence statistics (under various assumptions regarding the covariance matrix structure) and local in uence measures based on random perturbation models, speci cally variance-weighted perturbations from the Bayesian perspective. For researchers, the book’s main strength is its level of detail. The gory details are provided for almost every derivation and proof, which are numerous. This makes the book rather dense, but there are rewards for researchers or graduate students in multivariate analysis who work through the details. The “notation-theorem-proof-remark” school of writing drives the book, but the authors manage not to be pathologically succinct. Readers of Technometrics with backgrounds in multivariate analysis and/or regression diagnostics should  nd the book manageable. There are a number of obvious (but minor) typographic errors. This text is not a comprehensive guide to models for growth curve or repeated-measures data, but then was it not intended to be such. At the end of the introductory chapter, the authors state that “the selected materials in this book are also limited to the authors’ research interests,” and thus the focus is on selected aspects of one speci c model. Based on this, this book will be of limited value to those whose primary concern is in analyzing their data. Applied statisticians and scientists with data in hand may be interested in understanding more practical issues not addressed here, such as when to use the GCM (instead of, say, linear mixed models), strategies for missing or unbalanced data, computational issues, and bootstrapping techniques. The Preface states that a website containing S-PLUS and GENSTAT code for data analysis will be available “in due course. ” At the time of this review, the Springer web page for this book, http://www.springer-ny.com/detail.tpl? ISBN= 0387950532, provides a link to Dr. Fang’s web page (where the book is not mentioned). Software for analyzing growth curve data could not be located at either website. A lack of software would severely limit the utility of the text for applied statisticians and scientists. In summary, this book will be of limited value to data analysis practitioners, especially if no software is supplied. Readers interested in a more comprehensive approach for growth curve and repeated measures data could consult the text by Vonesh and Chinchilli (1997) or similar books. Theoreticians in multivariate analysis will  nd this book to be a good reference for this particular GCM and multivariate regression diagnostics.