Growth Curve Models and Statistical Diagnostics
Growth Curve Models and Statistical Diagnostics
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DOI：
10.1198/tech.2003.s773
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发表时间：
2003-08
期刊：
影响因子：
2.5
通讯作者：
A. M. Kuhn
中科院分区：
文献类型：
--
作者：
A. M. Kuhn
本书介绍了使用增长曲线模型（GCMs）分析重复测量和纵向数据的方法，特别关注广义多元方差分析（GMANOVA）模型。序言指出，"这本书是为研究人员谁是工作在该领域的理论研究有关的GCM"和"为应用统计学家工作的应用GCM的实际领域。封底副本指出，“从事分析纵向和重复测量数据的科学家也将发现这本书很有用。”这本书共有七章。第一章介绍了GCM模型的基本原理，并回顾了非核心观测值和外围观测值的概念。讨论了典型的协方差矩阵假设，包括Rao的简单协方差结构。这类结构，包括许多常见的模式（自回归结构是一个显著的例外），在整个文本中被广泛使用。一节有用的矩阵代数结果标点章。这个特殊的部分，沿着与Vonesh和Chinchili（1997）的文本中的类似部分，是学习多变量分析理论方面的学生和研究人员的宝贵资源。第2章，“广义最小二乘估计”，重点是在各种假设下估计模型参数。本章还介绍了几个用于说明每章中讨论的方法的数据集。本章和第3章"最大似然估计"的重点是围绕估计的理论问题（例如，无偏见，可受理性）。第3章集中了大量的注意力估计使用限制最大似然。接下来的四章集中在方法检测的特定的GCM模式在前面的章节中详细介绍的基本和离群观测。两个章节，“不一致的离群值和不一致的观察”和“基于可能性的局部不一致性”，推导出几个诊断程序，包括特定离群值生成模型的假设检验和对熟悉的量如库克距离的扩展。最后两章，"贝叶斯不一致性评估"和"贝叶斯局部不一致性"，重点讨论Kullback-Leibler散度统计（在关于协方差矩阵结构的各种假设下）和基于随机扰动模型的局部不一致性度量，特别是贝叶斯视角的方差加权扰动。对于研究人员来说，这本书的主要优点是它的细节水平。血淋淋的细节提供了几乎每一个推导和证明，这是无数的。这使得这本书相当密集，但有奖励的研究人员或研究生在多元分析谁的工作通过细节。"记法-定理-证明-注释"的写作流派推动了这本书的写作，但作者们设法不让自己变得病态地简洁。具有多元分析和/或回归诊断背景的技术计量学读者应该理解这本书的可管理性。有一些明显的（但很小的）印刷错误。本文不是增长曲线或重复测量数据模型的全面指南，但它并不打算这样做。在介绍性章节的最后，作者指出，"本书中所选的材料也仅限于作者的研究兴趣"，因此重点是一个特定模型的选定方面。基于这一点，这本书将是有限的价值，那些主要关注的是在分析他们的数据。掌握数据的应用统计学家和科学家可能有兴趣了解这里没有解决的更实际的问题，例如何时使用GCM（而不是线性混合模型），缺失或不平衡数据的策略，计算问题和自举技术。序言指出，将"在适当时候"建立一个网站，其中载有用于数据分析的S-PLUS和GENSTAT代码。在撰写本文时，本书的Springer网页www.example.com ISBN = 0387950532，提供了一个链接到方博士的网页（其中没有提到这本书）。在这两个网站上都找不到分析生长曲线数据的软件。缺乏软件将严重限制文本对应用统计学家和科学家的效用。总之，这本书对数据分析从业者的价值有限，特别是如果没有提供软件的话。对生长曲线和重复测量数据的更全面方法感兴趣的读者可以参考Vonesh和Chinchili（1997）的文本或类似书籍。在多元分析的理论家将programmed这本书是一个很好的参考，为这个特定的GCM和多元回归诊断。
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.