混合模型：理论与R语言应用

需积分: 10 123 浏览量更新于2024-07-17 1 收藏 38.31MB PDF 举报

"Mixed Models: Theory and Applications" 混合模型（Mixed Models）是一种统计分析方法，它在处理复杂数据结构时表现出强大的灵活性和适用性。这些模型主要用于处理以下多种情况： 1. 复杂集群或纵向数据：混合模型可以适应具有时间和空间依赖性的数据，例如在临床试验、教育研究或社会科学中的重复测量数据。它们能够捕捉到个体间和时间序列内的关联。 2. 多源变异数据：在存在不同层次变异的数据中，如多层次设计（如学生在班级内的成绩差异，班级在学校的差异），混合模型可以估计不同层次的影响。 3. 生物多样性和异质性：在生物学研究中，混合模型能处理生物种群内部的变异，例如基因型和环境相互作用产生的变异。 4. 频率主义与贝叶斯方法的折衷：混合模型提供了一种介于传统频率主义统计和贝叶斯统计之间的途径，允许对不确定性和随机效应进行建模，同时保持了参数估计的稳健性。 5. 统计模型的罚函数似然法：混合模型可以用于构建罚函数似然框架，这在正则化和变量选择问题中非常有用，有助于防止过拟合。 6. 健康阿卡伊信息准则（HAIC）的理论基础：混合模型提供了HAIC的理论支持，这是一个改进的信息准则，用于模型选择和复杂数据的评估。 7. 应对参数多维性：在有大量协变量或复杂交互项的情况下，混合模型可以有效地处理高维参数空间，通过随机效应来降低模型复杂性。 8. 解决欠定问题：混合模型可以应用于图像重建等欠定问题，通过统计方法处理这些问题，从而获得更稳定的结果。 9. 形状和图像建模：在计算机视觉和图像分析领域，混合模型可以用于捕获图像的形状变化和模式，对图像进行建模和识别。《Mixed Models: Theory and Applications with R》第二版由Eugene Demidenko撰写，详细介绍了如何使用R语言实现这些概念。这本书旨在提供混合模型的理论基础和实际应用，并通过实例和代码演示如何解决各种统计问题。作者不仅探讨了模型的理论方面，还关注了如何在实践中实施这些模型，使读者能够将混合模型应用于实际数据分析项目。

xiv Contents

9.6.4 Sensitivity to misclassification 517

9.6.5 Example: Finney data 522

9.7 Influence of correlation structure 524

9.8 Influence of measurement error 525

9.9 Influence analysis for the LME model 528

9.9.1 Example: Weight versus height 532

9.10 Appendix: MLE derivative with respect to σ

534

9.11 Summary points 535

10 Tumor Regrowth Curves 539

10.1 Survival curves 541

10.2 Double-exponential regrowth curve 543

10.2.1 Time to regrowth, T

546

10.2.2 Time to reach specific tumor volume, T* 547

10.2.3 Doubling time, T

547

10.2.4 Statistical model for regrowth 548

10.2.5 Variance estimation for tumor regrowth outcomes 549

10.2.6 Starting values 550

10.2.7 Example: chemotherapy treatment comparison 551

10.3 Exponential growth with fixed regrowth time 557

10.3.1 Statistical hypothesis testing 558

10.3.2 Synergistic or supra-additive effect 558

10.3.3 Example: combination of treatments 559

10.4 General regrowth curve 563

10.5 Double-exponential transient regrowth curve 564

10.5.1 Example: treatment of cellular spheroids 570

10.6 Gompertz transient regrowth curve 571

10.6.1 Example: tumor treated in mice 572

10.7 Summary points 574

11 Statistical Analysis of Shape 577

11.1 Introduction 577

11.2 Statistical analysis of random triangles 579

11.3 Face recognition 582

11.4 Scale-irrelevant shape model 583

11.4.1 Random effects scale-irrelevant shape model 585

11.4.2 Scale-irrelevant shape model on the log scale 586

11.4.3 Fixed or random size? 587

11.5 Gorilla vertebrae analysis 587

11.6 Procrustes estimation of the mean shape 589

11.6.1 Polygon estimation 592

11.6.2 Generalized Procrustes model 592

11.6.3 Random effects shape model 593

11.6.4 Random or fixed (Procrustes) effects model? 594

11.6.5 Maple leaf analysis 594

11.7 Fourier descriptor analysis 596

11.7.1 Analysis of a star shape 596

11.7.2 Random Fourier descriptor analysis 602

Preface

Preface xvii

Technological advances change the world, and statistics is no exception. The

cornerstone of classical statistics is the notion of sample. Today, data are richer:

We may have repeated measurements with thousands of clusters; data may come

in the form of shapes or images. This book is about statistical analysis of data

that constitute a sample of samples. In the first ten chapters we discuss statistical

models when data come in traditional form as a sequence of numbers. Chapter 11

deals with a sample (ensemble) of shapes, and in Chapter 12 we discuss how to

analyze an ensemble of images.

We take the statistical model based approach to analyzing data. Then the method

of analysis is a derivative. Although the method sometimes comes first, the model-

based approach has obvious advantages: Assumptions are clearly formulated, and

properties of several methods can be studied and compared. For example, least

squares is a method of fitting, but its pros and cons can be fully understood only

when a statistical model is put forward to describe how observations are obtained.

Then least squares is deduced, for example, from maximum likelihood.

Statistical treatment is carried out under a unifying mixed effects approach. This

approach becomes fruitful not only to analyze complex clustered data (a sample of

samples) but also as a statistical model for penalization and a common ground for

the Bayesian and frequentist camps.

Use of the mixed modeling technique in shape and image analysis is exciting and

promising. Much work remains to reveal the full power of this statistical approach

to these nontraditional statistical data.

The book is divided into three parts. The first eight chapters cover the theory of

mixed models: the linear mixed effects (LME) model, the generalized linear mixed

model (GLMM), and the nonlinear mixed effects (NLME) model. In Chapter 9

we discuss methods of model diagnostics and influential analysis. The final three

chapters are devoted to applications: tumor regrowth, shape, and image. Major

results and points of discussion in each chapter are written in lay language and are

collected in Summary Points sections so that the reader can get a quick chapter

overview.

I look forward to hearing from readers and invite them to visit the book web site

http://www.dartmouth.edu/~eugened

where some additional information with data and images is presented.

I would like to thank the many people I worked with on various projects that have

led up to this book. First, I would like to mention my long-term collaboration with

Thérèse Stukel and Tor Tosteson and thank them for their support. I am grateful to

Harold Swartz and Jack Hoopes for the exposure to biological problems, and to the

team led by Keith Paulsen, including Alex Hartov, Paul Meaney, and Brian Pogue,

all from Dartmouth, who introduced me to the world of image reconstruction. Many

剩余755页未读，继续阅读

gymjoh123

粉丝: 3
资源: 17

混合模型：理论与R语言应用

linear mixed models:practical guide using statistical software.

Mixed Effects Models in S and S-Plus (Statistics and Computing

解决Mixed Content: The page at https://xxx was loaded over HTTPS

ESLint: Mixed spaces and tabs. (no-mixed-spaces-and-tabs)

layer_settings = { "mixed4": 1.0, "mixed5": 1.5, "mixed6": 2.0, "mixed7": 2.5, }什么意思

layer_settings = { "mixed4": 1.0, "mixed5": 1.5, "mixed6": 2.0, "mixed7": 2.5,什么意思

解决Mixed Content: The page at..HTTPS中包含http的不安全问题

前端axios请求报Mixed Content:the page at‘http://XXXX‘ was loaded over HTTPS解决方法

错误:Mixed Content: The page at ‘https://XXX’ was loaded over HTTPS, but requested an insecure.......

linear mixed models a practical guide using statistical software

最新资源