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El. knyga: Introduction to General and Generalized Linear Models

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(Technical University of Denmark, Lyngby), (Technical University of Denmark, Lyngby)
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Bridging the gap between theory and practice for modern statistical model building, Introduction to General and Generalized Linear Models presents likelihood-based techniques for statistical modelling using various types of data. Implementations using R are provided throughout the text, although other software packages are also discussed. Numerous examples show how the problems are solved with R.

After describing the necessary likelihood theory, the book covers both general and generalized linear models using the same likelihood-based methods. It presents the corresponding/parallel results for the general linear models first, since they are easier to understand and often more well known. The authors then explore random effects and mixed effects in a Gaussian context. They also introduce non-Gaussian hierarchical models that are members of the exponential family of distributions. Each chapter contains examples and guidelines for solving the problems via R.

Providing a flexible framework for data analysis and model building, this text focuses on the statistical methods and models that can help predict the expected value of an outcome, dependent, or response variable. It offers a sound introduction to general and generalized linear models using the popular and powerful likelihood techniques. Ancillary materials are available at www.imm.dtu.dk/~hm/GLM

Recenzijos

This book presents a well-structured introduction to both general linear models and generalized linear models. I would recommend the book as a suitable text for senior undergraduate or postgraduate students studying statistics or a reference for researchers in areas of statistics and its applications. Shuangzhe Liu, International Statistical Review, 2012

This book is targeted to undergraduates in statistics but can be used by researchers as a reference manual as well. It is well written, easy to read and the discussion of the examples is clear. As a complement there is a collection of slides for an introductory course on general, generalized, and mixed effects models in the homepage cited in the preface of this book. This book has a good set of references I recommend this book as one of the textbooks to be discussed in a course for model building. Clarice G.B. Demétrio, Biometrics, February 2012

Preface xi
Notation
xiii
1 Introduction 1(8)
1.1 Examples of types of data
2(1)
1.2 Motivating examples
3(2)
1.3 A first view on the models
5(4)
2 The likelihood principle 9(32)
2.1 Introduction
9(1)
2.2 Point estimation theory
10(4)
2.3 The likelihood function
14(3)
2.4 The score function
17(1)
2.5 The information matrix
18(2)
2.6 Alternative parameterizations of the likelihood
20(1)
2.7 The maximum likelihood estimate (MLE)
21(1)
2.8 Distribution of the ML estimator
22(1)
2.9 Generalized loss-function and deviance
23(1)
2.10 Quadratic approximation of the log-likelihood
23(2)
2.11 Likelihood ratio tests
25(2)
2.12 Successive testing in hypothesis chains
27(6)
2.13 Dealing with nuisance parameters
33(5)
2.14 Problems
38(3)
3 General linear models 41(46)
3.1 Introduction
41(1)
3.2 The multivariate normal distribution
42(2)
3.3 General linear models
44(4)
3.4 Estimation of parameters
48(5)
3.5 Likelihood ratio tests
53(5)
3.6 Tests for model reduction
58(6)
3.7 Collinearity
64(6)
3.8 Inference on parameters in parameterized models
70(3)
3.9 Model diagnostics: residuals and influence
73(4)
3.10 Analysis of residuals
77(1)
3.11 Representation of linear models
78(3)
3.12 General linear models in R
81(2)
3.13 Problems
83(4)
4 Generalized linear models 87(70)
4.1 Types of response variables
89(1)
4.2 Exponential families of distributions
90(9)
4.3 Generalized linear models
99(3)
4.4 Maximum likelihood estimation
102(9)
4.5 Likelihood ratio tests
111(4)
4.6 Test for model reduction
115(1)
4.7 Inference on individual parameters
116(1)
4.8 Examples
117(35)
4.9 Generalized linear models in R
152(1)
4.10 Problems
153(4)
5 Mixed effects models 157(68)
5.1 Gaussian mixed effects model
159(1)
5.2 One-way random effects model
160(14)
5.3 More examples of hierarchical variation
174(5)
5.4 General linear mixed effects models
179(6)
5.5 Bayesian interpretations
185(6)
5.6 Posterior distributions
191(1)
5.7 Random effects for multivariate measurements
192(5)
5.8 Hierarchical models in metrology
197(2)
5.9 General mixed effects models
199(2)
5.10 Laplace approximation
201(17)
5.11 Mixed effects models in R
218(1)
5.12 Problems
219(6)
6 Hierarchical models 225(20)
6.1 Introduction, approaches to modeling of overdispersion
225(1)
6.2 Hierarchical Poisson Gamma model
226(7)
6.3 Conjugate prior distributions
233(4)
6.4 Examples of one-way random effects models
237(5)
6.5 Hierarchical generalized linear models
242(1)
6.6 Problems
243(2)
7 Real life inspired problems 245(10)
7.1 Dioxin emission
246(3)
7.2 Depreciation of used cars
249(1)
7.3 Young fish in the North Sea
250(1)
7.4 Traffic accidents
251(1)
7.5 Mortality of snails
252(3)
A Supplement on the law of error propagation 255(2)
A.1 Function of one random variable
255(1)
A.2 Function of several random variables
255(2)
B Some probability distributions 257(28)
B.1 The binomial distribution model
259(3)
B.2 The Poisson distribution model
262(2)
B.3 The negative binomial distribution model
264(2)
B.4 The exponential distribution model
266(2)
B.5 The gamma distribution model
268(7)
B.6 The inverse Gaussian distribution model
275(5)
B.7 Distributions derived from the normal distribution
280(4)
B.8 The Gamma-function
284(1)
C List of symbols 285(2)
Bibliography 287(6)
Index 293
Henrik Madsen is a professor in the Department of Informatics and Mathematical Modelling at the Technical University of Denmark in Lyngby. He has authored or coauthored more than 400 publications. Dr. Madsen has also led or participated in research projects involving wind power and energy load forecasting, financial forecasting and modeling, heat dynamics modeling, PK/PD modeling in drug development, data assimilation, zooneses modeling, and high performance and scientific computing.
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