Madsen / Thyregod Introduction to General and Generalized Linear Models

1. Auflage 2011
ISBN: 978-1-4398-9114-8
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 316 Seiten

Reihe: Chapman & Hall/CRC Texts in Statistical Science

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

Autoren/Hrsg.

Madsen, Henrik

Thyregod, Poul

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Introduction
Examples of types of data
Motivating examples
A first view on the models

The Likelihood Principle
Introduction
Point estimation theory
The likelihood function
The score function
The information matrix
Alternative parameterizations of the likelihood
The maximum likelihood estimate (MLE)
Distribution of the ML estimator
Generalized loss-function and deviance
Quadratic approximation of the log-likelihood
Likelihood ratio tests
Successive testing in hypothesis chains
Dealing with nuisance parameters

General Linear Models
Introduction
The multivariate normal distribution
General linear models
Estimation of parameters
Likelihood ratio tests
Tests for model reduction
Collinearity
Inference on parameters in parameterized models
Model diagnostics: residuals and influence
Analysis of residuals
Representation of linear models
General linear models in R

Generalized Linear Models
Types of response variables
Exponential families of distributions
Generalized linear models
Maximum likelihood estimation
Likelihood ratio tests
Test for model reduction
Inference on individual parameters
Examples
Generalized linear models in R

Mixed Effects Models
Gaussian mixed effects model
One-way random effects model
More examples of hierarchical variation
General linear mixed effects models
Bayesian interpretations
Posterior distributions
Random effects for multivariate measurements
Hierarchical models in metrology
General mixed effects models
Laplace approximation
Mixed effects models in R

Hierarchical Models
Introduction, approaches to modelling of overdispersion
Hierarchical Poisson gamma model
Conjugate prior distributions
Examples of one-way random effects models
Hierarchical generalized linear models

Real-Life Inspired Problems
Dioxin emission
Depreciation of used cars
Young fish in the North Sea
Traffic accidents
Mortality of snails

Appendix A: Supplement on the Law of Error Propagation
Appendix B: Some Probability Distributions
Appendix C: List of Symbols

Bibliography
Index

Problems appear at the end of each chapter.