Introduction to General and Generalized Linear Models

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.

Biography

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.

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