1st Edition

Introduction to General and Generalized Linear Models

By Henrik Madsen, Poul Thyregod Copyright 2010
    316 Pages 50 B/W Illustrations
    by CRC Press

    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

    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