Introduction to General and Generalized Linear Models -

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Résumé :
Since the mathematics behind generalized linear models is often difficult to follow while the mathematics behind general linear models is well understood, this text describes the methodology behind both models in a parallel setup.

Biographie:
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.

Sommaire:
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.

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. Demetrio, Biometrics, February 2012