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Introduction to General and Generalized Linear Models

Henrik Madsen and Poul Thyregod
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2010
Number of Pages: 
302
Format: 
Hardcover
Series: 
Texts in Statistical Science
Price: 
79.95
ISBN: 
9781420091557
Category: 
Textbook
We do not plan to review this book.

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

Dummy View - NOT TO BE DELETED