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.