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Introduction to General and Generalized Linear Models
Poul Thyregod og Henrik Madsen
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- Vital Source searchable e-book (Fixed pages)
- Udgiver: CRC Press (November 2010)
- ISBN: 9781439891148
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Detaljer om varen
- Hardback: 316 sider
- Udgiver: Taylor & Francis Group (November 2010)
- Forfattere: Poul Thyregod og Henrik Madsen
- ISBN: 9781420091557
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
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.