- Preface
- Notation
- Chapter 1:
Introduction
- Examples of types of data
- Motivating examples
- A first view on the models

- Chapter 2: 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
- Problems

- Chapter 3: General
Linear Models
- Introduction
- The multivariate normal distribution
- General Linear Models
- Estimation of parameters
- Likelihood ratio tests
- Tests for model reduction
- Collinearity
- Inference on individual parameters in parameterized models
- Model diagnostics: residuals and influence
- Residual analysis
- Representation of linear models
- General linear models in R
- Problems

- Chapter 4: 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
- Problems

- Chapter 5: 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 for multivariate normal distributions
- Random effects for multivariate measurements
- Hierarchical models in metrology
- General mixed effects models
- Laplace approximation
- Mixed effects models in R
- Problems

- Chapter 6:
Hierarchical models
- Introduction, approaches to modelling of overdispersion
- Hierarchical Poisson Gamma model
- Conjugate prior distributions
- Examples of generalized one-way random effects models
- Hierarchical generalized linear models
- Problems

- Chapter 7: Real life
inspired
problems
- Dioxin emission
- Depreciation of used cars
- Young fish in the North sea
- Traffic accidents
- Mortality of snails

- Chapter 8: Supplement
on the law
of error propagation
- Function of one random variable
- Function of several random variable

- Appendix A: Some
probability
distributions
- The binomial distribution model
- The Poisson distribution model
- The negative binomial distribution model
- The exponential distribution model
- The gamma distribution model
- The inverse Gaussian distribution model
- Distributions derived from the normal distribution
- The Gamma-function

- Appendix B: List of symbols
- Bibliography
- Index

Click on the chapter titles to see more.