Generalized Linear Models

Preface, Introduction, Background, The Origins of Generalized Linear Models, Scope of the Rest of the Book, An Outline of Generalized Linear Models, Processes in Model Fitting, The Components of a Generalized Linear Model, Measuring the goodness of Fit, Residuals, An Algorithm for Fitting Generalized Linear Models, Models for Continuous Data with Constant Variance, Introduction, Error Structure, Systematic Component (Linear Predictor), Model Formulae for Linear Predictors, Aliasing, Estimation, Tables as Data, Algorithms for Least Squares, Selection of Covariates, Binary Data , Introduction, Binomial Distribution, Models for Binary Responses, Likelihood functions for Binary Data, Over-Dispersion, Example, Models for Polytomous Data, Introduction, Measurement scales, The Multinomical Distribution, Likelihood Functions, Over-Dispersion, Examples, Log-Linear Models, Introduction, Likelihood Functions, Examples, Log-Linear Models and Multinomial Response Models, Multiple responses, Example, Conditional Likelihoods, Introduction, Marginal and conditional Likelihoods, Hypergeometric Distributions, Some Applications Involving Binary data, Some Aplications Involving Polytomous Data, Models with Constant Coefficient of Variation, Introduction, The Gamma Distribution, Models with Gamma-distributed Observations, Examples, Quasi-Likelihood Functions, Introduction, Independent Observations, Dependent Observations, Optimal Estimating Functions, Optimality Criteria, Extended Quasi-Likelihood, Joint Modelling of Mean and Dispersion, Introduction, Model Specification, Interaction between Mean and Dispersion Effects, Extended Quasi-Likelihood as a Criterion, Adjustments of the Estimating Equations, Joint Optimum Estimating Equations, Example: The Production of Leaf-Springs for Trucks, Models with Additional Non-Linear Parameters, Introduction, Pa