Generalized Linear Models

About this book

Provides a definitive and unified treatment of methods for the analysis of diverse types of data commonly met in agricultural, biological, health and social sciences.

Contents

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 Parameters in the Variance function Parameters in the Link Function Nonlinear Parameters in the Covariates Examples Model Ch ecking Introduction Techniqes in Model Checking Score Tests for Extra Parameters Smoothing as an Aid to Informal Checks The Raw Materials of Model Checking Checks for systematic Departure from Model Check for isolated Departures from the Model Examples A Strategy for Model Checking? Models for Survival Data Introduction Proportional-Hazards Models Estimation with a Specified Survival distribution Example: Remission Times for Leukemia Cox's Proportional-Hazards Model Components of Dispersion Introduction Linear Models Nonlinear Models Parameter Estimation Example: A Salamander mating Experiment Further Topics Introduction Bias Adjustment Computation of Bartlett Adjustments Generalized Additive Models Appendices Elementary Likelihood Theory Edgeworth Series Likeliho

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