Riassunto:
The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data. Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and other applications.
The authors focus on examining the way a response variable depends on a combination of explanatory variables, treatment, and classification variables. They give particular emphasis to the important case where the dependence occurs through some unknown, linear combination of the explanatory variables.
The Second Edition includes topics added to the core of the first edition, including conditional and marginal likelihood methods, estimating equations, and models for dispersion effects and components of dispersion. The discussion of other topics-log-linear and related models, log odds-ratio regression models, multinomial response models, inverse linear and related models, quasi-likelihood functions, and model checking-was expanded and incorporates significant revisions.
Comprehension of the material requires simply a knowledge of matrix theory and the basic ideas of probability theory, but for the most part, the book is self-contained. Therefore, with its worked examples, plentiful exercises, and topics of direct use to researchers in many disciplines, Generalized Linear Models serves as ideal text, self-study guide, and reference.
Contenuti:
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 Checking
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
Likelihood-Ratio Statistics
References
Index of Data Sets
Author Index
Subject Index
Each chapter also contains Bibliographic Notes and Exercises
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