**Also available as eBook on:**

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.

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

### Biography

P. McCullagh

"... an important, useful book, well-written by two authorities in the field..."

-Times Higher Education Supplement

"... an enormous range of work is covered... represents, perhaps, the most important field of research in theoretical and practical statistics. For all statisticians working in this field, the book is essential."

-Short Book Reviews

"... this is a rich book; rich in theory, rich in examples, and rich in a statistical sense. I highly recommend it."

-Biometrics

"... a definitive and unified presentation...by the outstanding experts of this field."

-Statistics

"This is a wonderful book... Reading the book is like listening to a good lecturer. The authors present the material clearly, and they treat the reader with respect. There is a balance between discussion, mathematical presentation of models, and examples."

-Technometrics

"... a complete introduction to the topic in a single monograph... a very readable book that provides the reader with great insight into a vast array of data analysis techniques...

-Siam Review

"... a unique and useful text for intermediate undergraduate teaching."

-THES