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An Introduction to Generalized Linear Models, Second Edition

By Annette J. Dobson

Series Editor: Chris Chatfield, Jim Zidek, Jim Lindsey

Chapman and Hall/CRC – 2001 – 240 pages

Series: Chapman & Hall/CRC Texts in Statistical Science

Purchasing Options:

  • Paperback:
    978-1-58488-165-0
    November 27th 2001
    Out-of-print

Description

Generalized linear models provide a unified theoretical and conceptual framework for many of the most commonly used statistical methods. In the ten years since publication of the first edition of this bestselling text, great strides have been made in the development of new methods and in software for generalized linear models and other closely related models.

Thoroughly revised and updated, An Introduction to Generalized Linear Models, Second Edition continues to initiate intermediate students of statistics, and the many other disciplines that use statistics, in the practical use of these models and methods. The new edition incorporates many of the important developments of the last decade, including survival analysis, nominal and ordinal logistic regression, generalized estimating equations, and multi-level models. It also includes modern methods for checking model adequacy and examples from an even wider range of application.

Statistics can appear to the uninitiated as a collection of unrelated tools. An Introduction to Generalized Linear Models, Second Edition illustrates how these apparently disparate methods are examples or special cases of a conceptually simple structure based on the exponential family of distribution, maximum likelihood estimation, and the principles of statistical modelling.

Reviews

" The second edition … is successful in, filling a void in the otherwise sparse literature on the subject of generalized linear models at the introductory level … a wide range of research applications are covered and ample workings are also provided to aid the reader in statistical calculations … I would highly recommend this text for a reader interested in finding out at an introductory level what the subject area of generalized linear models is all about, including the non-statistician, undergraduate and graduate-level student."

-Kerrie Nelson, Department of Statistics, LeConte College, University of South Carolina, Columbia, USA, in Statistics in Medicine, Vol. 23, 2004

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

-Times Higher Education Supplement

"…I liked Dobson's basic and relatively brief presentation…Thanks go to the publisher for the softcover edition and attendant modest price, another of the book's virtues besides its brevity. These attributes make this book a recommended purchase for those who need a book on logistic regression. It is a good place to start."

-Technometrics, November 2002

Contents

INTRODUCTION

Background

Scope

Notation

Distributions Related to the Normal Distribution

Quadratic Forms

Estimation

Exercises

MODEL FITTING

Introduction

Examples

Some Principles of Statistical Modelling

Notation and Coding for Explanatory Variables

Exercises

EXPONENTIAL FAMILY AND GENERALIZED LINEAR

MODELS

Introduction

Exponential Family of Distributions

Properties of Distributions in the Exponential Family

Generalized Linear Models

Examples

Exercises

ESTIMATION

Introduction

Example: Failure Times for Pressure Vessels

Maximum Likelihood Estimation

Poisson Regression Example

Exercises

INFERENCE

Introduction

Sampling Distribution for Score Statistics

Taylor Series Approximations

Sampling Distribution for Maximum Likelihood Estimators

Log-Likelihood Ratio Statistic

Sampling Distribution for the Deviance

Hypothesis Testing

Exercises

NORMAL LINEAR MODELS

Introduction

Basic Results

Multiple Linear Regression

Analysis of Variance

Analysis of Covariance

General Linear Models

Exercises

BINARY VARIABLES AND LOGISTIC REGRESSION

Probability Distributions

Generalized Linear Models

Dose Response Models

General Logistic Regression Model

Goodness of Fit Statistics

Residuals

Other Diagnostics

Example: Senility and WAIS

Exercises

NOMINAL AND ORDINAL LOGISTIC REGRESSION

Introduction

Multinominal Distribution

Nominal Logistic Regression

Ordinal Logistic Regression

General Comments

Exercises

COUNT DATA, POISSON REGRESSION, AND LOG-LINEAR MODELS

Introduction

Poisson Regression

Examples of Contingency Tables

Probability Models for Contingency Tables

Log-Linear Models

Inference for Log-Linear Models

Numerical Examples

Remarks

Exercises

SURVIVAL ANALYSIS

Introduction

Survivor Functions and Hazard Functions

Empirical Survivor Function

Estimation

Inference

Model checking

Example: Remission Times

Exercises

clustered and longitudinal data

Introduction

Example: Recovery from Stroke

Repeated Measures Models for Normal Data

Repeated Measures Models for NON-NORMAL DATA

Multilevel Models

Stroke Example Continued

Comments

Exercises

SOFTWARE

REFERENCES

INDEX

Name: An Introduction to Generalized Linear Models, Second Edition (eBook)Chapman and Hall/CRC 
Description: By Annette J. DobsonSeries Editor: Chris Chatfield, Jim Zidek, Jim Lindsey. Generalized linear models provide a unified theoretical and conceptual framework for many of the most commonly used statistical methods. In the ten years since publication of the first edition of this bestselling text, great strides have been made in the...
Categories: Statistics & Probability, Statistical Theory & Methods, Statistics for the Biological Sciences