An Introduction to Generalized Linear Models, Third Edition

An Introduction to Generalized Linear Models, Third Edition

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Series: Chapman & Hall/CRC Texts in Statistical Science.

Continuing to emphasize numerical and graphical methods, An Introduction to Generalized Linear Models, Third Edition provides a cohesive framework for statistical modeling. This new edition of a bestseller has been updated with Stata, R, and WinBUGS code as well as three new chapters on Bayesian analysis.

Like its predecessor, this edition presents the theoretical background of generalized linear models (GLMs) before focusing on methods for analyzing particular kinds of data. It covers normal, Poisson, and binomial distributions; linear regression models; classical estimation and model fitting methods; and frequentist methods of statistical inference. After forming this foundation, the authors explore multiple linear regression, analysis of variance (ANOVA), logistic regression, log-linear models, survival analysis, multilevel modeling, Bayesian models, and Markov chain Monte Carlo (MCMC) methods.

Using popular statistical software programs, this concise and accessible text illustrates practical approaches to estimation, model fitting, and model comparisons. It includes examples and exercises with complete data sets for nearly all the models covered.

Table of Contents

Introduction

Background

Scope

Notation

Distributions Related to the Normal Distribution

Quadratic Forms

Estimation

Model Fitting

Introduction

Examples

Some Principles of Statistical Modeling

Notation and Coding for Explanatory Variables

Exponential Family and Generalized Linear Models

Introduction

Exponential Family of Distributions

Properties of Distributions in the Exponential Family

Generalized Linear Models

Examples

Estimation

Introduction

Example: Failure Times for Pressure Vessels

Maximum Likelihood Estimation

Poisson Regression Example

Inference

Introduction

Sampling Distribution for Score Statistics

Taylor Series Approximations

Sampling Distribution for MLEs

Log-Likelihood Ratio Statistic

Sampling Distribution for the Deviance

Hypothesis Testing

Normal Linear Models

Introduction

Basic Results

Multiple Linear Regression

Analysis of Variance

Analysis of Covariance

General Linear Models

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

Nominal and Ordinal Logistic Regression

Introduction

Multinomial Distribution

Nominal Logistic Regression

Ordinal Logistic Regression

General Comments

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

Survival Analysis

Introduction

Survivor Functions and Hazard Functions

Empirical Survivor Function

Estimation

Inference

Model Checking

Example: Remission Times

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

Bayesian Analysis

Frequentist and Bayesian Paradigms

Priors

Distributions and Hierarchies in Bayesian Analysis

WinBUGS Software for Bayesian Analysis

Methods

Why Standard Inference Fails

Monte Carlo Integration

Markov Chains

Bayesian Inference

Diagnostics of Chain Convergence

Bayesian Model Fit: The DIC

Example Bayesian Analyses

Introduction

Binary Variables and Logistic Regression

Nominal Logistic Regression

Latent Variable Model

Survival Analysis

Random Effects

Longitudinal Data Analysis

Some Practical Tips for WinBUGS

Software

References

Index

Exercises appear at the end of each chapter.

Reviews

The comments of Lang in his review of the second edition, that ‘This relatively short book gives a nice introductory overview of the theory underlying generalized linear modelling. …’ can equally be applied to the new edition. … three new chapters on Bayesian analysis are also added. … suitable for experienced professionals needing to refresh their knowledge … .

—Pharmaceutical Statistics, 2011

The chapters are short and concise, and the writing is clear … explanations are fundamentally sound and aimed well at an upper-level undergrad or early graduate student in a statistics-related field. This is a very worthwhile book: a good class text and a practical reference for applied statisticians.

—Biometrics

This book promises in its introductory section to provide a unifying framework for many statistical techniques. It accomplishes this goal easily. … Furthermore, the text covers important topics that are frequently overlooked in introductory courses, such as models for ordinal outcomes. … This book is an excellent resource, either as an introduction to or a reminder of the technical aspects of generalized linear models and provides a wealth of simple yet useful examples and data sets.

—Journal of Biopharmaceutical Statistics, Issue 2

Praise for the Second Edition

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 … .

—Kerrie Nelson, Statistics in Medicine, Vol. 23