An Introduction to Generalized Linear Models, Second Edition: (Chapman & Hall/CRC Texts in Statistical Science)

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.

Table of 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