An Introduction to Generalized Linear Models, Second Edition

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