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

About the Book

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.

Review :
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