An Introduction to Generalized Linear Models, Second Edition

by ;
Edition: 2nd
Format: Paperback
Pub. Date: 2001-11-28
Publisher(s): Chapman & Hall/
List Price: $59.95

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Summary

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, the 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, and multi-level models. It also includes modern methods for checking model adequacy and examples from an even wider range of applications.

Author Biography

Annette J. Dobson is a Professor of Biostatistics at the University of Queensland, Australia.

Table of Contents

Preface ix
Introduction
1(16)
Background
1(1)
Scope
1(4)
Notation
5(1)
Distributions related to the Normal distribution
6(3)
Quadratic forms
9(1)
Estimation
10(4)
Exercises
14(3)
Model Fitting
17(26)
Introduction
17(1)
Examples
17(13)
Some principles of statistical modelling
30(5)
Notation and coding for explanatory variables
35(3)
Exercises
38(5)
Exponential Family and Generalized Linear Models
43(14)
Introduction
43(1)
Exponential family of distributions
44(2)
Properties of distributions in the exponential family
46(3)
Generalized linear models
49(1)
Examples
50(3)
Exercises
53(4)
Estimation
57(12)
Introduction
57(1)
Example: Failure times for pressure vessels
57(5)
Maximum likelihood estimation
62(2)
Poisson regression example
64(3)
Exercises
67(2)
Inference
69(16)
Introduction
69(1)
Sampling distribution for score statistics
70(2)
Taylor series approximations
72(1)
Sampling distribution for maximum likelihood estimators
73(2)
Log-likelihood ratio statistic
75(1)
Sampling distribution for the deviance
76(4)
Hypothesis testing
80(2)
Exercises
82(3)
Normal Linear Models
85(30)
Introduction
85(1)
Basic results
85(5)
Multiple linear regression
90(5)
Analysis of variance
95(11)
Analysis of covariance
106(2)
General linear models
108(2)
Exercises
110(5)
Binary Variables and Logistic Regression
115(20)
Probability distributions
115(1)
Generalized linear models
116(1)
Dose response models
116(5)
General logistic regression model
121(3)
Goodness of fit statistics
124(3)
Residuals
127(1)
Other diagnostics
128(1)
Example: Senility and WAIS
129(2)
Exercises
131(4)
Nominal and Ordinal Logistic Regression
135(16)
Introduction
135(1)
Multinomial distribution
135(2)
Nominal logistic regression
137(6)
Ordinal logistic regression
143(4)
General comments
147(1)
Exercises
148(3)
Count Data, Poisson Regression and Log-Linear Models
151(20)
Introduction
151(1)
Poisson regression
152(4)
Examples of contingency tables
156(5)
Probability models for contingency tables
161(1)
Log-linear models
162(2)
Inference for log-linear models
164(1)
Numerical examples
164(3)
Remarks
167(1)
Exercises
168(3)
Survival Analysis
171(20)
Introduction
171(2)
Survivor functions and hazard functions
173(4)
Empirical survivor function
177(3)
Estimation
180(2)
Inference
182(1)
Model checking
183(2)
Example: remission times
185(2)
Exercises
187(4)
Clustered and Longitudinal Data
191(22)
Introduction
191(2)
Example: Recovery from stroke
193(4)
Repeated measures models for Normal data
197(5)
Repeated measures models for non-Normal data
202(1)
Multilevel models
203(3)
Stroke example continued
206(1)
Comments
207(2)
Exercises
209(4)
Software 213(2)
References 215(6)
Index 221

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