An Introduction to Generalized Linear Models, Third Edition

by Dobson; Annette J.

• ISBN13: 9781584889502
• ISBN10: 1584889500
• Edition: 3rd
• Format: Nonspecific Binding
• Copyright: 2008-05-12
• Publisher: Chapman & Hall/

Summary

Continuing to emphasize numerical and graphical methods, An Introduction to Generalized Linear Models, Third Editionprovides 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

Preface
Introduction	p. 1
Background	p. 1
Scope	p. 1
Notation	p. 5
Distributions related to the Normal distribution	p. 7
Quadratic forms	p. 11
Estimation	p. 12
Exercises	p. 15
Model Fitting	p. 19
Introduction	p. 19
Examples	p. 19
Some principles of statistical modelling	p. 32
Notation and coding for explanatory variables	p. 37
Exercises	p. 40
Exponential Family and Generalized Linear Models	p. 45
Introduction	p. 45
Exponential family of distributions	p. 46
Properties of distributions in the exponential family	p. 48
Generalized linear models	p. 51
Examples	p. 52
Exercises	p. 55
Estimation	p. 59
Introduction	p. 59
Example: Failure times for pressure vessels	p. 59
Maximum likelihood estimation	p. 64
Poisson regression example	p. 66
Exercises	p. 69
Inference	p. 73
Introduction	p. 73
Sampling distribution for score statistics	p. 74
Taylor series approximations	p. 76
Sampling distribution for MLEs	p. 77
Log-likelihood ratio statistic	p. 79
Sampling distribution for the deviance	p. 80
Hypothesis testing	p. 85
Exercises	p. 87
Normal Linear Models	p. 89
Introduction	p. 89
Basic results	p. 89
Multiple linear regression	p. 95
Analysis of variance	p. 102
Analysis of covariance	p. 114
General linear models	p. 117
Exercises	p. 118
Binary Variables and Logistic Regression	p. 123
Probability distributions	p. 123
Generalized linear models	p. 124
Dose response models	p. 124
General logistic regression model	p. 131
Goodness of fit statistics	p. 135
Residuals	p. 138
Other diagnostics	p. 139
Example: Senility and WAIS	p. 140
Exercises	p. 143
Nominal and Ordinal Logistic Regression	p. 149
Introduction	p. 149
Multinomial distribution	p. 149
Nominal logistic regression	p. 151
Ordinal logistic regression	p. 157
General comments	p. 162
Exercises	p. 163
Poisson Regression and Log-Linear Models	p. 165
Introduction	p. 165
Poisson regression	p. 166
Examples of contingency tables	p. 171
Probability models for contingency tables	p. 175
Log-linear models	p. 177
Inference for log-linear models	p. 178
Numerical examples	p. 179
Remarks	p. 183
Exercises	p. 183
Survival Analysis	p. 187
Introduction	p. 187
Survivor functions and hazard functions	p. 189
Empirical survivor function	p. 193
Estimation	p. 195
Inference	p. 198
Model checking	p. 199
Example: Remission times	p. 201
Exercises	p. 202
Clustered and Longitudinal Data	p. 207
Introduction	p. 207
Example: Recovery from stroke	p. 209
Repeated measures models for Normal data	p. 213
Repeated measures models for non-Normal data	p. 218
Multilevel models	p. 219
Stroke example continued	p. 222
Comments	p. 224
Exercises	p. 225
Bayesian Analysis	p. 229
Frequentist and Bayesian paradigms	p. 229
Priors	p. 233
Distributions and hierarchies in Bayesian analysis	p. 238
WinBUGS software for Bayesian analysis	p. 238
Exercises	p. 241
Markov Chain Monte Carlo Methods	p. 243
Why standard inference fails	p. 243
Monte Carlo integration	p. 243
Markov chains	p. 245
Bayesian inference	p. 255
Diagnostics of chain convergence	p. 256
Bayesian model fit: the DIC	p. 260
Exercises	p. 262
Example Bayesian Analyses	p. 267
Introduction	p. 267
Binary variables and logistic regression	p. 267
Nominal logistic regression	p. 271
Latent variable model	p. 272
Survival analysis	p. 275
Random effects	p. 277
Longitudinal data analysis	p. 279
Some practical tips for WinBUGS	p. 286
Exercises	p. 288
Appendix	p. 291
Software	p. 293
References	p. 295
Index	p. 303
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