An Introduction to Generalized Linear Models, Third Edition
by Dobson; Annette J.Edition: 3rd
Format: Nonspecific Binding
Pub. Date: 2008-05-12
Publisher(s): Chapman & Hall/
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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 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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