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Contents
Preface 1 Introduction 1.1 Background 1.2 Scope 1.3 Notation 1.4 Distributions related to the Normal distribution 1.5 Quadratic forms 1.6 Estimation 1.7 Exercises 2 Model Fitting 2.1 Introduction 2.2 Examples 2.3 Some principles ofstatistica l modelling 2.4 Notation and coding for explanatory variables 2.5 Exercises 3 Exponential Family and Generalized Linear Models 3.1 Introduction 3.2 Exponential family of distributions 3.3 Properties ofdistribution s in the exponential family 3.4 Generalized linear models 3.5 Examples 3.6 Exercises 4 Estimation 4.1 Introduction 4.2 Example: Failure times for pressure vessels 4.3 Maximum likelihood estimation 4.4 Poisson regression example 4.5 Exercises 5 Inference 5.1 Introduction 5.2 Sampling distribution for score statistics ? 2002 by Chapman & Hall/CRC 5 5.3 Taylor series approximations 5.4 Sampling distribution for maximum likelihood estimators 5.5 Log-likelihood ratio statistic 5.6 Sampling distribution for the deviance 5.7 Hypothesis testing 5.8 Exercises 6 Normal Linear Models 6.1 Introduction 6.2 Basic results 6.3 Multiple linear regression 6.4 Analysis of variance 6.5 Analysis ofc ovariance 6.6 General linear models 6.7 Exercises 7 Binary Variables and Logistic Regression 7.1 Probability distributions 7.2 Generalized linear models 7.3 Dose response models 7.4 General logistic regression model 7.5 Goodness offi t statistics 7.6 Residuals 7.7 Other diagnostics 7.8 Example: Senility and WAIS 7.9 Exercises 8 Nominal and Ordinal Logistic Regression 8.1 Introduction 8.2 Multinomial distribution 8.3 Nominal logistic regression 8.4 Ordinal logistic regression 8.5 General comments 8.6 Exercises 9 Count Data, Poisson Regression and Log-Linear Models 9.1 Introduction 9.2 Poisson regression 9.3 Examples ofco ntingency tables 9.4 Probability models for contingency tables 9.5 Log-linear models 9.6 Inference for log-linear models 9.7 Numerical examples 9.8 Remarks 9.9 Exercises ? 2002 by Chapman & Hall/CRC 6 10 Survival Analysis 10.1 Introduction 10.2 Survivor functions and hazard functions 10.3 Empirical survivor function 10.4 Estimation 10.5 Inference 10.6 Model checking 10.7 Example: remission times 10.8 Exercises 11 Clustered and Longitudinal Data 11.1 Introduction 11.2 Example: Recovery from stroke 11.3 Repeated measures models for Normal data 11.4 Repeated measures models for non-Normal data 11.5 Multilevel models 11.6 Stroke example continued 11.7 Comments 11.8 Exercises Software References ? 2002 by Chapman & Hall/CRC 7 Preface Statistical tools for analyzing data are developing rapidly so that the 1990 edition ofthis book is now out ofdate. The original purpose ofthe book was to present a unified theoretical and conceptual framework for statistical modelling in a way that was accessible to undergraduate students and researchers in other fields. This new edition has been expanded to include nominal (or multinomial) and ordinal logistic regression, survival analysis and analysis oflongitudinal and clustered data. Although these topics do not fall strictly within the definition of generalized linear models, the underlying principles and methods are very similar and their inclusion is consistent with the original purpose ofthe book. The new edition relies on numerical methods more than the previous edition did. Some ofthe calculations can be performed with a spreadsheet while others require statistical software. There is an emphasis on graphical methods for exploratory data analysis, visualizing numerical optimization (for example, ofthe likelihood function) and plotting residuals to check the adequacy of models. Introduction 1.1 Background This book is designed to introduce the reader to generalized linear models; these provide a unifying framework for many commonly used statistical techniques. They also illustrate the ideas ofstatistical modelling. The reader is assumed to have some familiarity with statistical principles and methods. In particular, understanding the concepts ofestimation, sampling distributions and hypothesis testing is necessary. Experience in the use oft-tests, analysis ofv ariance, simple linear regression and chi-squared tests of independence for two-dimensional contingency tables is assumed. In addition, some knowledge ofmatrix algebra and calculus is required. The reader will find it necessary to have access to statistical computing facilities. Many statistical programs, languages or packages can now perform the analyses discussed in this book. Often, however, they do so with a different program or procedure for each type of analysis so that the unifying structure is not apparent. Some programs or languages which have procedures consistent with the approach used in this book are: Stata, S-PLUS, Glim, Genstat and SYSTAT. This list is not comprehensive as appropriate modules are continually being added to other programs. In addition, anyone working through this book may find it helpful to be able to use mathematical software that can perform matrix algebra, differentiation and iterative calculations. 1.2 Scope The statistical methods considered in this o梅雨 
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