Introduction to Statistical Modelling, 1983

This book is about generalized linear models as described by NeIder and Wedderburn (1972). This approach provides a unified theoretical and computational framework for the most commonly used statistical methods: regression, analysis of variance and covariance, logistic regression, log-linear models for contingency tables and several more specialized techniques. More advanced expositions of the subject are given by McCullagh and NeIder (1983) and Andersen (1980). The emphasis is on the use of statistical models to investigate substantive questions rather than to produce mathematical descriptions of the data. Therefore parameter estimation and hypothesis testing are stressed. I have assumed that the reader is familiar with the most commonly used statistical concepts and methods and has some basic knowledge of calculus and matrix algebra. Short numerical examples are used to illustrate the main points. In writing this book I have been helped greatly by the comments and criticism of my students and colleagues, especially Anne Young. However, the choice of material, and the obscurities and errors are my responsibility and I apologize to the reader for any irritation caused by them. For typing the manuscript under difficult conditions I am grateful to Anne McKim, Jan Garnsey, Cath Claydon and Julie Latimer.

1 Introduction.- 2 Model Fitting.- 3 Exponential Family of Distributions and Generalized Linear Models.- 4 Estimation.- 5 Inference.- 6 Multiple Regression.- 7 Analysis of Variance and Covariance.- 8 Binary Variables and Logistic Regression.- 9 Contingency Tables and Log-Linear Models.- Appendix 1.- Appendix 2.- Appendix 3.- Appendix 4.- References.