An Introduction to Generalized Linear Models: (Chapman & Hall Statistics Text Series)

This updated edition provides a unifying framework for many commonly used multivariate statistical methods including multiple regression and analysis of variance or covariance for continuous response data as well as logistic regression for binary responses and log-linear models for counted responses. The theory for these models is developed using the exponential, family of distributions, maximum likelihood estimation and likelihood ration tests. This is followed by information on each of the main types of generalized linear models. The statistical computing program GLIM which was developed to fit these models to data is used extensively and other programs, especially MINITAB, are used to illustrate particular issues. The reader is assumed to have a working knowledge of basic statistical concepts and methods (at the level of most introductory statistics courses) and some acquaintance with calculus and matrix algebra. The main changes from the first edition are that many sections have been extensively rewritten to provide more detailed explanations, GLIM and other programs are explicitly used, and many more numerical examples and exercises have been added. Outline of solutions for selected exercises are given. The methods described in this book are widely applicable for analysing data from the fields of medicine, agriculture, biology, engineering, industrial experimentation, and the social sciences.

Table of Contents:
Part 1 Background; scope; notation; distributions derived from normal distribution. Part 2 Model fitting: plant growth sample; birthweight sample; notation for linear models; exercises. Part 3 Exponential family of distributions and generalized linear models: exponential family of distributions; generalized linear models. Part 4 Estimation: method of maximum likelihood; method of least squares; estimation for generalized linear models; example of simple linear regression for Poisson responses; MINITAB program for simple linear regression with Poisson responses; GLIM. Part 5 Inference: sampling introduction for scores; sampling distribution for maximum likelihood estimators; confidence intervals for the model parameters; adequacy of a model; sampling distribution for the log-likelihood statistic; log-likelihood ratio statistic (deviance); assessing goodness of fit; hypothesis testing; residuals. Part 6 Multiple regression: maximum likelihood estimation; least squares estimation; log-likelihood ratio statistic; multiple correlation coefficient and R; numerical example; residual plots; orthogonality; collinearity; model selection; non-linear regression. Part 7 Analysis of variance and covariance: basic results; one-factor ANOVA; two-factor ANOVA with replication; crossed and nested factors; more complicated models; choice of constraint equations and dummy variables; analysis of covariance. Part 8 Binary variables and logistic regression: probability distributions; generalized linear models; dose response models; general logistic regression; maximum likelihood estimation and the log-likelihood ratio statistic; other criteria for goodness of fit; least squares methods; remarks. Part 9 Contingency tables and log-linear models: probability distributions; log-linear models; maximum likelihood estimation; hypothesis testing and goodness of fit; numerical examples; remarks. Appendices: conventional parametrizations with sum-to-zero constraints; corner-point parametrizations; three response variables; two response variables and one explanatory variable; one response variable and two explanatory variables.