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.
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An undergraduate-level introduction to the topic of generalized linear models
An Introduction to Generalized Linear Models-a new edition of An Introduction to Statistical Modelling-demonstrates how generalized linear models provide a unifying framework for many commonly used multivariate statistical methods, including multiple regression and analysis of variance or covariance for continuous response data, 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. Chapters on each of the main types of generalized linear models are included. The statistical computing program GLIM , developed to fit these models to data, is used extensively. Other programs, particularly MINITAB, are used to illustrate particular issues. The student 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. Methods described in this text are widely applicable for analyzing data from the fields of medicine, agriculture, biology, engineering, industrial experimentation, and the social sciences.
Continuing to emphasize numerical and graphical methods, An Introduction to Generalized Linear Models, Third Edition provides 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.
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