Foundations of Linear and Generalized Linear Models

Preface

PURPOSE OF THIS BOOK

Why yet another book on linear models? Over the years, a multitude of books have already been written about this well-traveled topic, many of which provide more comprehensive presentations of linear modeling than this one attempts. My book is intended to present an overview of the key ideas and foundational results of linear and generalized linear models. I believe this overview approach will be useful for students who lack the time in their program for a more detailed study of the topic. This situation is increasingly common in Statistics and Biostatistics departments. As courses are added on recent influential developments (such as “big data,” statistical learning, Monte Carlo methods, and application areas such as genetics and finance), programs struggle to keep room in their curriculum for courses that have traditionally been at the core of the field. Many departments no longer devote an entire year or more to courses about linear modeling.

Books such as those by Dobson and Barnett (2008), Fox (2008), and Madsen and Thyregod (2011) present fine overviews of both linear and generalized linear models. By contrast, my book has more emphasis on the theoretical foundations—showing how linear model fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about effects, deriving likelihood equations and likelihood-based inference, and providing extensive references for historical developments ...