Foundations of Linear and Generalized Linear Models: An interview with author Alan Agresti

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  • Author: Statistics Views
  • Date: 13 Mar 2015
  • Copyright: Photograph appears courtesy of Professor Agresti

This month, Wiley is proud to publish the latest book by best-selling author, Professor Alan AgrestiFoundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linear statistical models. The book presents a broad, in-depth overview of the most commonly used statistical models by discussing the theory underlying the models, R software applications,and examples with crafted models to elucidate key ideas and promote practical modelbuilding.

The book begins by illustrating the fundamentals of linear models, such as how the model-fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about the effects of explanatory variables. Subsequently, the book covers the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data. Focusing on the theoretical underpinnings of these models, Foundations of Linear and Generalized Linear Models also features:

  • An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methods
  • An overview of linear mixed models and generalized linear mixed models with random effects for clustered correlated data, Bayesian modeling, and extensions to handle problematic cases such as high dimensional problems
  • Numerous examples that use R software for all text data analyses
  • More than 400 exercises for readers to practice and extend the theory, methods, and data analysis
  • A supplementary website with datasets for the examples and exercises

An invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, Foundations of Linear and Generalized Linear Models is also an excellent reference for practicing statisticians and biostatisticians, as well as anyone who is interested in learning about the most important statistical models for analyzing data.

thumbnail image: Foundations of Linear and Generalized Linear Models: An interview with author Alan Agresti

1. Congratulations on the publication of Foundations of Linear and Generalized Linear Models. How did the writing process begin?

Thanks for the congrats! In recent years I’ve lived in Boston part of the year. Four years ago, the Statistics Department at Harvard University asked me (as a visiting professor) to develop an overview course on linear and generalized linear models for their graduate students. Although many books exist with in-depth treatments of linear models and other books cover generalized linear models, I did not find one that combined both topics for a one-semester overview course and that had the technical rigor needed for Statistics and Biostatistics graduate students. So, my goal was to write such a book based on the notes that I prepared to teach that course.

2. Who should read the book and why?

I intend the book to serve as a textbook for a one-semester or two-quarter course that covers both linear models and generalized linear models. The level is geared toward graduate students in the first or second year of Statistics and Biostatistics programs. It also can serve programs that have a heavy focus on statistical modelling, such as econometrics. I think it will also be useful to graduate students in the social, biological, and environmental sciences who choose Statistics as their minor area of concentration. Such students need to be familiar with the material in this book if they intend to be adequately trained as statistical scientists.

3. The book presents a broad, in-depth overview of the most commonly used statistical models by discussing the theory underlying the models, R software applications, and examples to elucidate key ideas and promote practical model building. What were your original objectives when writing the book?

As your question suggests, I really wanted the text to explain why and when the models work, but also show how modern software (R) can implement them.

I truly believe that in reading this book and also a standard text on probability and mathematical statistics, a person studying to become a professional statistician or biostatistician will have studied the basic foundations of the field.

4. The book also details the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data, and it includes more than 400 exercises. Did many of these exercises arise through teaching?

Yes, I developed many of these exercises from homework assignments for the course I taught at Harvard. Many exercises also came from courses that I’ve taught on categorical data analysis or from the books I’ve written for Wiley on that topic. Some exercises are geared toward the theoretical material and its extensions and some are designed to enable students to practice model-building with a variety of types of data sets.

5. What is it about the area of statistical modeling that fascinates you?

In analyzing data, most of what statisticians do is based on building and applying statistical models. In practice, the models that are most commonly used are the ones presented in this book. They are the models I’ve found most useful throughout my own career, especially in consulting that I’ve done with researchers in the life sciences and the social sciences.

6. Why is this book of particular interest now?

For a long time, ordinary normal linear models have been popular in many disciplines and have had a central place in the curriculum of Statistics graduate programs. But recently there has been increasing awareness of the need for other models, including models for categorical data and for count data and models that permit observations to be correlated. At the same time, it is becoming more difficult to find room in graduate curricula for all the relevant topics. I think that the material presented in this book is basic information with which any statistician or biostatistician should be familiar. With this background, they are equipped to study more complex models and to develop their own specialized models for particular application areas they study.

             Alan Agresti

7. Were there areas of the book that you found more challenging to write, and if so, why?

The introductory chapters on linear models were a particular challenge. I had never taught a course in linear models during my 38 years as a faculty member at the University of Florida. Most books on this topic are enormously detailed, and I had to determine what I thought were the most important elements to present in a couple of chapters. I then had to figure out how to organize and present the material and also assist the reader recall needed material on statistical theory and basic matrix algebra. It was also challenging to present the Bayesian approach to modelling and new methods for dealing with huge numbers of parameters. It’s essential for students of Statistics to see such material, but each of these topics is undergoing rapid growth, and giving chapter overviews was not easy.

8. Which element of the book are you proudest of?

I’m pleased that I was able to present this overview in about 400 pages of text. (Most books I’ve written tend to be much longer!) I truly believe that in reading this book and also a standard text on probability and mathematical statistics, a person studying to become a professional statistician or biostatistician will have studied the basic foundations of the field.

9. You have authored many publications such as the best-selling Categorical Data Analysis for Wiley as well as other titles such as on ordinal categorical data. What will be your next book-length undertaking?

I’ve written a couple of lower-level statistics books that periodically need new editions. I am now revising one of those. But I love new challenges, and I am also in the early stages of writing something quite different from anything I’ve done before. I’m reluctant to give details before I know whether this project will truly work out, but I hope you will see something new from me within a few years!

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