Robust Diagnostic Regression Analysis

by A. C. Atkinson    and     M. Riani

Springer. ISBN 0-387-95017-6.

Hardback: 241mm 160mm; xiv+328 pages, 192 illustrations

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The authors develop new, highly informative graphs for the analysis of regression data including generalized linear models. The graphs lead to the detection of model inadequacies, which may be systematic - perhaps a transformation of the data is needed - or there may be several outliers. These are identified and their importance established. Improved models can then be fitted and checked. The graphs are generated from a robust forward search through the data, which orders the observations by their closeness to the assumed model. The four main chapters cover regression, transformations of data in regression, nonlinear least squares and generalized linear models. As well as illustrating our new procedures, we develop the theory of the models used, particularly for generalized linear models. Exercises with solutions are given for these chapters. The book could thus be used as a text for a second course in regression as well providing statisticians and scientists with a new set of tools for data analysis. A companion volume on the analysis of multivariate data is in active preparation.


  1. Some Regression Examples
  2. Regression and the Forward Search
  3. Regression
  4. Transformations to Normality
  5. Nonlinear Least Squares
  6. Generalized Linear Models
  7. Appendix: data


This book is about using graphs to understand the relationship between a regression model and the data to which it is fitted. Because of the way in which models are fitted, for example by least squares, we can lose information about the effect of individual observations on inferences about the form and parameters of the model. The methods developed in this book reveal how the fitted regression model depends on individual observations and on groups of observations. Robust procedures can sometimes reveal this structure, but downweight or discard some observations. The novelty in our book is to combine robustness and a ``forward" search through the data with regression diagnostics and computer graphics. We provide easily understood plots which use information from the whole sample to display the effect of each observation on a wide variety of aspects of the fitted model. This bald statement of the contents of our book masks the excitement we feel about the methods we have developed based on the forward search. We are continuously amazed, each time we analyse a new set of data, by the amount of information the plots generate and the insights they provide. We believe our book uses comparatively elementary methods to move regression in a completely new and useful direction. We have written the book to be accessible to students and users of statistical methods, as well as for professional statisticians. Because statistics requires mathematics, computing and data, we give an elementary outline of the theory behind the statistical methods we employ. The programming was done in GAUSS, with graphs for publication prepared in S-Plus. We are now developing S-Plus functions and have set up a web site which includes programs and the data. As our work on the forward search grows, we hope that the material on the website will grow in a similar manner. The first chapter of this book contains three examples of the use of the forward search in regression. We show how single and multiple outliers can be identified and their effect on parameter estimates determined. The second chapter gives the theory of regression, including deletion diagnostics, and describes the forward search and its properties. Chapter Three returns to regression and analyses four further examples. In three of these a better model is obtained if the response is transformed, perhaps by regression with the logarithm of the response, rather than with the response itself. The transformation of a response to normality is the subject of Chapter Four which includes both theory and examples of data analysis. We use this chapter to illustrate the deleterious effect of outliers on methods based on deletion of single observations. Chapter Four ends with an example of transforming both sides of a regression model. This is one example of the nonlinear models which are the subject of Chapter Five. The sixth chapter is concerned with generalized linear models. Our methods are thus extended to the analysis of data from contingency tables and to binary data. The theoretical material is complemented by exercises. We give references to the statistical literature, but believe that our book is reasonably self contained. It should serve as a textbook for courses on applied regression and generalized linear models, even if the emphasis in such courses is not on the forward search. This book is concerned with data in which the observations are independent and in which the response is univariate. A companion volume, co-authored with Andrea Cerioli and tentatively called Robust Diagnostic Data Analysis, is under active preparation. This will cover topics in the analysis of multivariate data including regression, transformations, principal components analysis, discriminant analysis, clustering and the analysis of spatial data. The writing of this book, and the research on which it is based, has been both complicated and enriched by the fact that the authors are separated by half of Europe. Our travel has been supported by the Italian Ministry for Scientific Research, by the Staff Research Fund of the London School of Economics and, also at the LSE, by STICERD (The Suntory and Toyota International Centres for Economics and Related Disciplines). The development of S-PLus functions was supported by Doug Martin of MAthSoft Inc. Kjell Konis helped greatly with the programmimg. We are grateful to our numerous colleagues for their help in many ways. In England we thank especially Dr Martin Knott at the London School of Economics, who has been an unfailingly courteous source of help with both statistics and computing. In Italy we thank Prof. Sergio Zani of the University of Parma for his insightful comments and continuing support and Dr Aldo Corbellini of the same university who has devoted time, energy and skill to the creation of our web site. Anthony Atkinson's visits to Italy have been enriched by the warm hospitality of Giuseppina and Luigi Riani. To all our gratitude and thanks.

Anthony Atkinson

Marco Riani

London and Parma, February 2000


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Prof. A. C. Atkinson
Department of Statistics
London School of Economics

Web page:

Prof. M. Riani
Sezione di Statistica
Dipartimento di Economia
Via Kennedy 6
43100 PARMA

Web page:

[Anthony is on the left and Marco is on the right]


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