Robust Diagnostic Regression Analysis
Springer. ISBN 0387950176.
Hardback: 241mm 160mm; xiv+328 pages, 192
illustrations
Mirros of this material will be available in London and New York.
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.
 Some Regression Examples
 Regression and the Forward Search
 Regression
 Transformations to Normality
 Nonlinear Least Squares
 Generalized Linear Models
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 SPlus. We are now developing SPlus functions and have set up a web site http://stat.econ.unipr.it/riani/ar
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, coauthored 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 SPLus 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 a.c.atkinson@lse.ac.uk
Marco Riani mriani@unipr.it
London and Parma, February 2000
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