Robust Diagnostic Regression Analysis

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 infor mation 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 that 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 analyze 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.

Résumé

From the reviews:

MATHEMATICAL REVIEWS

"The text is lucidly written and theoretical discussions are amply complemented with examples and exercises. The book is accessible to students and users of statistical methods. It could, without doubt, serve as a textbook for courses on applied regression and generalized linear models. It will be a welcome addition to the resources of any applied statistician."

TECHNOMETRICS

"I would recommend practitioners of regression, this is, probably most of us, to read and use this book."

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION

"I would recommend ROBUST DIAGNOSTICS REGRESSION ANALYSIS and tools for anyone who does a fair amount of applied regression analysis on small- to moderate-sized datasets. It would be especially useful for anyone who uses nonlinear regression and/or generalized linear regression, where many fewer diagnostic tools are available. As a textbook, it would be good as a supplemental or even a primary text in a masters-level regression course. Researchers in other fields who do their own regression analysis also should be referred to this text, which they will find quite understandable."

"This book presents a host of graphical tools for regression data analysis, based on the 'forward search' approach. ... In order to make the work accessible to users, the authors have developed a number of SPlus programs. ... it would be an excellent reference book for students as well as other data analysts." (Debasis Sengupta, Sankhya, Vol. 65 (4), 2003)

"The topic of this monograph is the use of certain types of regression diagnostics, based on a robust forward search ... . the monograph is absolutely worth reading. ... The monograph is set up in a very instructive manner ... . The material is treated in a clear way, the book is very well written and understandable. Summarizing, this monograph can be recommended to readers who want to learn ... about theprocess of modeling in regression ... ." (C. Becker, Metrika, July, 2002)

"This book presents highly informative graphical methods to understand how a fitted regression model depends on ... observations. ... The book is intended to be accessible to students and practitioners, and ... provides useful material for professional statisticians. ... An S-Plus library of functions for implementing many of the methods presented in the book is available ... . This makes it very easy for anyone to apply the ideas ... . the authors have made an important contribution to the field of regression ... ." (Hariharan Iyer, Zentralblatt MATH, Vol. 964, 2001)

"This very down-to-earth volume explores regression models via a 'forward search' technique ... . Programming was done in GAUSS, and S-Plus functions have been developed. A web site provides programs and data ... . These methods provide additional analysis techniques for regression practitioners, and the book is a welcome addition to the literature." (N. R. Draper, Short Book Reviews, Vol. 21 (1), 2001)

Contenu
1 Some Regression Examples.- 1.1 Influence and Outliers.- 1.2 Three Examples.- 1.3 Checking and Building Models.- 2 Regression and the Forward Search.- 2.1 Least Squares.- 2.2 Added Variables.- 2.3 Deletion Diagnostics.- 2.4 The Mean Shift Outlier Model.- 2.5 Simulation Envelopes.- 2.6 The Forward Search.- 2.7 Further Reading.- 2.8 Exercises.- 2.9 Solutions.- 3 Regression.- 3.1 Hawkins' Data.- 3.2 Stack Loss Data.- 3.3 Salinity Data.- 3.4 Ozone Data.- 3.5 Exercises.- 3.6 Solutions.- 4 Transformations to Normality.- 4.1 Background.- 4.2 Transformations in Regression.- 4.3 Wool Data.- 4.4 Poison Data.- 4.5 Modified Poison Data.- 4.6 Doubly Modified Poison Data: An Example of Masking.- 4.7 Multiply Modified Poison DataMore Masking.- 4.8 Ozone Data.- 4.9 Stack Loss Data.- 4.10 Mussels' Muscles: Transformation of the Response.- 4.11 Transforming Both Sides of a Model.- 4.12 Shortleaf Pine.- 4.13 Other Transformations and Further Reading.- 4.14 Exercises.- 4.15 Solutions.- 5 Nonlinear Least Squares.- 5.1 Background.- 5.2 The Forward Search.- 5.3 Radioactivity and Molar Concentration of Nifedipene.- 5.4 Enzyme Kinetics.- 5.5 Calcium Uptake.- 5.6 Nitrogen in Lakes.- 5.7 Isomerization ofn-Pentane.- 5.8 Related Literature.- 5.9 Exercises.- 5.10 Solutions.- 6 Generalized Linear Models.- 6.1 Background.- 6.2 The Exponential Family.- 6.3 Mean, Variance, and Likelihood.- 6.4 Maximum Likelihood Estimation.- 6.5 Inference.- 6.6 Checking Generalized Linear Models.- 6.7 Gamma Models.- 6.8 Car Insurance Data.- 6.9 Dielectric Breakdown Strength.- 6.10 Poisson Models.- 6.11 British Train Accidents.- 6.12 Cellular Differentiation Data.- 6.13 Binomial Models.- 6.14 Bliss's Beetle Data.- 6.15 Mice with Convulsions.- 6.16 Toxoplasmosis and Rainfall.- 6.17 Binary Data.- 6.18 Theory: TheEffect of Perfect Fit and the Arcsine Link.- 6.19 Vasoconstriction Data and Perfect Fit.- 6.20 Chapman Data.- 6.21 Developments and Further Reading.- 6.22 Exercises.- 6.23 Solutions.- A Data.- Author Index.