Robust Diagnostic Regression Analysis

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August 2000



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 new 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 parametersof 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 this book is to combine robustness and a "forward" search through the data with regression diagnostics and computer graphics.


1 Some Regression Examples.- 1.1 Influence and Outliers.- 1.2 Three Examples.- 1.2.1 Forbes' Data.- 1.2.2 Multiple Regression Data.- 1.2.3 Wool Data.- 1.3 Checking and Building Models.- 2 Regression and the Forward Search.- 2.1 Least Squares.- 2.1.1 Parameter Estimates.- 2.1.2 Residuals and Leverage.- 2.1.3 Formal Tests.- 2.2 Added Variables.- 2.3 Deletion Diagnostics.- 2.3.1 The Algebra of Deletion.- 2.3.2 Deletion Residuals.- 2.3.3 Cook's Distance.- 2.4 The Mean Shift Outlier Model.- 2.5 Simulation Envelopes.- 2.6 The Forward Search.- 2.6.1 General Principles.- 2.6.2 Step 1: Choice of the Initial Subset.- 2.6.3 Step 2: Adding Observations During the Forward Search.- 2.6.4 Step 3: Monitoring the Search.- 2.6.5 Forward Deletion Formulae.- 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.- 4.2.1 Transformation of the Response.- 4.2.2 Graphics for Transformations.- 4.2.3 Transformation of an Explanatory Variable.- 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 Data-More Masking.- 4.7.1 A Diagnostic Analysis.- 4.7.2 A Forward Analysis.- 4.7.3 Other Graphics for Transformations.- 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.- 5.1.1 Nonlinear Models.- 5.1.2 Curvature.- 5.2 The Forward Search.- 5.2.1 Parameter Estimation.- 5.2.2 Monitoring 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.- 6.1.1 British Train Accidents.- 6.1.2 Bliss's Beetle Data.- 6.1.3 The Link Function.- 6.2 The Exponential Family.- 6.3 Mean, Variance, and Likelihood.- 6.3.1 One Observation.- 6.3.2 The Variance Function.- 6.3.3 Canonical Parameterization.- 6.3.4 The Likelihood.- 6.4 Maximum Likelihood Estimation.- 6.4.1 Least Squares.- 6.4.2 Weighted Least Squares.- 6.4.3 Newton's Method for Solving Equations.- 6.4.4 Fisher Scoring.- 6.4.5 The Algorithm.- 6.5 Inference.- 6.5.1 The Deviance.- 6.5.2 Estimation of the Dispersion Parameter.- 6.5.3 Inference About Parameters.- 6.6 Checking Generalized Linear Models.- 6.6.1 The Hat Matrix.- 6.6.2 Residuals.- 6.6.3 Cook's Distance.- 6.6.4 A Goodness of Link Test.- 6.6.5 Monitoring the Forward Search.- 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.- 6.16.1 A Forward Analysis.- 6.16.2 Comparison with Backwards Methods.- 6.17 Binary Data.- 6.17.1 Introduction: Vasoconstriction Data.- 6.17.2 The Deviance.- 6.17.3 The Forward Search for Binary Data.- 6.17.4 Perfect Fit.- 6.18 Theory: The Effect 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.


From the 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."
"I would recommend practitioners of regression, this is, probably most of us, to read and use this book."
"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 the process 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)
EAN: 9780387950174
ISBN: 0387950176
Untertitel: 'Springer Series in Statistics'. 2000. Auflage. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: August 2000
Seitenanzahl: 348 Seiten
Format: gebunden
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