Robust Diagnostic Regression Analysis

Graphs are used to understand the relationship between a regression model and the data to which it is fitted. The authors develop new, highly informative graphs for the analysis of regression data and for the detection of model inadequacies. As well as illustrating new procedures, the authors develop the theory of the models used, particularly for generalized linear models. The book provides statisticians and scientists with a new set of tools for data analysis. Software to produce the plots is available on the authors website.

Contenu

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.