Robust Diagnostic Regression Analysis (Hardcover)

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.