Methods and Applications of Linear Models
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Content
Preface to the Third Edition xvii
Preface to the Second Edition xix
Preface to the First Edition xxi
Part I Regression 1
1 Introduction to Linear Models 3
1.1 Background Information 3
1.2 Mathematical and Statistical Models 5
1.3 Definition of the Linear Model 8
1.4 Examples of Regression Models 13
1.5 Concluding Comments 21
Exercises 21
2 Regression on Functions of One Variable 23
2.1 The Simple Linear Regression Model 23
2.2 Parameter Estimation 25
2.3 Properties of the Estimators and Test Statistics 34
2.4 The Analysis of Simple Linear Regression Models 39
2.5 Examining the Data and the Model 50
2.6 Polynomial Regression Models 63
Exercises 72
3 Transforming the Data 81
3.1 The Need for Transformations 81
3.2 Weighted Least Squares 82
3.3 Variance Stabilizing Transformations 85
3.4 Transformations to Achieve a Linear Model 86
3.5 Analysis of the Transformed Model 92
Exercises 95
4 Regression on Functions of Several Variables 99
4.1 The Multiple Linear Regression Model 99
4.2 Preliminary Data Analysis 100
4.3 Analysis of the Multiple Linear Regression Model 103
4.4 Partial Correlation and Added-Variable Plots 113
4.5 Variable Selection 119
4.6 Model Specification 130
Exercises 137
5 Collinearity in Multiple Linear Regression 142
5.1 The Collinearity Problem 142
5.2 An Example with Collinearity 150
5.3 Collinearity Diagnostics 156
5.4 Remedial Solutions: Biased Estimators 1665.4.3 Ridge Regression 174
Exercises 178
6 Influential Observations in Multiple Linear Regression 182
6.1 The Influential Data Problem 182
6.2 The Hat Matrix 183
6.3 The Effects of Deleting Observations 188
6.4 Numerical Measures of Influence 192
6.5 The Dilemma Data 197
6.6 Plots for Identifying Unusual Cases 201
6.7 Robust/Resistant Methods in Regression Analysis 209
Exercises 213
7 Polynomial Models and Qualitative Predictors 216
7.1 Polynomial Models 216
7.2 The Analysis of Response Surfaces 220
7.3 Models with Qualitative Predictors 225
Exercises 247
8 Additional Topics 254
8.1 Nonlinear Regression Models 254
8.2 Nonparametric Model-Fitting Methods 260
8.3 Generalized Linear Models 265
8.4 Random Input Variables 274
8.5 Errors in the Inputs 276
8.6 Calibration 277
Exercises 278
Part II the Analysis of Variance 283
9 Classification Models I: Introduction 285
9.1 Background Information 285
9.2 The One-Way Classification Model 286
9.3 The Two-Way Classification Model: Balanced Data 304
9.4 The Two-Way Classification Model: Unbalanced Data 322
9.5 The Two-Way Classification Model: No Interaction 334
9.6 Concluding Comments 347
Exercises 347
10 The Mathematical Theory of Linear Models 359
10.1 The Distribution of Linear and Quadratic Forms 359
10.2 Estimation and Inference for Linear Models 368
10.3 Tests of Linear Hypotheses on ß 380
10.4 Confidence Regions and Intervals 392
Exercises 395
11 Classification Models II: Multiple Crossed and Nested Factors 405
11.1 The Three-Factor Cross-Classified Model 406
11.2 A General Structure for Balanced Factorial Models 412
11.3 The Twofold Nested Model 417
11.4 A General Structure for Balanced, Nested Models 426
11.5 A Three-Factor, Nested-Factorial Model 429
11.6 A General Structure for Balanced, Nested-Factorial Models 434
Exercises 438
12 Mixed Models I: The AOV Method with Balanced Data 443
12.1 Introduction 443
12.2 Examples of the Analysis of Mixed Models 444
12.3 The General Analysis for Balanced, Mixed Models 464
12.4 Additional Examples 479
12.5 Alternative Developments of Mixed Models 487
Exercises 493
13 Mixed Models II: The AVE Method with Balanced Data 499
13.1 Introduction 499
13.2 The Two-Way Cross-Classification Model 500
13.3 The Three-Factor, Cross-Classification Model 511
13.4 Nested Models 515
13.5 Nested-Factorial Models 518
13.6 A General Description of the AVE Table 524
13.7 Additional Examples 531
13.8 The Computational Procedure for the AVE Method 537
Exercises 537
14 Mixed Models III: Unbalanced Data 543
14.1 Introduction 543
14.2 Parameter Estimation: Likelihood Methods 545
14.3 ml and REml Estimates with Balanced Data 554
14.4 The EM Algorithm for REML Estimation 558
14.5 Diagnostic Analysis with the EM Algorithm 572
14.6 Models with Covariates 581
14.7 Summary 585
Exercises 585
15 Simultaneous Inference: Tests and Confidence Intervals 591
15.1 Simultaneous Tests 591
15.2 Simultaneous Confidence Intervals 610
Exercises 612
Appendix A Mathematics 615
Appendix B Statistics 634
Appendix C Data Tables 645
Appendix D Statistical Tables 660
References 669
Index 677
