Linear Models by Searle, Shayle R. -- Read -- Imperial Library of Trantor

Index

Cover Half Title page Title page Copyright page Preface Chapter 1: Generalized Inverse Matrices

1. Introduction 2. Solving Linear Equations 3. The Penrose Inverse 4. Other Definitions 5. Symmetric Matrices 6. Arbitrariness in a Generalized Inverse 7. Other Results 8. Exercises

Chapter 2: Distributions and Quadratic Forms

1. Introduction 2. Symmetric Matrices 3. Positive Definiteness 4. Distributions 5. Distribution of Quadratic Forms 6. Bilinear Forms 7. The Singular Normal Distribution 8. Exercises

Chapter 3: Regression, or the Full Rank Model

1. Introduction 2. Deviations from Means 3. Four Methods of Estimation 4. Consequences of Estimation 5. Distributional Properties 6. The General Linear Hypothesis 7. Related Topics 8. Summary of Regression Calculations 9. Exercises

Chapter 4: Introducing Linear Models: Regression on Dummy Variables

1. Regression on Allocated Codes 2. Regression on Dummy (0, 1) Variables 3. Describing Linear Models 4. The Normal Equations 5. Exercises

Chapter 5: Models Not of Full Rank

1. The Normal Equations 2. Consequences of a Solution 3. Distributional Properties 4. Estimable Functions 5. The General Linear Hypothesis 6. Restricted Models 7. The “Usual Constraints” 8. Generalizations 9. Summary 10. Exercises

Chapter 6: Two Elementary Models

1. Summary of General Results 2. The 1-Way Classification 3. Reductions in Sums of Squares 4. The 2-Way Nested Classification 5. Normal Equations for Design Models 6. Exercises

Chapter 7: The 2-Way Crossed Classification

1. The 2-Way Classification without Interaction 2. The 2-Way Classification with Interaction 3. Interpretation of Hypotheses 4. Connectedness 5. μij-Models 6. Exercises

Chapter 8: Some Other Analyses

1. Large-Scale Survey-Type Data 2. Covariance 3. Data Having all Cells Filled 4. Exercises

Chapter 9: Introduction to Variance Components

1. Fixed and Random Models 2. Mixed Models 3. Fixed or Random? 4. Finite Populations 5. Introduction to Estimation 6. Rules for Balanced Data 7. The 2-Way Classification 8. Estimating Variance Components from Balanced Data 9. Normality Assumptions 10. Exercises

Chapter 10: Methods of Estimating Variance Components from Unbalanced Data

1. Expectations of Quadratic Forms 2. Analysis of Variance Method (Henderson’s Method 1) 3. ADJUSTING for Bias in Mixed Models 4. Fitting Constants Method (Henderson’s Method 3) 5. Analysis of Means Methods 6. Symmetric Sums Methods 7. Infinitely Many Quadratics 8. Maximum Likelihood for Mixed Models 9. Mixed Models Having One Random Factor 10. Best Quadratic Unbiased Estimation 11. Exercises

Chapter 11: Variance Component Estimation from Unbalanced Data: Formulae

1. The 1-Way Classification 2. The 2-Way Nested Classification 3. The 3-Way Nested Classification 4. The 2-Way Classification with Interaction, Random Model 5. The 2-Way Classification with Interaction, Mixed Model 6. The 2-Way Classification without Interaction, Random Model 7. Mixed Models with One Random Factor 8. The 2-Way Classification without Interaction, Mixed Model 9. The 3-Way Classification, Random Model

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