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| Preface | |
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| Examples of the General Linear Model | |
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| Introduction | |
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| One-Sample Problem | |
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| Simple Linear Regression | |
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| Multiple Regression | |
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| One-Way ANOVA | |
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| First Discussion | |
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| Two-Way Nested Model | |
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| Two-Way Crossed Model | |
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| Analysis of Covariance | |
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| Autoregression | |
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| Discussion | |
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| Summary | |
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| Notes | |
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| Exercises | |
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| The Linear Least Squares Problem | |
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| The Normal Equations | |
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| The Geometry of Least Squares | |
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| Reparameterization | |
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| Gram-Schmidt Orthonormalization | |
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| Summary of Important Results | |
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| Notes | |
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| Exercises | |
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| Estimability and Least Squares Estimators | |
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| Assumptions for the Linear Mean Model | |
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| Confounding, Identifiability, and Estimability | |
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| Estimability and Least Squares Estimators | |
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| First Example: One-Way ANOVA | |
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| Second Example: Two-Way Crossed without Interaction | |
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| Two-Way Crossed with Interaction | |
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| Reparameterization Revisited | |
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| Imposing Conditions for a Unique Solution to the Normal Equations | |
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| Constrained Parameter Space | |
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| Summary | |
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| Exercises | |
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| Gauss-Markov Model | |
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| Model Assumptions | |
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| The Gauss-Markov Theorem | |
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| Variance Estimation | |
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| Implications of Model Selection | |
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| Underfitting or Misspecification | |
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| Overfitting and Multicollinearity | |
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| The Aitken Model and Generalized Least Squares | |
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| Estimability | |
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| Linear Estimator | |
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| Generalized Least Squares Estimators | |
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| Estimation of �2 | |
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| Application: Aggregation Bias | |
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| Best Estimation in a Constrained Parameter Space | |
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| Summary | |
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| Notes | |
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| Exercises | |
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| Addendum: Variance of Variance Estimator | |
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| Distributional Theory | |
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| Introduction | |
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| Multivariate Normal Distribution | |
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| Chi-Square and Related Distributions | |
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| Distribution of Quadratic Forms | |
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| Cochran's Theorem | |
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| Regression Models with Joint Normality | |
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| Summary | |
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| Notes | |
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| Exercises | |
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| Statistical Inference | |
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| Introduction | |
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| Results from Statistical Theory | |
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| Testing the General Linear Hypothesis | |
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| The Likelihood Ratio Test and Change in SSE | |
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| First Principles Test and LRT | |
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| Confidence Intervals and Multiple Comparisons | |
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| Identifiability | |
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| Summary | |
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| Notes | |
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| Exercises | |
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| Further Topics in Testing | |
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| Introduction | |
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| Reparameterization | |
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| Applying Cochran's Theorem for Sequential SS | |
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| Orthogonal Polynomials and Contrasts | |
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| Pure Error and the Lack of Fit Test | |
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| Heresy: Testing Nontestable Hypotheses | |
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| Summary | |
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| Exercises | |
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| Variance Components and Mixed Models | |
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| Introduction | |
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| Variance Components: One Way | |
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| Variance Components: Two-Way Mixed ANOVA | |
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| Variance Components: General Case | |
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| Maximum Likelihood | |
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| Restricted Maximum Likelihood (REML) | |
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| The ANOVA Approach | |
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| The Split Plot | |
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| Predictions and BLUPs | |
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| Summary | |
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| Notes | |
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| Exercises | |
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| The Multivariate Linear Model | |
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| Introduction | |
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| The Multivariate Gauss-Markov Model | |
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| Inference under Normality Assumptions | |
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| Testing | |
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| First Principles Again | |
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| Likelihood Ratio Test and Wilks' Lambda | |
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| Other Test Statistics | |
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| Power of Tests | |
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| Repeated Measures | |
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| Confidence Intervals | |
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| Summary | |
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| Notes | |
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| Exercises | |
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| Review of Linear Algebra | |
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| Notation and Fundamentals | |
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| Rank, Column Space, and Nullspace | |
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| Some Useful Results | |
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| Solving Equations and Generalized Inverses | |
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| Projections and Idempotent Matrices | |
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| Trace, Determinants, and Eigenproblems | |
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| Definiteness and Factorizations | |
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| Notes | |
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| Exercises | |
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| Lagrange Multipliers | |
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| Main Results | |
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| Notes | |
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| Exercises | |
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| Bibliography | |
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| Index | |