Linear Model Methodology

Linear Models: Some Historical Perspectives The Invention of Least Squares The Gauss-Markov Theorem Estimability Maximum Likelihood Estimation Analysis of Variance (ANOVA) Quadratic Forms and Craig's Theorem The Role of Matrix Algebra The Geometric Approach Basic Elements of Linear Algebra Introduction Vector Spaces Vector Subspaces Bases and Dimensions of Vector Spaces Linear Transformations Basic Concepts in Matrix Algebra Introduction and Notation Some Particular Types of Matrices Basic Matrix Operations Partitioned Matrices Determinants The Rank of a Matrix The Inverse of a Matrix Eigenvalues and Eigenvectors Idempotent and Orthogonal Matrices Quadratic Forms Decomposition Theorems Some Matrix Inequalities Function of Matrices Matrix Differentiation The Multivariate Normal Distribution History of the Normal Distribution The Univariate Normal Distribution The Multivariate Normal Distribution The Moment Generating Function Conditional Distribution The Singular Multivariate Normal Distribution Related Distributions Examples and Additional Results Quadratic Forms in Normal Variables The Moment Generating Function Distribution of Quadratic Forms Independence of Quadratic Forms Independence of Linear and Quadratic Forms Independence and Chi-Squaredness of Several Quadratic Forms Computing the Distribution of Quadratic Forms Appendix Full-Rank Linear Models Least-Squares Estimation Properties of Ordinary Least-Squares Estimation Generalized Least-Squares Estimation Least-Squares Estimation under Linear Restrictions on ss Maximum Likelihood Estimation Inference Concerning ss Examples and Applications Less-Than-Full-Rank Linear Models Parameter Estimation Some Distributional Properties Reparameterized Model Estimable Linear Functions Simultaneous Confidence Intervals on Estimable Linear Functions Simultaneous Confidence Intervals on All Contrasts among the Means with Heterogeneous Group Variances Further Results Concerning Contrasts and Estimable Linear Functions Balanced Linear Models Notation and Definitions The General Balanced Linear Model Properties of Balanced Models Balanced Mixed Models Complete and Sufficient Statistics ANOVA Estimation of Variance Components Confidence Intervals on Continuous Functions of the Variance Components Confidence Intervals on Ratios of Variance Components The Adequacy of Satterthwaite's Approximation Satterthwaite's Approximation Adequacy of Satterthwaite's Approximation Measuring the Closeness of Satterthwaite's Approximation Examples Appendix Unbalanced Fixed-Effects Models The R-Notation Two-Way Models without Interaction Two-Way Models with Interaction Higher-Order Models A Numerical Example The Method of Unweighted Means Unbalanced Random and Mixed Models Estimation of Variance Components Estimation of Estimable Linear Functions Inference Concerning the Random One-Way Model Inference Concerning the Random Two-Way Model Exact Tests for Random Higher-Order Models Inference Concerning the Mixed Two-Way Model Inference Concerning the Random Two-Fold Nested Model Inference Concerning the Mixed Two-Fold Nested Model Inference Concerning the General Mixed Linear Model Appendix Additional Topics in Linear Models Heteroscedastic Linear Models The Random One-Way Model with Heterogeneous Error Variances A Mixed Two-Fold Nested Model with Heteroscedastic Random Effects Response Surface Models Response Surface Models with Random Block Effects Linear Multiresponse Models Generalized Linear Models Introduction The Exponential Family Estimation of Parameters Goodness of Fit Hypothesis Testing Confidence Intervals Gamma-Distributed Response Bibliography Index Exercises appear at the end of each chapter, except for Chapter 1.