Fitting Linear Models

1. Preliminaries.- 1.1 Introduction.- 1.2 Notation Used in This Thesis.- 2. The Linear Model.- 2.1 The Gaussian Linear Model.- 2.2 Specifying an Arbitrary Model.- 2.3 Effective Balance.- 2.4 The Generalized Linear Model.- 3. The Conjugate Gradient Algorithm.- 3.1 Minimization Concepts.- 3.2 The Basic Algorithm.- 3.3 Convergence Considerations.- 3.4 The Non-Full Rank Case.- 3.5 Computational Details.- 3.6 Preconditioning.- 4. Applications: The Non-Full Rank Case.- 4.1 A Direct Sum Decomposition.- 4.2 Enumeration of Eigenvalues.- 4.3 Complete Factorial Designs.- 4.4 Other Designs.- 4.5 Preconditioning.- 5. Applications: The Full Rank Case.- 5.1 A Full Rank Parameterization.- 5.2 Hierarchical Models.- 5.3 Eigenvalues for Complete Factorial Designs.- 5.4 Other Designs.- 5.5 Preconditioning.- 6. Examples: Gaussian Linear Models.- 6.1 Implementation Details.- 6.2 The General 3-Way Case.- 6.3 A Blocked 23 Experiment.- 6.4 A Fractional 34 Experiment.- 6.5 A Quasi Latin Square Example.- 6.6 A Balanced Incomplete Block Example.- 7. Examples: Generalized Linear Models.- 7.1 Implementation Details.- 7.2 A 3x24 Loglinear Model.- 7.3 22 Loglinear Model on a Latin Square.- 7.4 A 3x22 Binomial Example.- 7.5 A Combined Loglinear and Binomial Example.- 8. Concluding Remarks.- References.- Appendices.- A. Algorithms.- A.I Hestenes-Stiefel Algorithm.- A.2 Beale Algorithm.- A.3 Preconditioned Hestenes-Stiefel Algorithm.- A.4 Hemmerle’s Algorithm with Line Search;.- A.5 Hestenes-Stiefel Algorithm with Hemmerle’s Preconditioning.- A.6 Eigenvalues, Non-Full Rank Parameterization.- A.7 Eigenvalues, Full Rank Parameterization.- B. GLIM Output.