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. Language: English