Author | Mclntosh, Allen. author |
---|---|
Title | Fitting Linear Models [electronic resource] : An Application of Conjugate Gradient Algorithms / by Allen Mclntosh |
Imprint | New York, NY : Springer New York, 1982 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5752-3 |
Descript | 200 p. online resource |
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 Hemmerleโs Algorithm with Line Search; -- A.5 Hestenes-Stiefel Algorithm with Hemmerleโs Preconditioning -- A.6 Eigenvalues, Non-Full Rank Parameterization -- A.7 Eigenvalues, Full Rank Parameterization -- B. GLIM Output