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Mathematics - Applications | Plane Answers to Complex Questions - The Theory of Linear Models

Plane Answers to Complex Questions

The Theory of Linear Models

Christensen, Ronald

2nd ed. 1996, XVII, 453 p.

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The second edition of Plane Answers has many additions and a couple of deletions. New material includes additional illustrative examples in Ap­ pendices A and B and Chapters 2 and 3, as well as discussions of Bayesian estimation, near replicate lack of fit tests, testing the independence assump­ tion, testing variance components, the interblock analysis for balanced in­ complete block designs, nonestimable constraints, analysis of unreplicated experiments using normal plots, tensors, and properties of Kronecker prod­ ucts and Vee operators. The book contains an improved discussion of the relation between ANOVA and regression, and an improved presentation of general Gauss-Markov models. The primary material that has been deleted are the discussions of weighted means and of log-linear models. The mate­ rial on log-linear models was included in Christensen (1990b), so it became redundant here. Generally, I have tried to clean up the presentation of ideas wherever it seemed obscure to me. Much of the work on the second edition was done while on sabbatical at the University of Canterbury in Christchurch, New Zealand. I would par­ ticularly like to thank John Deely for arranging my sabbatical. Through their comments and criticisms, four people were particularly helpful in con­ structing this new edition. I would like to thank Wes Johnson, Snehalata Huzurbazar, Ron Butler, and Vance Berger.

Content Level » Lower undergraduate

Keywords » ANOVA - Regression analysis - analysis of variance - data analysis - linear model theory - linear models - textbook

Related subjects » Applications - Statistical Theory and Methods

Table of contents 

1 Introduction.- 2 Estimation.- 3 Testing Hypotheses.- 4 One-Way ANOVA.- 5 Multiple Comparison Techniques.- 6 Regression Analysis.- 7 Multifactor Analysis of Variance.- 8 Experimental Design Models.- 9 Analysis of Covariance.- 10 Estimation and Testing in General Gauss—Markov Models.- 11 Split Plot Models.- 12 Mixed Models and Variance Components.- 13 Checking Assumptions, Residuals, and Influential Observations.- 14 Variable Selection and Collinearity.- Appendix A: Vector Spaces.- Appendix B: Matrix Results.- B.1 Basic Ideas.- B.2 Eigenvalues and Related Results.- B.3 Projections.- B.4 Miscellaneous Results.- B.5 Properties of Kronecker Products and Vec Operators.- B.6 Tensors.- Appendix C: Some Univariate Distributions.- Appendix D: Multivariate Distributions.- Appendix E: Tests and Confidence Intervals.- E.1 Confidence Intervals.- E.2 Hypothesis Testing.- Appendix F: Equivalent Linear Models.- F.1 Constrained and Unconstrained Models.- F.2 Estimable and Nonestimable Constraints.- Appendix G: Randomization Theory Models.- G.1 Simple Random Sampling.- G.2 Completely Randomized Designs.- G.3 Randomized Complete Block Designs.- References.- Author Index.

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