# Plane Answers to Complex Questions

## The Theory of Linear Models

• Ronald Christensen
Book

Part of the Springer Texts in Statistics book series (STS)

1. Front Matter
Pages i-xix
2. Ronald Christensen
Pages 1-17
3. Ronald Christensen
Pages 18-49
4. Ronald Christensen
Pages 50-90
5. Ronald Christensen
Pages 91-105
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Pages 106-121
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Pages 122-155
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Pages 156-195
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Pages 279-319
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15. Ronald Christensen
Pages 369-390
16. Back Matter
Pages 391-476

### Introduction

The third edition of Plane Answers includes fundamental changes in how some aspects of the theory are handled. Chapter 1 includes a new section that introduces generalized linear models. Primarily, this provides a defini­ tion so as to allow comments on how aspects of linear model theory extend to generalized linear models. For years I have been unhappy with the concept of estimability. Just because you cannot get a linear unbiased estimate of something does not mean you cannot estimate it. For example, it is obvious how to estimate the ratio of two contrasts in an ANOVA, just estimate each one and take their ratio. The real issue is that if the model matrix X is not of full rank, the parameters are not identifiable. Section 2.1 now introduces the concept of identifiability and treats estimability as a special case of identifiability. This change also resulted in some minor changes in Section 2.2. In the second edition, Appendix F presented an alternative approach to dealing with linear parametric constraints. In this edition I have used the new approach in Section 3.3. I think that both the new approach and the old approach have virtues, so I have left a fair amount of the old approach intact. Chapter 8 contains a new section with a theoretical discussion of models for factorial treatment structures and the introduction of special models for homologous factors. This is closely related to the changes in Section 3.3.

### Keywords

ANOVA Analysis Analysis of variance Factor analysis Regression analysis best fit mathematical statistics

#### Authors and affiliations

• Ronald Christensen
• 1
1. 1.Department of Mathematics and StatisticsUniversity of New MexicoAlbuquerqueUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-0-387-21544-0
• Copyright Information Springer-Verlag New York 2002
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4419-2971-6
• Online ISBN 978-0-387-21544-0
• Series Print ISSN 1431-875X