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Plane Answers plex
Questions:
The Theory of Linear Models
Ronald Christensen
Department of Mathematics and Statistics
University of New Mexico
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To Dad, Mom, Sharon, Fletch, and Don
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Preface to the Third Edition
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 ments 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 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 .
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 . 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 .
In Chapter 9, reliance on the normal equations has been eliminated from
the discussion of estimation in ACOVA models — something I should have
done years ago! In the previous editions, Exercise has indicated that
Section should be don