Clarke, Brenton R.
Linear Models: The Theory and Application of Analysis of Variance
Linear Models explores the theory of linear models and the dynamic relationships that these models have with Analysis of Variance (ANOVA), experimental design, and random and mixedmodel effects. This oneofakind book emphasizes an approach that clearly explains the distribution theory of linear models and experimental design starting from basic mathematical concepts in linear algebra.
The author begins with a presentation of the classic fixedeffects linear model and goes on to illustrate eight common linear models, along with the value of their use in statistics. From this foundation, subsequent chapters introduce concepts pertaining to the linear model, starting with vector space theory and the theory of leastsquares estimation. An outline of the Helmert matrix is also presented, along with a thorough explanation of how the ANOVA is created in both typical twoway and higher layout designs, ultimately revealing the distribution theory. Other important topics covered include:

Vector space theory

The theory of least squares estimation

GaussMarkov theorem

Kronecker products

Diagnostic and robust methods for linear models

Likelihood approaches to estimation
A discussion of Bayesian theory is also included for purposes of comparison and contrast, and numerous illustrative exercises assist the reader with uncovering the nature of the models, using both classic and new data sets. Requiring only a working knowledge of basic probability and statistical inference, Linear Models is a valuable book for courses on linear models at the upperundergraduate and graduate levels. It is also an excellent reference for practitioners who use linear models to conduct research in the fields of econometrics, psychology, sociology, biology, and agriculture.
Keywords: ANOVA, linear regression, advanced statistics, experimental design, design of experiments, vector matrix, applied statistics
 Author(s)
 Clarke, Brenton R.
 Publisher
 John Wiley and Sons, Inc.
 Publication year
 2008
 Language
 en
 Edition
 1
 Series
 Wiley Series in Probability and Statistics
 Page amount
 288 pages
 Category
 Natural Sciences
 Format
 Ebook
 eISBN (PDF)
 9780470377970
 Printed ISBN
 9780470025666