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Statistics - Statistical Theory and Methods | Plane Answers to Complex Questions - The Theory of Linear Models

Plane Answers to Complex Questions

The Theory of Linear Models

Christensen, Ronald

4th ed. 2011, XXII, 494 p.

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  • Updated version of a classic textbook in Statistics
  • Focus on Fisherian inference, rather than the previous blend of Fisherian and Neyman–Pearson inference
  • Illustrates the practical application of the projective approach to linear models

This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The author's emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate-level course. All of the standard topics are covered in depth: ANOVA, estimation including Bayesian estimation, hypothesis testing, multiple comparisons, regression analysis, and experimental design models. In addition, the book covers topics that are not usually treated at this level, but which are important in their own right: balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, variance component estimation, best linear and best linear unbiased prediction, collinearity, and variable selection. This new edition includes a more extensive discussion of best prediction and associated ideas of R2, as well as new sections on inner products and perpendicular projections for more general spaces and Milliken and Graybill’s generalization of Tukey’s one degree of freedom for nonadditivity test.

Content Level » Research

Keywords » data analysis - linear model theory - linear models - textbook

Related subjects » Statistical Theory and Methods

Table of contents / Preface / Sample pages 

Introduction.- Estimation.- Testing.- One-Way ANOVA.- Multiple Comparison Techniques.- Regression Analysis.- Multifactor Analysis of Variance.- Experimental Design Models.- Analysis of Covariance.- General Gauss-Markov Models.- Split Plot Models.- Mixed Models and Variance Components.- Model Diagnostics.- Variable Selection.- Collinearity and Alternative Estimates.-

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