Plane Answers to Complex Questions: The Theory of Linear Models

ISBN-13: 9781461428855 / Angielski / Miękka / 2013 / 494 str.

Ronald Christensen

Opis

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.

Recenzje

From the reviews of the fourth edition:

"Researchers and students interested in linear statistical models. ... I admire Christensen's very personal and somehow easy-going writing style. ... All in all, Christensen's fourth edition is an excellent course and reference book ... ." (Simo Puntanen, International Statistical Review, Vol. 79 (3), 2011)

Spis treści

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.-

O autorze

Ronald Christensen is Professor of Statistics at the University of New Mexico, Fellow of the American Statistical Association (ASA) and the Institute of Mathematical Statistics, and former Chair of the ASA Section on Bayesian Statistical Science.