Plane Answers to Complex Questions: The Theory of Linear Models

This textbook provides a comprehensive introduction to linear models for analyzing data, covering estimation, significance testing, ANOVA, multiple comparisons, regression analysis, and experimental design. It also covers topics such as best linear and best linear unbiased prediction, split plot models, balanced incomplete block designs, testing for lack of fit, independence, models with singular covariance matrices, diagnostics, collinearity, and variable selection. The new edition includes new sections on alternatives to least squares estimation, expanded discussion of variable selection, and more.

Format: Paperback / softback
Length: 529 pages
Publication date: 26 August 2021
Publisher: Springer Nature Switzerland AG

This comprehensive textbook offers a thorough exploration of the application and theoretical foundations of linear models for data analysis. The author's primary focus lies in presenting a unified treatment of linear models, encompassing analysis of variance (ANOVA) models and regression models, rooted in projections, orthogonality, and other vector space concepts. Each chapter is accompanied by an abundance of exercises and illustrative examples, making it an ideal resource for advanced-level courses. The book comprehensively covers all the standard topics, delving into detailed explanations of estimation techniques such as biased and Bayesian estimation, significance testing, ANOVA, multiple comparisons, regression analysis, and experimental design models. Furthermore, it addresses topics that often receive less attention but are nonetheless crucial in their own right. These include best linear and best linear unbiased prediction, split plot models, balanced incomplete block designs, testing for lack of fit, testing for independence, models with singular covariance matrices, diagnostics, collinearity, and variable selection.

In this updated edition, several new sections have been added to provide further insights. These include discussions on alternatives to least squares estimation and the variance-bias tradeoff, expanded discussions on variable selection, new material on characterizing the interaction space in an unbalanced two-way ANOVA, Freedman's critique of the sandwich estimator, and numerous other valuable additions.

By presenting a comprehensive and up-to-date treatment of linear models, this textbook serves as a valuable resource for students, researchers, and practitioners in the fields of statistics, economics, and other applied disciplines. Its clear explanations, extensive examples, and practical applications make it an essential tool for anyone seeking to understand and apply linear models in data analysis.

Weight: 836g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030320997
Edition number: 5th ed. 2020