Plane Answers to Complex Questions

The Theory of Linear Models
Fifth Auflage 2020
ISBN: 978-3-030-32096-6
Verlag: Springer International Publishing

Buch, Englisch, 529 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 986 g

Reihe: Springer Texts in Statistics

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: estimation including biased and Bayesian estimation, significance testing, ANOVA, 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: 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. This new edition includes new sections on alternatives to least squares estimation and the variance-bias tradeoff, expanded discussion of variable selection, new material on characterizing the interaction space in an unbalanced two-way ANOVA, Freedman's critique of the sandwich estimator, and much more.

Zielgruppe

Graduate

Autoren/Hrsg.

Christensen, Ronald

Fachgebiete

• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Sozialwissenschaften Soziologie | Soziale Arbeit Soziologie Allgemein Empirische Sozialforschung, Statistik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung

Inhaltsverzeichnis

1. Introduction.- 2. Estimation.- 3. Testing.- 4. One-Way ANOVA.- 5. Multiple Comparison Techniques.- 6. Regression Analysis.- 7. Multifactor Analysis of Variance.- 8. Experimental Design Models.- 9. Analysis of Covariance.- 10. General Gauss-Markov Models.- 11. Split Plot Models.- 12. Model Diagnostics.- 13. Collinearity and Alternative Estimates.- 14. Variable Selection.- Appendix A - 6.- References.- Index.- Author Index.

Über Autor(innen)

Ronald Christensen is a Professor of Statistics at the University of New Mexico, Fellow of the American Statistical Association (ASA) and the Institute of Mathematical Statistics, former Chair of the ASA Section on Bayesian Statistical Science and former Editor of The American Statistician. His book publications include Advanced Linear Modeling (Springer, new edition forthcoming), Log-Linear Models and Logistic Regression (Springer 1997), Analysis of Variance, Design, and Regression (1996, 2016), and Bayesian Ideas and Data Analysis (2010, with Johnson, Branscum and Hanson).