The essential introduction to the theory and application of linear models—now in a valuable new editionSince most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed.Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression.
Frank Wood, [email protected] Linear Regression Models Lecture 11, Slide 20 Hat Matrix – Puts hat on Y. We can also directly express the fitted values in terms of only the X and Y matrices and we can further define H, the “hat matrix”. The hat matrix plans an important role in diagnostics for regression analysis. Write H on board. The book should also be a strong candidate for any M.S. Course in linear models because of the numerous exercises with solutions and clear writing style.' (Technometrics, Vol. 4, May 2001) 'Rencher's textbook is certainly of interest for students and instructors looking for a mathematical introduction to linear statistical models.'
Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Rencher, PhD, is Professor of Statistics at Brigham Young University. Rencher is a Fellow of the American Statistical Association and the author of Methods of Multivariate Analysis and Multivariate Statistical Inference and Applications, both published by Wiley.G. Bruce Schaalje, PhD, is Professor of Statistics at Brigham Young University.
He has authored over 120 journal articles in his areas of research interest, which include mixed linear models, small sample inference, and design of experiments. Matrix Algebra.3. Random Vectors and Matrices.4. Multivariate Normal Distribution.5.
Distribution of Quadratic Forms in y.6. Simple Linear Regression.7. Multiple Regression: Estimation.8. Multiple Regression: tests of Hypotheses and Confidence Intervals.9.
Multiple Regression: Model Validation and Diagnostics.10. Multiple Regression: random x's.11. Multiple Regression: Bayesian Inference.12.
Analysis-of-Variance Models.13. One-Way Analysis-of-Variance: balanced Case.14. Two-Way Analysis-of Variance: Balanced Case.15. Analysis-of-Variance: The Cell Means Model for Unbalanced Data.16.
Linear Mixed Models.18. Additional Models.Appendix A.
Answers and Hits to the Problems.References.Index.
Comments are closed.
|
AuthorWrite something about yourself. No need to be fancy, just an overview. Archives
March 2023
Categories |