Ronald R. Hocking

Methods and Applications of Linear Models, Third Edition

• Gebundenes Buch

Produktbeschreibung

The new edition of this "essential desktop reference book . . . [that] should definitely be on your bookshelf" (Technometrics) features a newly reorganized approach to linear regression that promotes the understanding of theory and models concurrently, featuring newly-developed topics in the field and the use of software applications. It includes numerous exercises; graphics and computations developed using JMP software; a new chapter on recent developments with the distribution of linear and quadratic forms; and new topical coverage of least squares, the cell means model, and more.

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Praise for the Second Edition
"An essential desktop reference book . . . it should definitely be on your bookshelf." - Technometrics

A thoroughly updated book, Methods and Applications of Linear Models: Regression and the Analysis of Variance, Third Edition features innovative approaches to understanding and working with models and theory of linear regression. The Third Edition provides readers with the necessary theoretical concepts, which are presented using intuitive ideas rather than complicated proofs, to describe the inference that is appropriate for the methods being discussed.

The book presents a unique discussion that combines coverage of mathematical theory of linear models with analysis of variance models, providing readers with a comprehensive understanding of both the theoretical and technical aspects of linear models. With a new focus on fixed effects models, Methods and Applications of Linear Models: Regression and the Analysis of Variance, Third Edition also features:

Newly added topics including least squares, the cell means model, and graphical inspection of data in the AVE method
Frequent conceptual and numerical examples for clarifying the statistical analyses and demonstrating potential pitfalls
Graphics and computations developed using JMP® software to accompany the concepts and techniques presented
Numerous exercises presented to test readers and deepen their understanding of the material
An ideal book for courses on linear models and linear regression at the undergraduate and graduate levels, the Third Edition of Methods and Applications of Linear Models: Regression and the Analysis of Variance is also a valuable reference for applied statisticians and researchers who utilize linear model methodology.

Produktdetails

• Wiley Series in Probability and Statistics
• Verlag: Wiley & Sons
• 3. Aufl.
• Seitenzahl: 718
• Erscheinungstermin: 19. Juli 2013
• Englisch
• Abmessung: 240mm x 161mm x 43mm
• Gewicht: 666g
• ISBN-13: 9781118329504
• ISBN-10: 1118329503
• Artikelnr.: 38130313

Autorenporträt

RONALD R. HOCKING, PhD, is Professor Emeritus in the Department of Statistics and Founder of the Ronald R. Hocking Lecture Series at Texas A&M University. A Fellow of the American Statistical Association, Dr. Hocking is the recipient of numerous honors in the statistical community including the Shewell Award, the Youden Award, the Wilcoxon Award, the Snedecor Award, and the Owen Award.

Inhaltsangabe

Preface to the Third Edition xvii Preface to the Second Edition xix Preface to the First Edition xxi PART I REGRESSION 1 1 Introduction to Linear Models 3 1.1 Background Information
3 1.2 Mathematical and Statistical Models
5 1.3 Definition of the Linear Model
8 1.4 Examples of Regression Models
13 1.5 Concluding Comments
21 Exercises
21 2 Regression on Functions of One Variable 23 2.1 The Simple Linear Regression Model
23 2.2 Parameter Estimation
25 2.3 Properties of the Estimators and Test Statistics
34 2.4 The Analysis of Simple Linear Regression Models
39 2.5 Examining the Data and the Model
50 2.6 Polynomial Regression Models
63 Exercises
72 3 Transforming the Data 81 3.1 The Need for Transformations
81 3.2 Weighted Least Squares
82 3.3 Variance Stabilizing Transformations
85 3.4 Transformations to Achieve a Linear Model
86 3.5 Analysis of the Transformed Model
92 Exercises
95 4 Regression on Functions of Several Variables 99 4.1 The Multiple Linear Regression Model
99 4.2 Preliminary Data Analysis
100 4.3 Analysis of the Multiple Linear Regression Model
103 4.4 Partial Correlation and Added-Variable Plots
113 4.5 Variable Selection
119 4.6 Model Specification
130 Exercises
137 5 Collinearity in Multiple Linear Regression 142 5.1 The Collinearity Problem
142 5.2 An Example with Collinearity
150 5.3 Collinearity Diagnostics
156 5.4 Remedial Solutions: Biased Estimators
166 Exercises
178 6 Influential Observations in Multiple Linear Regression 182 6.1 The Influential Data Problem
182 6.2 The Hat Matrix
183 6.3 The Effects of Deleting Observations
188 6.4 Numerical Measures of Influence
192 6.5 The Dilemma Data
197 6.6 Plots for Identifying Unusual Cases
201 6.7 Robust/Resistant Methods in Regression Analysis
209 Exercises
213 7 Polynomial Models and Qualitative Predictors 216 7.1 Polynomial Models
216 7.2 The Analysis of Response Surfaces
220 7.3 Models with Qualitative Predictors
225 Exercises
247 8 Additional Topics 254 8.1 Nonlinear Regression Models
254 8.2 Nonparametric Model-Fitting Methods
260 8.3 Generalized Linear Models
265 8.4 Random Input Variables
274 8.5 Errors in the Inputs
276 8.6 Calibration
277 Exercises
278 PART II THE ANALYSIS OF VARIANCE 283 9 Classification Models I: Introduction 285 9.1 Background Information
285 9.2 The One-Way Classification Model
286 9.3 The Two-Way Classification Model: Balanced Data
304 9.4 The Two-Way Classification Model: Unbalanced Data
322 9.5 The Two-Way Classification Model: No Interaction
334 9.6 Concluding Comments
347 Exercises
347 10 The Mathematical Theory of Linear Models 359 10.1 The Distribution of Linear and Quadratic Forms
359 10.2 Estimation and Inference for Linear Models
368 10.3 Tests of Linear Hypotheses on ß
380 10.4 Confidence Regions and Intervals
392 Exercises
395 11 Classification Models II: Multiple Crossed and Nested Factors 405 11.1 The Three-Factor Cross-Classified Model
406 11.2 A General Structure for Balanced
Factorial Models
412 11.3 The Twofold Nested Model
417 11.4 A General Structure for Balanced
Nested Models
426 11.5 A Three-Factor
Nested-Factorial Model
429 11.6 A General Structure for Balanced
Nested-Factorial Models
434 Exercises
438 12 Mixed Models I: The AOV Method with Balanced Data 443 12.1 Introduction
443 12.2 Examples of the Analysis of Mixed Models
444 12.3 The General Analysis for Balanced
Mixed Models
464 12.4 Additional Examples
479 12.5 Alternative Developments of Mixed Models
487 Exercises
493 13 Mixed Models II: The AVE Method with Balanced Data 499 13.1 Introduction
499 13.2 The Two-Way Cross-Classification Model
500 13.3 The Three-Factor
Cross-Classification Model
511 13.4 Nested Models
515 13.5 Nested-Factorial Models
518 13.6 A General Description of the AVE Table
524 13.7 Additional Examples
531 13.8 The Computational Procedure for the AVE Method
537 Exercises
537 14 Mixed Models III: Unbalanced Data 543 14.1 Introduction
543 14.2 Parameter Estimation: Likelihood Methods
545 14.3 ML and REML Estimates with Balanced Data
554 14.4 The EM Algorithm for REML Estimation
558 14.5 Diagnostic Analysis with the EM Algorithm
572 14.6 Models with Covariates
581 14.7 Summary
585 Exercises
585 15 Simultaneous Inference: Tests and Confidence Intervals 591 15.1 Simultaneous Tests
591 15.2 Simultaneous Confidence Intervals
610 Exercises
612 Appendix A Mathematics 615 A.I Matrix Algebra
615 A.I.1 Notation
615 A.I.2 The Rank of a Matrix
616 A.I.3 The Trace of a Matrix
617 A.I.4 Eigenvalues and Eigenvectors
617 A.I.5 Quadratic Forms and Definite Matrices
618 A.I.6 Special Matrices
619 A.I.7 The Diagonalization of Matrices
620 A.I.8 Kronecker Products of Matrices
620 A.I.9 Factorization of Matrices
621 A.I.10 Matrix Inversion
622 A.I.11 The Solution of Linear Equations
624 A.I.12 Generalized Inverses
627 A.I.13 Cauchy-Schwartz Inequalities
630 A.II Optimization
630 A.II.1 The Differentiation of Matrices and Determinants
630 A.II.2 The Differentiation of a Function with Respect to a Vector
631 A.II.3 The Optimization of a Function
632 Appendix B Statistics 634 B.I Distributions
634 B.I.1 The Normal Distribution
634 B.I.2 The chi2-Distribution
637 B.I.3 The t-Distribution
638 B.I.4 The F-distribution
639 B.II The Distribution of Quadratic Forms
639 B.III Estimation
642 B.III.1 Maximum Likelihood Estimation
642 B.III.2 Constrained Maximum Likelihood Estimation
642 B.III.3 Complete
Sufficient Statistics
643 B.IV Tests of Hypotheses and Confidence Regions
643 B.IV.1 Tests of Hypotheses
643 B.IV.2 Confidence Intervals and Regions
644 Appendix C Data Tables 645 C.I Downloading Data Files from FTP Server
645 C.II Listing of Data Set Files
645 Appendix D Statistical Tables 660 References 669 Index 677