Note: Supplemental materials are not guaranteed with Rental or Used book purchases.
Purchase Benefits
What is included with this book?
Preface | p. xv |
Author | p. xix |
Linear Models: Some Historical Perspectives | p. 1 |
The Invention of Least Squares | p. 3 |
The Gauss-Markov Theorem | p. 4 |
Estimability | p. 4 |
Maximum Likelihood Estimation | p. 5 |
Analysis of Variance | p. 6 |
Balanced and Unbalanced Data | p. 7 |
Quadratic Forms and Craig's Theorem | p. 8 |
The Role of Matrix Algebra | p. 9 |
The Geometric Approach | p. 10 |
Basic Elements of Linear Algebra | p. 13 |
Introduction | p. 13 |
Vector Spaces | p. 13 |
Vector Subspaces | p. 14 |
Bases and Dimensions of Vector Spaces | p. 16 |
Linear Transformations | p. 17 |
Exercises | p. 20 |
Basic Concepts in Matrix Algebra | p. 23 |
Introduction and Notation | p. 23 |
Notation | p. 24 |
Some Particular Types of Matrices | p. 24 |
Basic Matrix Operations | p. 25 |
Partitioned Matrices | p. 27 |
Determinants | p. 28 |
The Rank of a Matrix | p. 31 |
The Inverse of a Matrix | p. 33 |
Generalized Inverse of a Matrix | p. 34 |
Eigenvalues and Eigenvectors | p. 34 |
Idempotent and Orthogonal Matrices | p. 36 |
Parameterization of Orthogonal Matrices | p. 36 |
Quadratic Forms | p. 39 |
Decomposition Theorems | p. 40 |
Some Matrix Inequalities | p. 43 |
Function of Matrices | p. 46 |
Matrix Differentiation | p. 48 |
Exercises | p. 52 |
The Multivariate Normal Distribution | p. 59 |
History of the Normal Distribution | p. 59 |
The Univariate Normal Distribution | p. 60 |
The Multivariate Normal Distribution | p. 61 |
The Moment Generating Function | p. 63 |
The General Case | p. 63 |
The Case of the Multivariate Normal | p. 65 |
Conditional Distribution | p. 67 |
The Singular Multivariate Normal Distribution | p. 69 |
Related Distributions | p. 69 |
The Central Chi-Squared Distribution | p. 70 |
The Noncentral Chi-Squared Distribution | p. 70 |
The t-Distribution | p. 73 |
The F-Distribution | p. 74 |
The Wishart Distribution | p. 75 |
Examples and Additional Results | p. 75 |
Some Misconceptions about the Normal Distribution | p. 77 |
Characterization Results | p. 78 |
Exercises | p. 80 |
Quadratic Forms in Normal Variables | p. 89 |
The Moment Generating Function | p. 89 |
Distribution of Quadratic Forms | p. 94 |
Independence of Quadratic Forms | p. 103 |
Independence of Linear and Quadratic Forms | p. 108 |
Independence and Chi-Squaredness of Several Quadratic Forms | p. 111 |
Computing the Distribution of Quadratic Forms | p. 118 |
Distribution of a Ratio of Quadratic Forms | p. 119 |
Positive Definiteness of the Matrix Wt-1 in (5.2) | p. 120 |
A¿ is Idempotent if and Only If ¿1/2 A¿1/2is Idempotent | p. 121 |
Exercises | p. 121 |
Full-Rank Linear Models | p. 127 |
Least-Squares Estimation | p. 128 |
Estimation of the Mean Response | p. 130 |
Properties of Ordinary Least-Squares Estimation | p. 132 |
Distributional Properties | p. 132 |
Properties under the Normality Assumption | p. 133 |
The Gauss-Markov Theorem | p. 134 |
Generalized Least-Squares Estimation | p. 137 |
Least-Squares Estimation under Linear Restrictions on ß | p. 137 |
Maximum Likelihood Estimation | p. 140 |
Properties of Maximum Likelihood Estimators | p. 141 |
Inference Concerning ß | p. 146 |
Confidence Regions and "Confidence Intervals | p. 148 |
Simultaneous Confidence Intervals | p. 148 |
The Likelihood Ratio Approach to Hypothesis Testing | p. 149 |
Examples and Applications | p. 151 |
Confidence Region for the Location of the Optimum | p. 151 |
Confidence Interval on the True Optimum | p. 154 |
Confidence Interval for a Ratio | p. 157 |
Demonstrating the Gauss-Markov Theorem | p. 159 |
Comparison of Two Linear Models | p. 162 |
Exercises | p. 169 |
Less-Than-Full-Rank Linear Models | p. 179 |
Parameter Estimation | p. 179 |
Some Distributional Properties | p. 180 |
Reparameterized Model | p. 181 |
Estimable Linear Functions | p. 184 |
Properties of Estimable Functions | p. 185 |
Testable Hypotheses | p. 187 |
Simultaneous Confidence Intervals on Estimable Linear Functions | p. 192 |
The Relationship between Scheffé's Simultaneous Confidence Intervals and the F-Test Concerning H0 : Aß = 0 | p. 194 |
Determination of an Influential Set of Estimable Linear Functions | p. 196 |
Bonferroni's Intervals | p. 199 |
¿idák's Intervals | p. 200 |
Simultaneous Confidence Intervals on All Contrasts among the Means with Heterogeneous Group Variances | p. 202 |
The Brown-Forsythe Intervals | p. 202 |
Spjøtvoll's Intervals | p. 203 |
The Special Case of Contrasts | p. 205 |
Exact Conservative Intervals | p. 206 |
Further Results Concerning Contrasts and Estimable Linear Functions | p. 209 |
A Geometrical Representation of Contrasts | p. 209 |
Simultaneous Confidence Intervals for Two Estimable Linear Functions and their Ratio | p. 213 |
Simultaneous Confidence Intervals Based on Scheffé's Method | p. 213 |
Simultaneous Confidence Intervals Based on the Bonferroni Inequality | p. 214 |
Conservative Simultaneous Confidence Intervals | p. 214 |
Exercises | p. 216 |
Balanced Linear Models | p. 225 |
Notation and Definitions | p. 225 |
The General Balanced Linear Model | p. 229 |
Properties of Balanced Models | p. 232 |
Balanced Mixed Models | p. 237 |
Distribution of Sums of Squares | p. 238 |
Estimation of Fixed Effects | p. 240 |
Complete and Sufficient Statistics | p. 249 |
ANOVA Estimation of Variance Components | p. 254 |
The Probability of a Negative ANOVA Estimator | p. 254 |
Confidence Intervals on Continuous Functions of the Variance Components | p. 257 |
Confidence Intervals on Linear Functions of the Variance Components | p. 259 |
Confidence Intervals on Ratios of Variance Components | p. 263 |
Exercises | p. 266 |
The Adequacy of Satterthwaite's Approximation | p. 271 |
Satterthwaite's Approximation | p. 271 |
A Special Case: The Behrens-Fisher Problem | p. 274 |
Adequacy of Satterthwaite's Approximation | p. 278 |
Testing Departure from Condition (9.35) | p. 282 |
Measuring the Closeness of Satterthwaite's Approximation | p. 287 |
Determination of ¿sup | p. 290 |
Examples | p. 290 |
The Behrens-Fisher Problem | p. 291 |
A Confidence Interval on the Total Variation | p. 293 |
A Linear Combination of Mean Squares | p. 296 |
Determination of the Matrix G in Section 9.2.1 | p. 297 |
Exercises | p. 297 |
Unbalanced Fixed-Effects Models | p. 301 |
The R-Notation | p. 301 |
Two-Way Models without Interaction | p. 304 |
Estimable Linear Functions for Model (10.10) | p. 305 |
Testable Hypotheses for Model (10.10) | p. 306 |
Type I Testable Hypotheses | p. 309 |
Type II Testable Hypotheses | p. 310 |
Two-Way Models with Interaction | p. 314 |
Tests of Hypotheses | p. 315 |
Testing the Interaction Effect | p. 318 |
Type III Analysis in SAS | p. 322 |
Other Testable Hypotheses | p. 324 |
Higher-Order Models | p. 327 |
A Numerical Example | p. 331 |
The Method of Unweighted Means | p. 336 |
Distributions of SSAu, SSBu, and SSABu | p. 338 |
Approximate Distributions of SSAu, SSBu and SSABu | p. 340 |
Exercises | p. 342 |
Unbalanced Random and Mixed Models | p. 349 |
Estimation of Variance Components | p. 350 |
ANOVA Estimation-Henderson's Methods | p. 350 |
Henderson's Method III | p. 351 |
Maximum Likelihood Estimation | p. 357 |
Restricted Maximum Likelihood Estimation | p. 362 |
Properties of REML Estimators | p. 366 |
Estimation of Estimable Linear Functions | p. 369 |
Inference Concerning the Random One-Way Model | p. 373 |
Adequacy of the Approximation | p. 376 |
Confidence Intervals on ¿¿2 and ¿¿2/¿ϵ2 | p. 379 |
Inference Concerning the Random Two-Way Model | p. 380 |
Approximate Tests Based on the Method of Unweighted Means | p. 380 |
Adequacy of the Approximation | p. 384 |
Exact Tests | p. 385 |
Exact Test Concerning H0 : ¿¿ß = 0 | p. 386 |
Exact Tests Concerning ¿¿2 and ¿ß2 | p. 388 |
Exact Tests for Random Higher-Order Models | p. 397 |
Inference Concerning the Mixed Two-Way Model | p. 398 |
Exact Tests Concerning ¿ß2 and ¿¿ß2 | p. 398 |
An Exact Test for the Fixed Effects | p. 401 |
Inference Concerning the Random Two-Fold Nested Model | p. 406 |
An Exact Test Concerning ¿ß2 | p. 407 |
Inference Concerning the Mixed Two-Fold Nested Model | p. 411 |
An Exact Test Concerning ¿ß(¿)2 | p. 411 |
An Exact Test for the Fixed Effects | p. 412 |
Inference Concerning the General Mixed Linear Model | p. 415 |
Estimation and Testing of Fixed Effects | p. 416 |
Tests Concerning the Random Effects | p. 417 |
Appendix 11.A | p. 421 |
Appendix 11.B | p. 422 |
Exercises | p. 422 |
Additional Topics in Linear Models | p. 427 |
Heteroscedastic Linear Models | p. 427 |
The Random One-Way Model with Heterogeneous Error Variances | p. 428 |
An Approximate Test Concerning H0 : &sigma¿2 = 0 | p. 430 |
Point and Interval Estimation of &sigma¿2 | p. 433 |
Detecting Heterogeneity in Error Variances | p. 435 |
A Mixed Two-Fold Nested Model with Heteroscedastic Random Effects | p. 437 |
Tests Concerning the Fixed Effects | p. 438 |
Tests Concerning the Random Effects | p. 441 |
Response Surface Models | p. 443 |
Response Surface Models with Random Block Effects | p. 446 |
Analysis Concerning the Fixed Effects | p. 448 |
Analysis Concerning the Random Effects | p. 449 |
Linear Multiresponse Models | p. 453 |
Parameter Estimation | p. 454 |
Hypothesis Testing | p. 456 |
Hypothesis of Concurrence | p. 457 |
Hypothesis of Parallelism | p. 458 |
Testing for Lack of Fit | p. 459 |
Responses Contributing to LOF | p. 462 |
Exercises | p. 467 |
Generalized Linear Models | p. 473 |
Introduction | p. 473 |
The Exponential Family | p. 474 |
Likelihood Function | p. 478 |
Estimation of Parameters | p. 479 |
Estimation of the Mean Response | p. 483 |
Asymptotic Distribution of ß | p. 484 |
Computation of ß in SAS | p. 485 |
Goodness of Fit | p. 487 |
The Deviance | p. 487 |
Pearson's Chi-Square Statistic | p. 490 |
Residuals | p. 491 |
Hypothesis Testing | p. 497 |
Wald Inference | p. 497 |
Likelihood Ratio Inference | p. 498 |
Confidence Intervals | p. 499 |
Wald's Confidence Intervals | p. 499 |
Likelihood Ratio-Based Confidence Intervals | p. 500 |
Gamma-Distributed Response | p. 504 |
Deviance for the Gamma Distribution | p. 506 |
Variance-Covariance Matrix of ß | p. 506 |
Exercises | p. 509 |
Bibliography | p. 515 |
Index | p. 535 |
Table of Contents provided by Ingram. All Rights Reserved. |
The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.