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ALVIN C. RENCHER is Professor Emeritus in the Department of Statistics at Brigham Young University. A Fellow of the American Statistical Association, he is the author of Linear Models in Statistics, Second Edition and Multivariate Statistical Inference and Applications, both published by Wiley.
WILLIAM F. CHRISTENSEN is Professor in the Department of Statistics at Brigham Young University. He has been published extensively in his areas of research interest, which include multivariate analysis, resampling methods, and spatial and environmental statistics.
Preface | p. xvii |
Acknowledgments | p. xxi |
Introduction | p. 1 |
Why Multivariate Analysis? | p. 1 |
Prerequisites | p. 3 |
Objectives | p. 3 |
Basic Types of Data And Analysis | p. 4 |
Matrix Algebra | p. 7 |
Introduction | p. 7 |
Notation and Basic Definitions | p. 8 |
Operations | p. 11 |
Partitioned Matrices | p. 22 |
Rank | p. 23 |
Inverse | p. 25 |
Positive Definite Matrices | p. 26 |
Determinants | p. 28 |
Trace | p. 31 |
Orthogonal Vectors and Matrices | p. 31 |
Eigenvalues and Eigenvectors | p. 32 |
Kronecker and VEC Notation | p. 37 |
Problems | p. 39 |
Characterizing and Displaying Multivariate Data | p. 47 |
Mean and Variance of a Univariate Random Variable | p. 47 |
Covariance and Correlation Of Bivariate Random Variables | p. 49 |
Scatter Plots of Bivariate Samples | p. 55 |
Graphical Displays for Multivariate Samples | p. 56 |
Dynamic Graphics | p. 58 |
Mean Vectors | p. 63 |
Covariance Matrices | p. 66 |
Correlation Matrices | p. 69 |
Mean Vectors and Covariance Matrices for Subsets of Variables | p. 71 |
Two Subsets | p. 71 |
Three or More Subsets | p. 73 |
Linear Combinations of Variables | p. 75 |
Sample Properties | p. 75 |
Population Properties | p. 81 |
Measures of Overall Variability | p. 81 |
Estimation of Missing Values | p. 82 |
Distance Between Vectors | p. 84 |
Problems | p. 85 |
The Multivariate Normal Distribution | p. 91 |
Multivariate Normal Density Function | p. 91 |
Properties of Multivariate Normal Random Variables | p. 94 |
Estimation in the Multivariate Normal | p. 99 |
Assessing Multivariate Normality | p. 101 |
Transformations to Normality | p. 108 |
Outliers | p. 111 |
Problems | p. 117 |
Tests on One or Two Mean Vectors | p. 125 |
Multivariate Versus Univariate Tests | p. 125 |
Tests on µ With ??Known | p. 126 |
Tests on µ When ??is Unknown | p. 130 |
Comparing two Mean Vectors | p. 134 |
Tests on Individual Variables Conditional on Rejection of H0 by the T2-test | p. 139 |
Computation of T2 | p. 143 |
Paired Observations Test | p. 145 |
Test for Additional Information | p. 149 |
Profile Analysis | p. 152 |
Profile Analysis | p. 154 |
Problems | p. 161 |
Multivariate Analysis of Variance | p. 169 |
One-way Models | p. 169 |
Comparison of the Four Manova Test Statistics | p. 189 |
Contrasts | p. 191 |
Tests on Individual Variables Following Rejection of H0 by the Overall Manova Test | p. 195 |
Two-Way Classification | p. 198 |
Other Models | p. 207 |
Checking on the Assumptions | p. 210 |
Profile Analysis | p. 211 |
Repeated Measures Designs | p. 215 |
Growth Curves | p. 232 |
Tests on a Subvector | p. 241 |
Problems | p. 244 |
Tests on Covariance Matrices | p. 259 |
Introduction | p. 259 |
Testing a Specified Pattern for ∑ | p. 259 |
Tests Comparing Covariance Matrices | p. 265 |
Tests of Independence | p. 269 |
Problems | p. 276 |
Discriminant Analysis: Description of Group Separation | p. 281 |
Introduction | p. 281 |
The Discriminant Function for two Groups | p. 282 |
Relationship Between two-group Discriminant Analysis and Multiple Regression | p. 286 |
Discriminant Analysis for Several Groups | p. 288 |
Standardized Discriminant Functions | p. 292 |
Tests of Significance | p. 294 |
Interpretation of Discriminant Functions | p. 298 |
Scatter Plots | p. 301 |
Stepwise Selection of Variables | p. 303 |
Problems | p. 306 |
Classification Analysis: Allocation of Observations to Groups | p. 309 |
Introduction | p. 309 |
Classification into two Groups | p. 310 |
Classification into Several Groups | p. 314 |
Estimating Misclassification Rates | p. 318 |
Improved Estimates of Error Rates | p. 320 |
Subset Selection | p. 322 |
Nonparametric Procedures | p. 326 |
Problems | p. 336 |
Multivariate Regression | p. 339 |
Introduction | p. 339 |
Multiple Regression: Fixed X’s | p. 340 |
Multiple Regression: Random X’s | p. 354 |
Multivariate Multiple Regression: Estimation | p. 354 |
Multivariate Multiple Regression: Hypothesis Tests | p. 364 |
Multivariate Multiple Regression: Prediction | p. 370 |
Measures of Association Between the Y’s and the X’s | p. 372 |
Subset Selection | p. 374 |
Multivariate Regression: Random X’s | p. 380 |
Problems | p. 381 |
Canonical Correlation | p. 385 |
Introduction | p. 385 |
Canonical Correlations and Canonical Variates | p. 385 |
Properties of Canonical Correlations | p. 390 |
Tests of Significance | p. 391 |
Interpretation | p. 395 |
Relationships of Canonical Correlation Analysis to Other Multivariate Problems | p. 402 |
Principal Component Analysis | p. 405 |
Introduction | p. 405 |
Geometric and Algebraic Bases of Principal Components | p. 406 |
Principal Components and Perpendicular Regression | p. 412 |
Plotting of Principal Components | p. 414 |
Principal Components from the Correlation Matrix | p. 419 |
Deciding How Many Components to Retain | p. 423 |
Information in the Last Few Principal Components | p. 427 |
Interpretation of Principal Components | p. 427 |
Selection of Variables | p. 430 |
Problems | p. 432 |
Exploratory Factor Analysis | p. 435 |
Introduction | p. 435 |
Orthogonal Factor Model | p. 437 |
Estimation of Loadings and Communalities | p. 442 |
Choosing the Number of Factors, m | p. 453 |
Rotation | p. 457 |
Factor Scores | p. 466 |
Validity of the Factor Analysis Model | p. 470 |
Relationship of Factor Analysis to Principal Component Analysis | p. 475 |
Problems | p. 476 |
Confirmatory Factor Analysis | p. 479 |
Introduction | p. 479 |
Model Specification and Identification | p. 480 |
Parameter Estimation and Model Assessment | p. 487 |
Inference for Model Parameters | p. 492 |
Factor Scores | p. 495 |
Problems | p. 496 |
Cluster Analysis | p. 501 |
Introduction | p. 501 |
Measures of Similarity or Dissimilarity | p. 502 |
Hierarchical Clustering | p. 505 |
Nonhierarchical Methods | p. 531 |
Choosing the Number of Clusters | p. 544 |
Cluster Validity | p. 546 |
Clustering Variables | p. 547 |
Problems | p. 548 |
Graphical Procedures | p. 555 |
Multidimensional Scaling | p. 555 |
Correspondence Analysis | p. 565 |
Biplots | p. 580 |
Problems | p. 588 |
Tables | p. 597 |
Answers and Hints to Problems | p. 637 |
Data Sets and SAS Files | p. 727 |
References | p. 729 |
Index | p. 747 |
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