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Methods of multivariate analysis / Alvin C. Rencher, William F. Christensen, Department of Statistics, Brigham Young University, Provo, UT.

By: Rencher, Alvin C, 1934-.
Contributor(s): Christensen, William F, 1970-.
Material type: TextTextSeries: Wiley series in probability and statistics.Publisher: New Jersey: John Wiley & Sons, 2012Edition: 3rd ed.Description: xxv, 758 p. : ill. ; 25 cm.ISBN: 9780470178966 (hardback).Subject(s): Multivariate analysis | MATHEMATICS / Probability & Statistics / Multivariate AnalysisDDC classification: 519.535 Other classification: MAT029020 Online resources: WorldCat details | Ebook Fulltext
Contents:
Table of contents Preface xvii <p>Acknowledgments xxi <p>1 Introduction 1 <p>1.1 Why Multivariate Analysis? 1 <p>1.2 Prerequisites 3 <p>1.3 Objectives 3 <p>1.4 Basic Types of Data And Analysis 4 <p>2 Matrix Algebra 7 <p>2.1 Introduction 7 <p>2.2 Notation and Basic Definitions 8 <p>2.3 Operations 11 <p>2.4 Partitioned Matrices 22 <p>2.5 Rank 23 <p>2.6 Inverse 25 <p>2.7 Positive Definite Matrices 26 <p>2.8 Determinants 28 <p>2.9 Trace 31 <p>2.10 Orthogonal Vectors and Matrices 31 <p>2.11 Eigenvalues and Eigenvectors 32 <p>2.12 Kronecker and VEC Notation 37 <p>Problems 39 <p>3 Characterizing and Displaying Multivariate Data 47 <p>3.1 Mean and Variance of a Univariate Random Variable 47 <p>3.2 Covariance and Correlation Of Bivariate Random Variables49 <p>3.3 Scatter Plots of Bivariate Samples 55 <p>3.4 Graphical Displays for Multivariate Samples 56 <p>3.5 Dynamic Graphics 58 <p>3.6 Mean Vectors 63 <p>3.7 Covariance Matrices 66 <p>3.8 Correlation Matrices 69 <p>3.9 Mean Vectors and Covariance Matrices for Subsets ofVariables 71 <p>3.9.1 Two Subsets 71 <p>3.9.2 Three or More Subsets 73 <p>3.10 Linear Combinations of Variables 75 <p>3.10.1 Sample Properties 75 <p>3.10.2 Population Properties 81 <p>3.11 Measures of Overall Variability 81 <p>3.12 Estimation of Missing Values 82 <p>3.13 Distance Between Vectors 84 <p>Problems 85 <p>4 The Multivariate Normal Distribution 91 <p>4.1 Multivariate Normal Density Function 91 <p>4.2 Properties of Multivariate Normal Random Variables 94 <p>4.3 Estimation in the Multivariate Normal 99 <p>4.4 Assessing Multivariate Normality 101 <p>4.5 Transformations to Normality 108 <p>4.6 Outliers 111 <p>Problems 117 <p>5 Tests on One or Two Mean Vectors 125 <p>5.1 Multivariate Versus Univariate Tests 125 <p>5.2 Tests on ?? With ??Known 126 <p>5.3 Tests on ?? When ??is Unknown 130 <p>5.4 Comparing two Mean Vectors 134 <p>5.5 Tests on Individual Variables Conditional on Rejection of H0by the T2-test <p>139 <p>5.6 Computation of T2 143 <p>5.7 Paired Observations Test 145 <p>5.8 Test for Additional Information 149 <p>5.9 Profile Analysis 152 <p>Profile Analysis 154 <p>Problems 161 <p>6 Multivariate Analysis of Variance 169 <p>6.1 One-way Models 169 <p>6.2 Comparison of the Four Manova Test Statistics 189 <p>6.3 Contrasts 191 <p>6.4 Tests on Individual Variables Following Rejection of H0 bythe Overall Manova Test 195 <p>6.5 Two-Way Classification 198 <p>6.6 Other Models 207 <p>6.7 Checking on the Assumptions 210 <p>6.8 Profile Analysis 211 <p>6.9 Repeated Measures Designs 215 <p>6.10 Growth Curves 232 <p>6.11 Tests on a Subvector 241 <p>Problems 244 <p>7 Tests on Covariance Matrices 259 <p>7.1 Introduction 259 <p>7.2 Testing a Specified Pattern for 259 <p>7.3 Tests Comparing Covariance Matrices 265 <p>7.4 Tests of Independence 269 <p>Problems 276 <p>8 Discriminant Analysis: Description of Group Separation281 <p>8.1 Introduction 281 <p>8.2 The Discriminant Function for two Groups 282 <p>8.3 Relationship Between two-group Discriminant Analysis andMultiple Regression 286 <p>8.4 Discriminant Analysis for Several Groups 288 <p>8.5 Standardized Discriminant Functions 292 <p>8.6 Tests of Significance 294 <p>8.7 Interpretation of Discriminant Functions 298 <p>8.8 Scatter Plots 301 <p>8.9 Stepwise Selection of Variables 303 <p>Problems 306 <p>9 Classification Analysis: Allocation of Observations toGroups309 <p>9.1 Introduction 309 <p>9.2 Classification into two Groups 310 <p>9.3 Classification into Several Groups 314 <p>9.4 Estimating Misclassification Rates 318 <p>9.5 Improved Estimates of Error Rates 320 <p>9.6 Subset Selection 322 <p>9.7 Nonparametric Procedures 326 <p>Problems 336 <p>10 Multivariate Regression 339 <p>10.1 Introduction 339 <p>10.2 Multiple Regression: Fixed X s 340 <p>10.3 Multiple Regression: Random X s 354 <p>10.4 Multivariate Multiple Regression: Estimation 354 <p>10.5 Multivariate Multiple Regression: Hypothesis Tests 364 <p>10.6 Multivariate Multiple Regression: Prediction 370 <p>10.7 Measures of Association Between the Y s and theX s 372 <p>10.8 Subset Selection 374 <p>10.9 Multivariate Regression: Random X s 380 <p>Problems 381 <p>11 Canonical Correlation 385 <p>11.1 Introduction 385 <p>11.2 Canonical Correlations and Canonical Variates 385 <p>11.3 Properties of Canonical Correlations 390 <p>11.4 Tests of Significance 391 <p>11.5 Interpretation 395 <p>11.6 Relationships of Canonical Correlation Analysis to OtherMultivariate <p>Problems 402 <p>12 Principal Component Analysis 405 <p>12.1 Introduction 405 <p>12.2 Geometric and Algebraic Bases of Principal Components406 <p>12.3 Principal Components and Perpendicular Regression 412 <p>12.4 Plotting of Principal Components 414 <p>12.5 Principal Components from the Correlation Matrix 419 <p>12.6 Deciding How Many Components to Retain 423 <p>12.7 Information in the Last Few Principal Components 427 <p>12.8 Interpretation of Principal Components 427 <p>12.9 Selection of Variables 430 <p>Problems 432 <p>13 Exploratory Factor Analysis 435 <p>13.1 Introduction 435 <p>13.2 Orthogonal Factor Model 437 <p>13.3 Estimation of Loadings and Communalities 442 <p>13.4 Choosing the Number of Factors, m 453 <p>13.5 Rotation 457 <p>13.6 Factor Scores 466 <p>13.7 Validity of the Factor Analysis Model 470 <p>13.8 Relationship of Factor Analysis to Principal ComponentAnalysis 475 <p>Problems 476 <p>14 Confirmatory Factor Analysis 479 <p>14.1 Introduction 479 <p>14.2 Model Specification and Identification 480 <p>14.3 Parameter Estimation and Model Assessment 487 <p>14.4 Inference for Model Parameters 492 <p>14.5 Factor Scores 495 <p>Problems 496 <p>15 Cluster Analysis 501 <p>15.1 Introduction 501 <p>15.2 Measures of Similarity or Dissimilarity 502 <p>15.3 Hierarchical Clustering 505 <p>15.4 Nonhierarchical Methods 531 <p>15.5 Choosing the Number of Clusters 544 <p>15.6 Cluster Validity 546 <p>15.7 Clustering Variables 547 <p>Problems 548 <p>16 Graphical Procedures 555 <p>16.1 Multidimensional Scaling 555 <p>16.2 Correspondence Analysis 565 <p>16.3 Biplots 580 <p>Problems 588 <p>Appendix A: Tables 597 <p>Appendix B: Answers and Hints to Problems 637 <p>Appendix C: Data Sets and SAS Files 727 <p>References 729 <p>Index 747
Summary: "This new edition, now with a co-author, offers a complete and up-to-date examination of the field. The authors have streamlined previously tedious topics, such as multivariate regression and MANOVA techniques, to add newer, more timely content. Each chapter contains exercises, providing readers with the opportunity to test and extend their understanding. The new edition also presents several expanded topics in Kronecker product; prediction errors; maximum likelihood estimation; and selective key, but accessible proofs. This resource meets the needs of both statistics majors and those of students and professionals in other fields"--
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Includes bibliographical references (pages 728-744) and index.

Table of contents Preface xvii <p>Acknowledgments xxi <p>1 Introduction 1 <p>1.1 Why Multivariate Analysis? 1 <p>1.2 Prerequisites 3 <p>1.3 Objectives 3 <p>1.4 Basic Types of Data And Analysis 4 <p>2 Matrix Algebra 7 <p>2.1 Introduction 7 <p>2.2 Notation and Basic Definitions 8 <p>2.3 Operations 11 <p>2.4 Partitioned Matrices 22 <p>2.5 Rank 23 <p>2.6 Inverse 25 <p>2.7 Positive Definite Matrices 26 <p>2.8 Determinants 28 <p>2.9 Trace 31 <p>2.10 Orthogonal Vectors and Matrices 31 <p>2.11 Eigenvalues and Eigenvectors 32 <p>2.12 Kronecker and VEC Notation 37 <p>Problems 39 <p>3 Characterizing and Displaying Multivariate Data 47 <p>3.1 Mean and Variance of a Univariate Random Variable 47 <p>3.2 Covariance and Correlation Of Bivariate Random Variables49 <p>3.3 Scatter Plots of Bivariate Samples 55 <p>3.4 Graphical Displays for Multivariate Samples 56 <p>3.5 Dynamic Graphics 58 <p>3.6 Mean Vectors 63 <p>3.7 Covariance Matrices 66 <p>3.8 Correlation Matrices 69 <p>3.9 Mean Vectors and Covariance Matrices for Subsets ofVariables 71 <p>3.9.1 Two Subsets 71 <p>3.9.2 Three or More Subsets 73 <p>3.10 Linear Combinations of Variables 75 <p>3.10.1 Sample Properties 75 <p>3.10.2 Population Properties 81 <p>3.11 Measures of Overall Variability 81 <p>3.12 Estimation of Missing Values 82 <p>3.13 Distance Between Vectors 84 <p>Problems 85 <p>4 The Multivariate Normal Distribution 91 <p>4.1 Multivariate Normal Density Function 91 <p>4.2 Properties of Multivariate Normal Random Variables 94 <p>4.3 Estimation in the Multivariate Normal 99 <p>4.4 Assessing Multivariate Normality 101 <p>4.5 Transformations to Normality 108 <p>4.6 Outliers 111 <p>Problems 117 <p>5 Tests on One or Two Mean Vectors 125 <p>5.1 Multivariate Versus Univariate Tests 125 <p>5.2 Tests on ?? With ??Known 126 <p>5.3 Tests on ?? When ??is Unknown 130 <p>5.4 Comparing two Mean Vectors 134 <p>5.5 Tests on Individual Variables Conditional on Rejection of H0by the T2-test <p>139 <p>5.6 Computation of T2 143 <p>5.7 Paired Observations Test 145 <p>5.8 Test for Additional Information 149 <p>5.9 Profile Analysis 152 <p>Profile Analysis 154 <p>Problems 161 <p>6 Multivariate Analysis of Variance 169 <p>6.1 One-way Models 169 <p>6.2 Comparison of the Four Manova Test Statistics 189 <p>6.3 Contrasts 191 <p>6.4 Tests on Individual Variables Following Rejection of H0 bythe Overall Manova Test 195 <p>6.5 Two-Way Classification 198 <p>6.6 Other Models 207 <p>6.7 Checking on the Assumptions 210 <p>6.8 Profile Analysis 211 <p>6.9 Repeated Measures Designs 215 <p>6.10 Growth Curves 232 <p>6.11 Tests on a Subvector 241 <p>Problems 244 <p>7 Tests on Covariance Matrices 259 <p>7.1 Introduction 259 <p>7.2 Testing a Specified Pattern for 259 <p>7.3 Tests Comparing Covariance Matrices 265 <p>7.4 Tests of Independence 269 <p>Problems 276 <p>8 Discriminant Analysis: Description of Group Separation281 <p>8.1 Introduction 281 <p>8.2 The Discriminant Function for two Groups 282 <p>8.3 Relationship Between two-group Discriminant Analysis andMultiple Regression 286 <p>8.4 Discriminant Analysis for Several Groups 288 <p>8.5 Standardized Discriminant Functions 292 <p>8.6 Tests of Significance 294 <p>8.7 Interpretation of Discriminant Functions 298 <p>8.8 Scatter Plots 301 <p>8.9 Stepwise Selection of Variables 303 <p>Problems 306 <p>9 Classification Analysis: Allocation of Observations toGroups309 <p>9.1 Introduction 309 <p>9.2 Classification into two Groups 310 <p>9.3 Classification into Several Groups 314 <p>9.4 Estimating Misclassification Rates 318 <p>9.5 Improved Estimates of Error Rates 320 <p>9.6 Subset Selection 322 <p>9.7 Nonparametric Procedures 326 <p>Problems 336 <p>10 Multivariate Regression 339 <p>10.1 Introduction 339 <p>10.2 Multiple Regression: Fixed X s 340 <p>10.3 Multiple Regression: Random X s 354 <p>10.4 Multivariate Multiple Regression: Estimation 354 <p>10.5 Multivariate Multiple Regression: Hypothesis Tests 364 <p>10.6 Multivariate Multiple Regression: Prediction 370 <p>10.7 Measures of Association Between the Y s and theX s 372 <p>10.8 Subset Selection 374 <p>10.9 Multivariate Regression: Random X s 380 <p>Problems 381 <p>11 Canonical Correlation 385 <p>11.1 Introduction 385 <p>11.2 Canonical Correlations and Canonical Variates 385 <p>11.3 Properties of Canonical Correlations 390 <p>11.4 Tests of Significance 391 <p>11.5 Interpretation 395 <p>11.6 Relationships of Canonical Correlation Analysis to OtherMultivariate <p>Problems 402 <p>12 Principal Component Analysis 405 <p>12.1 Introduction 405 <p>12.2 Geometric and Algebraic Bases of Principal Components406 <p>12.3 Principal Components and Perpendicular Regression 412 <p>12.4 Plotting of Principal Components 414 <p>12.5 Principal Components from the Correlation Matrix 419 <p>12.6 Deciding How Many Components to Retain 423 <p>12.7 Information in the Last Few Principal Components 427 <p>12.8 Interpretation of Principal Components 427 <p>12.9 Selection of Variables 430 <p>Problems 432 <p>13 Exploratory Factor Analysis 435 <p>13.1 Introduction 435 <p>13.2 Orthogonal Factor Model 437 <p>13.3 Estimation of Loadings and Communalities 442 <p>13.4 Choosing the Number of Factors, m 453 <p>13.5 Rotation 457 <p>13.6 Factor Scores 466 <p>13.7 Validity of the Factor Analysis Model 470 <p>13.8 Relationship of Factor Analysis to Principal ComponentAnalysis 475 <p>Problems 476 <p>14 Confirmatory Factor Analysis 479 <p>14.1 Introduction 479 <p>14.2 Model Specification and Identification 480 <p>14.3 Parameter Estimation and Model Assessment 487 <p>14.4 Inference for Model Parameters 492 <p>14.5 Factor Scores 495 <p>Problems 496 <p>15 Cluster Analysis 501 <p>15.1 Introduction 501 <p>15.2 Measures of Similarity or Dissimilarity 502 <p>15.3 Hierarchical Clustering 505 <p>15.4 Nonhierarchical Methods 531 <p>15.5 Choosing the Number of Clusters 544 <p>15.6 Cluster Validity 546 <p>15.7 Clustering Variables 547 <p>Problems 548 <p>16 Graphical Procedures 555 <p>16.1 Multidimensional Scaling 555 <p>16.2 Correspondence Analysis 565 <p>16.3 Biplots 580 <p>Problems 588 <p>Appendix A: Tables 597 <p>Appendix B: Answers and Hints to Problems 637 <p>Appendix C: Data Sets and SAS Files 727 <p>References 729 <p>Index 747

"This new edition, now with a co-author, offers a complete and up-to-date examination of the field. The authors have streamlined previously tedious topics, such as multivariate regression and MANOVA techniques, to add newer, more timely content. Each chapter contains exercises, providing readers with the opportunity to test and extend their understanding. The new edition also presents several expanded topics in Kronecker product; prediction errors; maximum likelihood estimation; and selective key, but accessible proofs. This resource meets the needs of both statistics majors and those of students and professionals in other fields"--

Applied Statistics

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