{"product_id":"methods-of-multivariate-analysis-isbn-9780470178966","title":"Methods of Multivariate Analysis","description":"\u003cp\u003e\u003cb\u003ePraise for the \u003ci\u003eSecond Edition\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e\"This book is a systematic, well-written, well-organized text on multivariate analysis packed with intuition and insight . . . There is much practical wisdom in this book that is hard to find elsewhere.\"\u003cbr\u003e \u003ci\u003e—IIE Transactions\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eFilled with new and timely content, \u003ci\u003eMethods of Multivariate Analysis, Third Edition\u003c\/i\u003e provides examples and exercises based on more than sixty real data sets from a wide variety of scientific fields. It takes a \"methods\" approach to the subject, placing an emphasis on how students and practitioners can employ multivariate analysis in real-life situations.\u003c\/p\u003e \u003cp\u003eThis \u003ci\u003eThird Edition\u003c\/i\u003e continues to explore the key descriptive and inferential procedures that result from multivariate analysis. Following a brief overview of the topic, the book goes on to review the fundamentals of matrix algebra, sampling from multivariate populations, and the extension of common univariate statistical procedures (including \u003ci\u003et\u003c\/i\u003e-tests, analysis of variance, and multiple regression) to analogous multivariate techniques that involve several dependent variables. The latter half of the book describes statistical tools that are uniquely multivariate in nature, including procedures for discriminating among groups, characterizing low-dimensional latent structure in high-dimensional data, identifying clusters in data, and graphically illustrating relationships in low-dimensional space. In addition, the authors explore a wealth of newly added topics, including:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eConfirmatory Factor Analysis\u003c\/li\u003e \u003cli\u003eClassification Trees\u003c\/li\u003e \u003cli\u003eDynamic Graphics\u003c\/li\u003e \u003cli\u003eTransformations to Normality\u003c\/li\u003e \u003cli\u003ePrediction for Multivariate Multiple Regression\u003c\/li\u003e \u003cli\u003eKronecker Products and Vec Notation\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eNew exercises have been added throughout the book, allowing readers to test their comprehension of the presented material. Detailed appendices provide partial solutions as well as supplemental tables, and an accompanying FTP site features the book's data sets and related SAS® code.\u003c\/p\u003e \u003cp\u003eRequiring only a basic background in statistics, \u003ci\u003eMethods of Multivariate Analysis, Third Edition\u003c\/i\u003e is an excellent book for courses on multivariate analysis and applied statistics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for both statisticians and researchers across a wide variety of disciplines.\u003c\/p\u003e  Preface xvii  \u003cp\u003eAcknowledgments xxi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Why Multivariate Analysis? 1\u003c\/p\u003e \u003cp\u003e1.2 Prerequisites 3\u003c\/p\u003e \u003cp\u003e1.3 Objectives 3\u003c\/p\u003e \u003cp\u003e1.4 Basic Types of Data And Analysis 4\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Matrix Algebra 7\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 7\u003c\/p\u003e \u003cp\u003e2.2 Notation and Basic Definitions 8\u003c\/p\u003e \u003cp\u003e2.3 Operations 11\u003c\/p\u003e \u003cp\u003e2.4 Partitioned Matrices 22\u003c\/p\u003e \u003cp\u003e2.5 Rank 23\u003c\/p\u003e \u003cp\u003e2.6 Inverse 25\u003c\/p\u003e \u003cp\u003e2.7 Positive Definite Matrices 26\u003c\/p\u003e \u003cp\u003e2.8 Determinants 28\u003c\/p\u003e \u003cp\u003e2.9 Trace 31\u003c\/p\u003e \u003cp\u003e2.10 Orthogonal Vectors and Matrices 31\u003c\/p\u003e \u003cp\u003e2.11 Eigenvalues and Eigenvectors 32\u003c\/p\u003e \u003cp\u003e2.12 Kronecker and VEC Notation 37\u003c\/p\u003e \u003cp\u003eProblems 39\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Characterizing and Displaying Multivariate Data 47\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Mean and Variance of a Univariate Random Variable 47\u003c\/p\u003e \u003cp\u003e3.2 Covariance and Correlation Of Bivariate Random Variables 49\u003c\/p\u003e \u003cp\u003e3.3 Scatter Plots of Bivariate Samples 55\u003c\/p\u003e \u003cp\u003e3.4 Graphical Displays for Multivariate Samples 56\u003c\/p\u003e \u003cp\u003e3.5 Dynamic Graphics 58\u003c\/p\u003e \u003cp\u003e3.6 Mean Vectors 63\u003c\/p\u003e \u003cp\u003e3.7 Covariance Matrices 66\u003c\/p\u003e \u003cp\u003e3.8 Correlation Matrices 69\u003c\/p\u003e \u003cp\u003e3.9 Mean Vectors and Covariance Matrices for Subsets of Variables 71\u003c\/p\u003e \u003cp\u003e3.9.1 Two Subsets 71\u003c\/p\u003e \u003cp\u003e3.9.2 Three or More Subsets 73\u003c\/p\u003e \u003cp\u003e3.10 Linear Combinations of Variables 75\u003c\/p\u003e \u003cp\u003e3.10.1 Sample Properties 75\u003c\/p\u003e \u003cp\u003e3.10.2 Population Properties 81\u003c\/p\u003e \u003cp\u003e3.11 Measures of Overall Variability 81\u003c\/p\u003e \u003cp\u003e3.12 Estimation of Missing Values 82\u003c\/p\u003e \u003cp\u003e3.13 Distance Between Vectors 84\u003c\/p\u003e \u003cp\u003eProblems 85\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 The Multivariate Normal Distribution 91\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Multivariate Normal Density Function 91\u003c\/p\u003e \u003cp\u003e4.2 Properties of Multivariate Normal Random Variables 94\u003c\/p\u003e \u003cp\u003e4.3 Estimation in the Multivariate Normal 99\u003c\/p\u003e \u003cp\u003e4.4 Assessing Multivariate Normality 101\u003c\/p\u003e \u003cp\u003e4.5 Transformations to Normality 108\u003c\/p\u003e \u003cp\u003e4.6 Outliers 111\u003c\/p\u003e \u003cp\u003eProblems 117\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Tests on One or Two Mean Vectors 125\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Multivariate Versus Univariate Tests 125\u003c\/p\u003e \u003cp\u003e5.2 Tests on µ With ??Known 126\u003c\/p\u003e \u003cp\u003e5.3 Tests on µ When ??is Unknown 130\u003c\/p\u003e \u003cp\u003e5.4 Comparing two Mean Vectors 134\u003c\/p\u003e \u003cp\u003e5.5 Tests on Individual Variables Conditional on Rejection of H0 by the T2-test\u003c\/p\u003e \u003cp\u003e139\u003c\/p\u003e \u003cp\u003e5.6 Computation of T2 143\u003c\/p\u003e \u003cp\u003e5.7 Paired Observations Test 145\u003c\/p\u003e \u003cp\u003e5.8 Test for Additional Information 149\u003c\/p\u003e \u003cp\u003e5.9 Profile Analysis 152\u003c\/p\u003e \u003cp\u003eProfile Analysis 154\u003c\/p\u003e \u003cp\u003eProblems 161\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Multivariate Analysis of Variance 169\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 One-way Models 169\u003c\/p\u003e \u003cp\u003e6.2 Comparison of the Four Manova Test Statistics 189\u003c\/p\u003e \u003cp\u003e6.3 Contrasts 191\u003c\/p\u003e \u003cp\u003e6.4 Tests on Individual Variables Following Rejection of H0 by the Overall Manova Test 195\u003c\/p\u003e \u003cp\u003e6.5 Two-Way Classification 198\u003c\/p\u003e \u003cp\u003e6.6 Other Models 207\u003c\/p\u003e \u003cp\u003e6.7 Checking on the Assumptions 210\u003c\/p\u003e \u003cp\u003e6.8 Profile Analysis 211\u003c\/p\u003e \u003cp\u003e6.9 Repeated Measures Designs 215\u003c\/p\u003e \u003cp\u003e6.10 Growth Curves 232\u003c\/p\u003e \u003cp\u003e6.11 Tests on a Subvector 241\u003c\/p\u003e \u003cp\u003eProblems 244\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Tests on Covariance Matrices 259\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 259\u003c\/p\u003e \u003cp\u003e7.2 Testing a Specified Pattern for ∑ 259\u003c\/p\u003e \u003cp\u003e7.3 Tests Comparing Covariance Matrices 265\u003c\/p\u003e \u003cp\u003e7.4 Tests of Independence 269\u003c\/p\u003e \u003cp\u003eProblems 276\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Discriminant Analysis: Description of Group Separation 281\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 281\u003c\/p\u003e \u003cp\u003e8.2 The Discriminant Function for two Groups 282\u003c\/p\u003e \u003cp\u003e8.3 Relationship Between two-group Discriminant Analysis and Multiple Regression 286\u003c\/p\u003e \u003cp\u003e8.4 Discriminant Analysis for Several Groups 288\u003c\/p\u003e \u003cp\u003e8.5 Standardized Discriminant Functions 292\u003c\/p\u003e \u003cp\u003e8.6 Tests of Significance 294\u003c\/p\u003e \u003cp\u003e8.7 Interpretation of Discriminant Functions 298\u003c\/p\u003e \u003cp\u003e8.8 Scatter Plots 301\u003c\/p\u003e \u003cp\u003e8.9 Stepwise Selection of Variables 303\u003c\/p\u003e \u003cp\u003eProblems 306\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Classification Analysis: Allocation of Observations to Groups309\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 309\u003c\/p\u003e \u003cp\u003e9.2 Classification into two Groups 310\u003c\/p\u003e \u003cp\u003e9.3 Classification into Several Groups 314\u003c\/p\u003e \u003cp\u003e9.4 Estimating Misclassification Rates 318\u003c\/p\u003e \u003cp\u003e9.5 Improved Estimates of Error Rates 320\u003c\/p\u003e \u003cp\u003e9.6 Subset Selection 322\u003c\/p\u003e \u003cp\u003e9.7 Nonparametric Procedures 326\u003c\/p\u003e \u003cp\u003eProblems 336\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Multivariate Regression 339\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 339\u003c\/p\u003e \u003cp\u003e10.2 Multiple Regression: Fixed X’s 340\u003c\/p\u003e \u003cp\u003e10.3 Multiple Regression: Random X’s 354\u003c\/p\u003e \u003cp\u003e10.4 Multivariate Multiple Regression: Estimation 354\u003c\/p\u003e \u003cp\u003e10.5 Multivariate Multiple Regression: Hypothesis Tests 364\u003c\/p\u003e \u003cp\u003e10.6 Multivariate Multiple Regression: Prediction 370\u003c\/p\u003e \u003cp\u003e10.7 Measures of Association Between the Y’s and the X’s 372\u003c\/p\u003e \u003cp\u003e10.8 Subset Selection 374\u003c\/p\u003e \u003cp\u003e10.9 Multivariate Regression: Random X’s 380\u003c\/p\u003e \u003cp\u003eProblems 381\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Canonical Correlation 385\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 385\u003c\/p\u003e \u003cp\u003e11.2 Canonical Correlations and Canonical Variates 385\u003c\/p\u003e \u003cp\u003e11.3 Properties of Canonical Correlations 390\u003c\/p\u003e \u003cp\u003e11.4 Tests of Significance 391\u003c\/p\u003e \u003cp\u003e11.5 Interpretation 395\u003c\/p\u003e \u003cp\u003e11.6 Relationships of Canonical Correlation Analysis to Other Multivariate\u003c\/p\u003e \u003cp\u003eProblems 402\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Principal Component Analysis 405\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 405\u003c\/p\u003e \u003cp\u003e12.2 Geometric and Algebraic Bases of Principal Components 406\u003c\/p\u003e \u003cp\u003e12.3 Principal Components and Perpendicular Regression 412\u003c\/p\u003e \u003cp\u003e12.4 Plotting of Principal Components 414\u003c\/p\u003e \u003cp\u003e12.5 Principal Components from the Correlation Matrix 419\u003c\/p\u003e \u003cp\u003e12.6 Deciding How Many Components to Retain 423\u003c\/p\u003e \u003cp\u003e12.7 Information in the Last Few Principal Components 427\u003c\/p\u003e \u003cp\u003e12.8 Interpretation of Principal Components 427\u003c\/p\u003e \u003cp\u003e12.9 Selection of Variables 430\u003c\/p\u003e \u003cp\u003eProblems 432\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Exploratory Factor Analysis 435\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 435\u003c\/p\u003e \u003cp\u003e13.2 Orthogonal Factor Model 437\u003c\/p\u003e \u003cp\u003e13.3 Estimation of Loadings and Communalities 442\u003c\/p\u003e \u003cp\u003e13.4 Choosing the Number of Factors, \u003ci\u003em\u003c\/i\u003e 453\u003c\/p\u003e \u003cp\u003e13.5 Rotation 457\u003c\/p\u003e \u003cp\u003e13.6 Factor Scores 466\u003c\/p\u003e \u003cp\u003e13.7 Validity of the Factor Analysis Model 470\u003c\/p\u003e \u003cp\u003e13.8 Relationship of Factor Analysis to Principal Component Analysis 475\u003c\/p\u003e \u003cp\u003eProblems 476\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Confirmatory Factor Analysis 479\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 479\u003c\/p\u003e \u003cp\u003e14.2 Model Specification and Identification 480\u003c\/p\u003e \u003cp\u003e14.3 Parameter Estimation and Model Assessment 487\u003c\/p\u003e \u003cp\u003e14.4 Inference for Model Parameters 492\u003c\/p\u003e \u003cp\u003e14.5 Factor Scores 495\u003c\/p\u003e \u003cp\u003eProblems 496\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Cluster Analysis 501\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 501\u003c\/p\u003e \u003cp\u003e15.2 Measures of Similarity or Dissimilarity 502\u003c\/p\u003e \u003cp\u003e15.3 Hierarchical Clustering 505\u003c\/p\u003e \u003cp\u003e15.4 Nonhierarchical Methods 531\u003c\/p\u003e \u003cp\u003e15.5 Choosing the Number of Clusters 544\u003c\/p\u003e \u003cp\u003e15.6 Cluster Validity 546\u003c\/p\u003e \u003cp\u003e15.7 Clustering Variables 547\u003c\/p\u003e \u003cp\u003eProblems 548\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Graphical Procedures 555\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Multidimensional Scaling 555\u003c\/p\u003e \u003cp\u003e16.2 Correspondence Analysis 565\u003c\/p\u003e \u003cp\u003e16.3 Biplots 580\u003c\/p\u003e \u003cp\u003eProblems 588\u003c\/p\u003e \u003cp\u003eAppendix A: Tables 597\u003c\/p\u003e \u003cp\u003eAppendix B: Answers and Hints to Problems 637\u003c\/p\u003e \u003cp\u003eAppendix C: Data Sets and SAS Files 727\u003c\/p\u003e \u003cp\u003eReferences \u003cb\u003e729\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIndex 747\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eALVIN C. RENCHER\u003c\/b\u003e is Professor Emeritus in the Department of Statistics at Brigham Young University. A Fellow of the American Statistical Association, he is the author of \u003ci\u003eLinear Models in Statistics, Second Edition\u003c\/i\u003e and \u003ci\u003eMultivariate Statistical Inference and Applications,\u003c\/i\u003e both published by Wiley.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eWILLIAM F. CHRISTENSEN\u003c\/b\u003e 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.\u003c\/p\u003e  \u003cp\u003e\u003cb\u003ePraise for the \u003ci\u003eSecond Edition\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e\"This book is a systematic, well-written, well-organized text on multivariate analysis packed with intuition and insight . . . There is much practical wisdom in this book that is hard to find elsewhere.\"\u003cbr\u003e \u003ci\u003e—IIE Transactions\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eFilled with new and timely content, \u003ci\u003eMethods of Multivariate Analysis, Third Edition\u003c\/i\u003e provides examples and exercises based on more than sixty real data sets from a wide variety of scientific fields. It takes a \"methods\" approach to the subject, placing an emphasis on how students and practitioners can employ multivariate analysis in real-life situations.\u003c\/p\u003e \u003cp\u003eThis \u003ci\u003eThird Edition\u003c\/i\u003e continues to explore the key descriptive and inferential procedures that result from multivariate analysis. Following a brief overview of the topic, the book goes on to review the fundamentals of matrix algebra, sampling from multivariate populations, and the extension of common univariate statistical procedures (including \u003ci\u003et\u003c\/i\u003e-tests, analysis of variance, and multiple regression) to analogous multivariate techniques that involve several dependent variables. The latter half of the book describes statistical tools that are uniquely multivariate in nature, including procedures for discriminating among groups, characterizing low-dimensional latent structure in high-dimensional data, identifying clusters in data, and graphically illustrating relationships in low-dimensional space. In addition, the authors explore a wealth of newly added topics, including:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eConfirmatory Factor Analysis\u003c\/li\u003e \u003cli\u003eClassification Trees\u003c\/li\u003e \u003cli\u003eDynamic Graphics\u003c\/li\u003e \u003cli\u003eTransformations to Normality\u003c\/li\u003e \u003cli\u003ePrediction for Multivariate Multiple Regression\u003c\/li\u003e \u003cli\u003eKronecker Products and Vec Notation\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eNew exercises have been added throughout the book, allowing readers to test their comprehension of the presented material. Detailed appendices provide partial solutions as well as supplemental tables, and an accompanying FTP site features the book's data sets and related SAS® code.\u003c\/p\u003e \u003cp\u003eRequiring only a basic background in statistics, \u003ci\u003eMethods of Multivariate Analysis, Third Edition\u003c\/i\u003e is an excellent book for courses on multivariate analysis and applied statistics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for both statisticians and researchers across a wide variety of disciplines.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989616279781,"sku":"NP9780470178966","price":148.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470178966.jpg?v=1761784824","url":"https:\/\/k12savings.com\/es\/products\/methods-of-multivariate-analysis-isbn-9780470178966","provider":"K12savings","version":"1.0","type":"link"}