# Methods of multivariate analysis

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<ul><li> 1. Methods of Multivariate Analysis [Hardcover] </li></ul><p> 2. Contents Cover Half Title page Title page Copyright page Preface Acknowledgments Chapter 1: Introduction 1.1 Why Multivariate Analysis? 1.2 Prerequisites 1.3 Objectives 1.4 Basic Types of Data and Analysis Chapter 2: Matrix Algebra 2.1 Introduction 2.2 Notation and Basic Definitions 2.3 Operations 2.4 Partitioned Matrices 2.5 Rank 2.6 Inverse 2.7 Positive Definite Matrices 2.8 Determinants 2.9 Trace 2.10 Orthogonal Vectors and Matrices 2.11 Eigenvalues and Eigenvectors 2.12 Kronecker and Vec Notation Problems Chapter 3: Characterizing and Displaying Multivariate Data 3.1 Mean and Variance of a Univariate Random Variable 3.2 Covariance and Correlation of Bivariate Random Variables 3.3 Scatterplots of Bivariate Samples 3.4 Graphical Displays for Multivariate Samples 3.5 Dynamic Graphics 3.6 Mean Vectors 3.7 Covariance Matrices 3.8 Correlation Matrices 3.9 Mean Vectors and Covariance Matrices for Subsets of Variables 3.10 Linear Combinations of Variables 3.11 Measures of Overall Variability 3. 3.12 Estimation of Missing Values 3.13 Distance Between Vectors Problems Chapter 4: The Multivariate Normal Distribution 4.1 Multivariate Normal Density Function 4.2 Properties of Multivariate Normal Random Variables 4.3 Estimation in the Multivariate Normal 4.4 Assessing Multivariate Normality 4.5 Transformations to Normality 4.6 Outliers Problems Chapter 5: Tests on One or Two Mean Vectors 5.1 Multivariate Versus Univariate Tests 5.2 Tests on With Known 5.3 Tests on When Is Unknown 5.4 Comparing Two Mean Vectors 5.5 Tests on Individual Variables Conditional on Rejection of H0 By the T2- Test 5.6 Computation of T2 5.7 Paired Observations Test 5.8 Test for Additional Information 5.9 Profile Analysis Problems Chapter 6: Multivariate Analysis of Variance 6.1 One-Way Models 6.2 Comparison of the Four Manova Test Statistics 6.3 Contrasts 6.4 Tests on Individual Variables Following Rejection ofH0 By the Overall Manova Test 6.5 Two-Way Classification 6.6 Other Models 6.7 Checking on the Assumptions 6.8 Profile Analysis 6.9 Repeated Measures Designs 6.10 Growth Curves 6.11 Tests on a Subvector Problems Chapter 7: Tests on Covariance Matrices 7.1 Introduction 7.2 Testing a Specified Pattern for 7.3 Tests Comparing Covariance Matrices 4. 7.4 Tests of Independence Problems Chapter 8: Discriminant Analysis: Description of Group Separation 8.1 Introduction 8.2 The Discriminant Function for Two Groups 8.3 Relationship Between Two-Group Discriminant Analysis and Multiple Regression 8.4 Discriminant Analysis for Several Groups 8.5 Standardized Discriminant Functions 8.6 Tests of Significance 8.7 Interpretation of Discriminant Functions 8.8 Scatterplots 8.9 Stepwise Selection of Variables Problems Chapter 9: Classification Analysis: Allocation of Observations to Groups 9.1 Introduction 9.2 Classification Into Two Groups 9.3 Classification Into Several Groups 9.4 Estimating Misclassification Rates 9.5 Improved Estimates of Error Rates 9.6 Subset Selection 9.7 Nonparametric Procedures Problems Chapter 10: Multivariate Regression 10.1 Introduction 10.2 Multiple Regression: Fixed xs 10.4 Multivariate Multiple Regression: Estimation 10.5 Multivariate Multiple Regression: Hypothesis Tests 10.6 Multivariate Multiple Regression: Prediction 10.7 Measures of Association Between the ys and the xs 10.8 Subset Selection 10.9 Multivariate Regression: Random xs Problems Chapter 11: Canonical Correlation 11.1 Introduction 11.2 Canonical Correlations and Canonical Variates 11.3 Properties of Canonical Correlations 11.4 Tests of Significance 11.5 Interpretation 5. 11.6 Relationships of Canonical Correlation Analysis to Other Multivariate Techniques Problems Chapter 12: Principal Component Analysis 12.1 Introduction 12.2 Geometric and Algebraic Bases of Principal Components 12.3 Principal Components and Perpendicular Regression 12.4 Plotting of Principal Components 12.5 Principal Components From the Correlation Matrix 12.6 Deciding How Many Components to Retain 12.7 Information in the Last Few Principal Components 12.8 Interpretation of Principal Components 12.9 Selection of Variables Problems Chapter 13: Exploratory Factor Analysis 13.1 Introduction 13.2 Orthogonal Factor Model 13.3 Estimation of Loadings and Communalities 13.4 Choosing the Number of Factors, M 13.5 Rotation 13.6 Factor Scores 13.7 Validity of the Factor Analysis Model 13.8 Relationship of Factor Analysis to Principal Component Analysis Problems Chapter 14: Confirmatory Factor Analysis 14.1 Introduction 14.2 Model Specification and Identification 14.3 Parameter Estimation and Model Assessment 14.4 Inference for Model Parameters 14.5 Factor Scores Problems Chapter 15: Cluster Analysis 15.1 Introduction 15.2 Measures of Similarity or Dissimilarity 15.3 Hierarchical Clustering 15.4 Nonhierarchical Methods 15.5 Choosing the Number of Clusters 15.6 Cluster Validity 15.7 Clustering Variables Problems Chapter 16: Graphical Procedures 6. 16.1 Multidimensional Scaling 16.2 Correspondence Analysis 16.3 Biplots Problems Appendix A: Tables Appendix B: Answers and Hints to Problems Appendix C: Data Sets and Sas Files References Index METHODS OF MULTIVARIATE ANALYSIS WILEY SERIES IN PROBABILITY AND STATISTICS ESTABLISHED BY WALTER A. SHEWHART AND SAMUEL S. WILKS Editors: David J. Balding, Noel A. C. Cressie, Garrett M. Fitzmaurice, Harvey Goldstein, Iain M. Johnstone, Geert Molenberghs, David W. Scott, Adrian F. M. Smith, Ruey S. Tsay, Sanford Weisberg Editors Emeriti: Vic Barnett, J. Stuart Hunter, Joseph B. Kadane, Jozef L. Teugels The Wiley Series in Probability and Statistics is well established and authoritative. It covers many topics of current research interest in both pure and applied statistics and probability theory. Written by leading statisticians and institutions, the titles span both state-of-the-art developments in the field and classical methods. Reflecting the wide range of current research in statistics, the series encompasses applied, methodological and theoretical statistics, ranging from applications and new techniques made possible by advances in computerized practice to rigorous treatment of theoretical approaches. This series provides essential and invaluable reading for all statisticians, whether in academia, industry, government, or research. ABRAHAM and LEDOLTER Statistical Methods for Forecasting AGRESTI Analysis of Ordinal Categorical Data, Second Edition AGRESTI An Introduction to Categorical Data Analysis, Second Edition AGRESTI Categorical Data Analysis, Second Edition ALTMAN, GILL, and McDONALD Numerical Issues in Statistical Computing for the Social Scientist AMARATUNGA and CABRERA Exploration and Analysis of DNA Microarray and Protein Array Data AND L Mathematics of Chance ANDERSON An Introduction to Multivariate Statistical Analysis, Third Edition * ANDERSON The Statistical Analysis of Time Series ANDERSON, AUQUIER, HAUCK, OAKES, VANDAELE, and WEISBERG Statistical Methods for Comparative Studies ANDERSON and LOYNES The Teaching of Practical Statistics ARMITAGE and DAVID (editors) Advances in Biometry ARNOLD, BALAKRISHNAN, and NAGARAJA Records * ARTHANARI and DODGE Mathematical Programming in Statistics * BAILEY The Elements of Stochastic Processes with Applications to the Natural Sciences BAJORSKI Statistics for Imaging, Optics, and Photonics BALAKRISHNAN and KOUTRAS Runs and Scans with Applications BALAKRISHNAN and NG Precedence-Type Tests and Applications BARNETT Comparative Statistical Inference, Third Edition BARNETT Environmental Statistics BARNETT and LEWIS Outliers in Statistical Data, Third Edition BARTHOLOMEW, KNOTT, and MOUSTAKI Latent Variable Models and Factor Analysis: A Unified Approach, Third Edition 7. BARTOSZYNSKI and NIEWIADOMSKA-BUGAJ Probability and Statistical Inference, Second Edition BASILEVSKY Statistical Factor Analysis and Related Methods: Theory and Applications BATES and WATTS Nonlinear Regression Analysis and Its Applications BECHHOFER, SANTNER, and GOLDSMAN Design and Analysis of Experiments for Statistical Selection, Screening, and Multiple Comparisons BEIRLANT, GOEGEBEUR, SEGERS, TEUGELS, and DE WAAL Statistics of Extremes: Theory and Applications BELSLEY Conditioning Diagnostics: Collinearity and Weak Data in Regression BELSLEY, KUH, and WELSCH Regression Diagnostics: Identifying Influential Data and Sources of Collinearity BENDAT and PIERSOL Random Data: Analysis and Measurement Procedures,Fourth Edition BERNARDO and SMITH Bayesian Theory BHAT and MILLER Elements of Applied Stochastic Processes, Third Edition BHATTACHARYA and WAYMIRE Stochastic Processes with Applications BIEMER, GROVES, LYBERG, MATHIOWETZ, and SUDMAN Measurement Errors in Surveys BILLINGSLEY Convergence of Probability Measures, Second Edition BILLINGSLEY Probability and Measure, Anniversary Edition BIRKES and DODGE Alternative Methods of Regression BISGAARD and KULAHCI Time Series Analysis and Forecasting by Example BISWAS, DATTA, FINE, and SEGAL Statistical Advances in the Biomedical Sciences: Clinical Trials, Epidemiology, Survival Analysis, and Bioinformatics BLISCHKE and MURTHY (editors) Case Studies in Reliability and Maintenance BLISCHKE and MURTHY Reliability: Modeling, Prediction, and Optimization BLOOMFIELD Fourier Analysis of Time Series: An Introduction, Second Edition BOLLEN Structural Equations with Latent Variables BOLLEN and CURRAN Latent Curve Models: A Structural Equation Perspective BOROVKOV Ergodicity and Stability of Stochastic Processes BOSQ and BLANKE Inference and Prediction in Large Dimensions BOULEAU Numerical Methods for Stochastic Processes * BOX and TIAO Bayesian Inference in Statistical Analysis BOX Improving Almost Anything, Revised Edition * BOX and DRAPER Evolutionary Operation: A Statistical Method for Process Improvement BOX and DRAPER Response Surfaces, Mixtures, and Ridge Analyses, Second Edition BOX, HUNTER, and HUNTER Statistics for Experimenters: Design, Innovation, and Discovery, Second Editon BOX, JENKINS, and REINSEL Time Series Analysis: Forcasting and Control, Fourth Edition BOX, LUCEO, and PANIAGUA-QUIONES Statistical Control by Monitoring and Adjustment, Second Edition * BROWN and HOLLANDER Statistics: A Biomedical Introduction CAIROLI and DALANG Sequential Stochastic Optimization CASTILLO, HADI, BALAKRISHNAN, and SARABIA Extreme Value and Related Models with Applications in Engineering and Science CHAN Time Series: Applications to Finance with R and S-Plus, Second Edition CHARALAMBIDES Combinatorial Methods in Discrete Distributions CHATTERJEE and HADI Regression Analysis by Example, Fourth Edition CHATTERJEE and HADI Sensitivity Analysis in Linear Regression CHERNICK Bootstrap Methods: A Guide for Practitioners and Researchers, Second Edition CHERNICK and FRIIS Introductory Biostatistics for the Health Sciences CHILS and DELFINER Geostatistics: Modeling Spatial Uncertainty, Second Edition CHOW and LIU Design and Analysis of Clinical Trials: Concepts and Methodologies,Second Edition CLARKE Linear Models: The Theory and Application of Analysis of Variance CLARKE and DISNEY Probability and Random Processes: A First Course with Applications, Second Edition * COCHRAN and COX Experimental Designs, Second Edition COLLINS and LANZA Latent Class and Latent Transition Analysis: With Applications in the Social, Behavioral, and Health Sciences CONGDON Applied Bayesian Modelling CONGDON Bayesian Models for Categorical Data 8. CONGDON Bayesian Statistical Modelling, Second Edition CONOVER Practical Nonparametric Statistics, Third Edition COOK Regression Graphics COOK and WEISBERG An Introduction to Regression Graphics COOK and WEISBERG Applied Regression Including Computing and Graphics CORNELL A Primer on Experiments with Mixtures CORNELL Experiments with Mixtures, Designs, Models, and the Analysis of Mixture Data, Third Edition COX A Handbook of Introductory Statistical Methods CRESSIE Statistics for Spatial Data, Revised Edition CRESSIE and WIKLE Statistics for Spatio-Temporal Data CSRG and HORVTH Limit Theorems in Change Point Analysis DAGPUNAR Simulation and Monte Carlo: With Applications in Finance and MCMC DANIEL Applications of Statistics to Industrial Experimentation DANIEL Biostatistics: A Foundation for Analysis in the Health Sciences, Eighth Edition * DANIEL Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition DASU and JOHNSON Exploratory Data Mining and Data Cleaning DAVID and NAGARAJA Order Statistics, Third Edition * DEGROOT, FIENBERG, and KADANE Statistics and the Law DEL CASTILLO Statistical Process Adjustment for Quality Control DEMARIS Regression with Social Data: Modeling Continuous and Limited Response Variables DEMIDENKO Mixed Models: Theory and Applications DENISON, HOLMES, MALLICK and SMITH Bayesian Methods for Nonlinear Classification and Regression DETTE and STUDDEN The Theory of Canonical Moments with Applications in Statistics, Probability, and Analysis DEY and MUKERJEE Fractional Factorial Plans DILLON and GOLDSTEIN Multivariate Analysis: Methods and Applications * DODGE and ROMIG Sampling Inspection Tables, Second Edition * DOOB Stochastic Processes DOWDY, WEARDEN, and CHILKO Statistics for Research, Third Edition DRAPER and SMITH Applied Regression Analysis, Third Edition DRYDEN and MARDIA Statistical Shape Analysis DUDEWICZ and MISHRA Modern Mathematical Statistics DUNN and CLARK Basic Statistics: A Primer for the Biomedical Sciences, Fourth Edition DUPUIS and ELLIS A Weak Convergence Approach to the Theory of Large Deviations EDLER and KITSOS Recent Advances in Quantitative Methods in Cancer and Human Health Risk Assessment * ELANDT-JOHNSON and JOHNSON Survival Models and Data Analysis ENDERS Applied Econometric Time Series, Third Edition ETHIER and KURTZ Markov Processes: Characterization and Convergence EVANS, HASTINGS, and PEACOCK Statistical Distributions, Third Edition EVERITT, LANDAU, LEESE, and STAHL Cluster Analysis, Fifth Edition FEDERER and KING Variations on Split Plot and Split Block Experiment Designs FELLER An Introduction to Probability Theory and Its Applications, Volume I, Third Edition, Revised; Volume II, Second Edition FITZMAURICE, LAIRD, and WARE Applied Longitudinal Analysis, Second Edition * FLEISS The Design and Analysis of Clinical Experiments FLEISS Statistical Methods for Rates and Proportions, Third Edition FLEMING and HARRINGTON Counting Processes and Survival Analysis FUJIKOSHI, ULYANOV, and SHIMIZU Multivariate Statistics: High-Dimensional and Large-Sample Approximations FULLER Introduction to Statistical Time Series, Second Edition FULLER Measurement Error Models GALLANT Nonlinear Statistical Models GEISSER Modes of Parametric Statistical Inference 9. GELMAN and MENG Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspe...</p>