Springer Texts in Statistics

6 Contingency Tables.- 6.1 Multivariate Data Analysis Data Matrices and Measurement Scales.- 6.1.1 Data Matrices.- 6.1.2 Measurement Scales.- Quantitative Scales.- Qualitative Scales.- Measurement Scales and Analysis.- 6.1.3 Data Collection and Statistical Inference.- Probability Samples and Random Samples.- Exploratory and Confirmatory Analysis.- 6.1.4 An Outline of the Techniques to be Studied.- Topics in Volume.- 6.2 Two-Dimensional Contingency Tables.- 6.2.1 Bivariate Distributions for Categorical Data.- Joint Density Table.- Indepencence.- Row and Column Proportions.- Row and Column Profiles.- Odds Ratios.- 6.2.2 Statistical Inference in Two-Dimensional Tables.- The Two-Dimensional Contingency Table.- Sampling Models for Contingency Tables.- Multinomial.- Hypergeometric.- Poisson.- Product Multinomial.- Test of Independence.- Sampling Model Assumptions.- Poisson Distribution.- Product Multinomial Distribution.- Standardized Residuals.- Correspondence Analysis.- 6.2.3 Measures of Association.- Goodman and Kruskal's Lambda.- Inference for Lambda.- 6.2.4 Models for Two-Dimensional Tables.- Equal Cell Probability Model.- Constant Row or Column Densities.- The Independence Model as a Composite of Three Simple Models.- The Saturated Model.- Loglinear Characterization for Cell Densities.- A Loglinear Model for Independence.- Parameters for the Loglinear Model.- The Loglinear Model with Interaction.- Matrix Notation for Loglinear Model.- 6.2.5 Statistical Inference for Loglinear Models.- The Loglinear Model Defined in Terms of Cell Frequencies.- Multiplicative Form of the Loglinear Model.- Estimation for the Loglinear Model.- Standardized Estimates of Loglinear Parameters.- A Loglinear Representation for Some Simpler Models.- Inference Procedures for the Three Simple Models.- 6.2.6 An Additive Characterization for Cell Densities.- 6.2.7 Two-Dimensional Contingency Tables in a Multivariate Setting.- Simpson's Paradox.- 6.2.8 Other Sources of Information.- 6.3 Multidimensional Contingency Tables.- 6.3.1 The Three-Dimensional Contingency Table.- Models for Three-Way Tables.- Inference for the Independence Model.- Other Models for Three-Way Tables.- Partial Independence.- Conditional Independence.- No Three-Way Interaction.- Saturated Model.- Loglinear Models for Three-Way Tables.- Definitions of Parameters in Terms of Cell Frequencies.- Independence Model.- Partial Independence Model.- Conditional Independence Model.- No Three-Way Interactions Model.- Saturated Model.- Multiplicative Form of the Loglinear Model.- Hierarchical Models.- Notation for Loglinear Models.- Model Selection.- Standardized Estimates and Standardized Residuals.- Summary of Loglinear Model Fitting Procedure.- Product Multinomial Sampling.- 6.3.2 Some Examples.- Three-way Interaction.- Goodness of Fit and Model Selection.- 6.3.3 Four-Dimensional Contingency Tables and Stepwise.- Fitting Procedures 70 Stepwise Model Selection.- Tests of Partial and Marginal Association.- Marginal Association.- 6.3.4 The Effects of Collapsing a Contingency Table and.- Structural Zeroes.- Collapsing Contingency Tables.- Random Zeroes.- Structural Zeroes and Incomplete Tables.- Quasi-loglinear Models for Incomplete Tables.- 6.3.5 Logit Models for Response Variables.- The Logit Function.- Fitting a Logit Model.- Relationship to Logistic Regression.- Polychotomous Response Variables.- 6.3.6 Other Sources of Information.- 6.4 The Weighted Least Squares Approach.- 6.4.1 The Weighted Least Squares Theory.- The Product Multinomial Distribution Assumption.- Sampling Properties of the Row Proportions.- Determining Linear Functions Among the Row Proportions.- The Linear Model to be Estimated.- Determining the Weighted Least Squares Estimator.- 6.4.2 Statistical Inference for the Weighted Least Squares.- Procedure.- 6.4.3 Some Alternative Analyses.- Marginal Analysis.- Continuation Differences.- Averaging or Summing Response Functions.- Weighted Sums for Ordinal Responses.- 6.4.4 Weighted Least Squares Estimation for Logit Models.- The Logit Model as a Special Case of a Weighted.- Least Squares Model.- Continuation Ratios.- 6.4.5 Two or More Response Variables.- Defining Response Functions.- Repeated Measurement Designs.- Adding Interaction Effects.- 6.4.6 Other Sources of Information.- Cited Literature and References.- Exercises for Chapter 6.- Questions for Chapter 6.- 7 Multivariate Distributions Inference Regression and Canonical Correlation.- 7.1 Multivariate Random Variables and Samples.- 7.1.1 Multivariate Distributions and Multivariate Random Variables.- Joint Distribution.- Partitioning the Random Variable.- Conditional Distributions and Independence.- Mean Vector and Covariance Matrix.- Correlation Matrix.- 7.1.2 Multivariate Samples.- Sample Mean Vector and Covariance Matrix.- Sample Correlation Matrix.- Sums of Squares and Cross Product Matrices.- Multivariate Central Limit Theorem.- 7.1.3 Geometric Interpretations for Data Matrices.- p-Dimensional Space.- n-Dimensional Space.- Mahalanobis Distance and Generalized Variance.- p-Dimensional Ellipsoid.- Generalized Variance.- Trace Measure of Overall Variance.- Generalized Variance for Correlation Matrices.- Eigenvalues and Eigenvectors for Sums of Squares and Cross Product Matrices.- 7.1.4 Other Sources of Information.- 7.2 The Multivariate Normal Distribution.- 7.2.1 The Multivariate Normal.- Multivariate Normal Density.- Constant Probability Density Contour.- Linear Transformations.- Distribution of Probability Density Contour.- 7.2.2 Partitioning the Normal.- Marginal Distributions.- Conditional Distributions.- Multivariate Regression Function.- Partial Correlation.- 7.3 Testing for Normality Outliers and Robust Estimation.- 7.3.1 Testing for Normality.- Mahalanobis Distances from the Sample Mean.- Mul-.- tivariate Skewness and Kurtosis.- Transforming to Normality.- 7.3.2 Multivariate Outliers.- Multivariate Outliers and Mahalanobis Distance.- Testing for Multivariate Outliers.- Multiple Outliers.- 7.3.3 Robust Estimation.- Obtaining Robust Estimators of Covariance and Cor-.- relation Matrices.- Multivariate Trimming.- 7.3.4 Other Sources of Information.- 7.4 Inference for the Multivariate Normal.- 7.4.1 Inference Procedures for the Mean Vector.- Sample Likelihood Function.- Hotelling's T2.- Inference.- Simultaneous Confidence Regions.- Inferences for Linear Functions.- 7.4.2 Repeated Measures Comparisons.- Repeated Measurements on a Single Variable.- Profile Characterization.- Repeated Measures in a Randomized Block Design.- Necessary and Sufficient Conditions for Validity of Univariate FTest.- 7.4.3 Mahalanobis Distance of the Mean Vector from the Origin.- Mahalanobis Distance of Mean Vector from the Origin.- Application to Financial Portfolios.- 7.4.4 Inference for the Covariance and the Correlation Matrices.- Wishart Distribution.- Sphericity Test and Test for Independence.- A Test for Zero Correlation.- Test Statistics for Repeated Measures Designs.- Test for Equal Variance-Equal Covariance Structure.- Test for the Hyunh-Feldt Pattern.- Equal Correlation Structure.- Independent Blocks.- Partial and Multiple Correlation.- 7.4.5 Other Sources of Information.- 7.5 Multivariate Regression and Canonical Correlation.- 7.5.1 Multivariate Regression.- The Multivariate Regression Function.- Estimation of the Multivariate Regression Model.- Relationship to Ordinary Least Squares.- Residuals.- Influence.- Outliers and Cross Validation.- Estimation of the Error Covariance Matrix.- Relationship to Multiple Linear Regression.- Testing the Hypothesis that Some Coefficients are Zero.- Other Tests.- Inferences for Linear Functions.- Relationship to Generalized Least Squares.- Zellner's Seemingly Unrelated Regression Model.- 7.5.2 Canonical Correlation.- Derivation of Canonical Relationships.- An Eigenvalue Problem.- The Canonical Variables.- Sample Canonical Correlation Analysis.- Canonical Weights and Canonical Variables.- Inference for Canonical Correlation.- An Alternative Test Statistic.- Structure Correlations or Canonical Loadings.- Redundancy Analysis and Proportion of Variance Explained.- Redundancy Measure for a Given Canonical Variate.- Total Redundancy.- Relation to Multiple Regression.- Residuals.- Influence.- Outliers and Cross Validation.- 7.5.3 Other Sources of Information.- Cited Literature and References.- Exercises for Chapter 7.- Questions for Chapter 7.- 8 Manova Discriminant Analysis and Qualitative Response Models.- 8.1 Multivariate Analysis of Variance.- 8.1.1 One-Way Multivariate Analysis of Variance.- Comparison to Univariate Analysis of Variance.- Notation for Several Multivariate Populations.- Mean Vector for Group kand Common Covariance Matrix.- Grand Mean Vector.- Notation for Samples.- Sample Mean Vector and Sample Covariance Matrix for Group k.- Sample Grand Mean Vector.- The Multivariate Analysis of Variance Model.- Within Group Sum of Squares Matrix.- Among Group Sum of Squares Matrix.- Total Sum of Squares Matrix.- Statistical Inference for MANOVA.- Wilk's Lambda Likelihood.- Ratio F-Statistic.- An Alternative Test Statistic.- Correlation Ratio.- The Special Case of Two Groups.- A Bonferroni Approximation.- Multiple Comparison Procedures Based on Two Group Comparisons.- Testing for the Equality of Covariance Matrices.- 8.1.2 Indicator Variables Multivariate Regression and Analysis of Covariance.- Some Relationships to the Multivariate Regression Test for H0:ABM =0.- Cell Parameter Coding.- The Non-Full Rank Design Matrix.- Multivariate Analysis of Covariance.- 8.1.3 Profile Analysis with Repeated Measurements.- Comparing Profiles.- Parallel Profiles.- Equal Profiles Given Parallel Profiles.- Horizontal Profiles Given Parallel Profiles.- Horizontal Profiles.- 8.1.4 Balanced Two-Way MANOVA.- The Model.- Sums of Squares Matrices.- Inference.- The Multivariate Paired Comparison Test.- 8.1.5 An Unbalanced MANOVA with Covariate.- 8.1.6 Other Sources of Information.- 8.2 Discriminant Analysis.- 8.2.1 Fisher's Discriminant Criterion and Canonical Discriminant Analysis.- Fisher's Discriminant Criterion.- An Eigenvalue Problem.- Canonical Discriminant Functions.- Inferences for Canonical Discriminant Functions.- Bartlett's Test.- An Alternative Test Statistic-F.- Interpretation of the Discriminant Analysis Solution.- Interpretation Using Correlations.- Graphical Approach to Group Characterization.- Comparison of Correlation Coefficients and Discriminant Function Coefficients.- Effect of Correlation Structure on Discriminant Analysis.- Discriminant Analysis and Canonical Correlation.- Discriminant Analysis and Dimension Reduction.- 8.2.2 Discriminant Functions and Classification.- Discrimination Between Two Groups with Parameters Known.- Classification of an Unknown.- Fisher Criterion and Mahalanobis Distance.- Maximum Likelihood Criterion.- Minimum Total Probability of Misclassification Criterion.- Bayes Theorem Criterion.- Minimax Criterion.- Minimum Cost Criterion.- Summary.- Quadratic Discriminant Function and Unequal Covariance Matrices.- Classification in Practice.- Evaluation of a Discriminant Function as a Classification Mechanism.- Split Sample.- Jackknife Procedure.- Multiple Group Classification.- Bias When Parameters are Unknown.- 8.2.3 Tests of Sufficiency and Variable Selection.- Two Groups.- More Than Two Groups.- 8.2.4 Discrimination Without Normality.- Discrimination Using Ranks.- Nearest Neighbor Method.- 8.2.5 Other Sources of Information.- 8.3 Qualitative Response Regression Models and Logistic Regression.- 8.3.1 The Dichotomous Response Model.- The Point Binomial.- Probability as a Function of Other Variables.- Alternative Response Functions.- Logistic Regression with cExplanatory Variables.- Maximum Likelihood Estimation for Dichotomous Logistic Regression.- Newton-Raphson Procedure.- Inference for the Dichotomous Logistic Regression Model.- Comparing Nested Models and Inference for Coefficients.- Goodness of Fit.- Hosmer-Lemeshow Goodness of Fit Test.- Covariance Matrix for Estimated Coefficients.- The Role of the Intercept and Categorical Variables.- Testing for Zero Intercept.- Dummy Variables as Explanatory Variables - A Caution.- The Fitted Model and Classification.- The Jackknife Approach.- Stepwise Logistic Regression.- Influence Diagnostics.- The Chi Statistic.- The Deviance Statistic.- Leverage.- Influence.- The DFBETA Measure.- 8.3.2 The Probit Model.- 8.3.3 Logistic Regression and Probit Analysis: A Second Example.- 8.3.4 Multiple Observations and Design Variables.- The Model and Maximum Likelihood Estimation.- The Chi and Deviance Statistics.- Weighted Least Squares or Minimum Logit Chi-Square Estimation.- 8.3.5 Other Sources of Information.- 8.3.6 The Multinomial Logit Model.- Parameterization of the Model.- Inference for the Multinomial Logit.- Using Multinomial Logit Models.- Estimation Using Single Equation Methods.- Continuation Ratios.- Other Nested Partitions.- 8.3.7 Other Sources of Information.- 8.3.8 The Conditional Logit Model and Consumer Choice.- 8.3.9 Multivariate Qualitative Response Models.- Loglinear Models for Dependent Variables.- Relation Between Loglinear Parameters and Logits.- A Conditional Probability Approach.- Cited Literature and References.- Exercises for Chapter 8.- Questions for Chapter 8.- 9 Principal Components Factors and Correspondence Analysis.- 9.1 Principal Components.- 9.1.1 A Classic Example.- 9.1.2 An Ad Hoc Approach.- 9.1.3 The Principal Components Approach.- Characterizing the First Principal Component.- The Eigenvalue Problem.- Generalization to rPrincipal Components.- Spectral Decomposition.- The Full Rank Case.- Alternative Characterizations and Geometry.- Principal Components and Multivariate Random Variables.- Principal Component Scores.- 9.1.4 The Various Forms of X'X and Principal Components.- Interpretations Using Correlations.- Standardized Principal Components.- Communality or Variance Explained.- How Many Principal Components.- Average Criterion.- Geometric Mean Criterion.- A Test for Equality of Eigenvalues in Covariance Matrices.- A Cross Validation Approach.- Should all the Variables be Retained.- 9.1.5 Principal Components.- Multiple Regression and Supplementary Points.- Multiple Regression.- Supplementary Dimensions and Points.- 9.1.6 Outliers and Robust Principal Components Analysis.- Identification of Outliers.- Influence.- Robust Principal Components Analysis.- Rank Correlation and Robust Principal Components Analysis.- 9.1.7 Other Sources of Information.- 9.2 The Exploratory Factor Analysis Model.- 9.2.1 The Factor Analysis Model and Estimation.- The Model.- Factor Analysis Using the Correlation Matrix.- Indeterminacy.- Estimation of the Factor Model Using Principal Components.- Estimation of the Common Factor Model.- Determination of the Number of Factors.- A Useful Preliminary Test.- Scree Test.- The Broken Stick Model.- Equal Correlation Structure and the Number of Factors.- Principal Factor Approach.- 9.2.2 Factor Rotation.- The Theory of Rigid Rotation.- Varimax.- Other Rotation Methods.- Quartimax Criterion.- Orthomax.- Oblique Rotation.- Procrustes Rotation.- The Geometry of Factor Analysis.- 9.2.3 Factor Scores.- 9.2.4 The Maximum Likelihood Estimation Method.- The Maximum Likelihood Approach.- Goodness of Fit.- Cross Validation.- Akaike and Schwartz Criteria.- 9.2.5 Results From a Simulation Study.- 9.2.6 A Second Example.- 9.2.7 Other Sources of Information.- 9.3 Singular Value Decomposition and Matrix Approximation.- 9.3.1 Singular Value Decomposition and Principal Components.- 9.3.2 Biplots and Matrix Approximation.- Constructing Biplots.- The Principal Components Biplot.- Covariance Biplot.- Symmetric Biplot.- 9.3.3 Other Sources of Information.- 9.4 Correspondence Analysis.- 9.4.1 Correspondence Analysis for Two-Dimensional Tables.- Some Notation.- Correspondence Matrix and Row and Column Masses.- Row and Column Profiles.- Departure from Independence.- Averaging the Profiles.- Relationship to Pearson Chi-square Statistic.- Total Inertia.- Generalized Singular Value Decomposition.- Coordinates for Row and Column Profiles.- Partial Contributions to Total Inertia.- Squared Cosines.- Principle of Distributional Equivalence.- Generalized Least Squares Approximation.- Relationship to Generalized Singular Value Decomposition of O.- Row and Column Profile Deviations and Eigenvectors.- Correspondence Analysis for Multidimensional Tables.- 9.4.2 Other Sources of Information.- 9.4.3 Correspondence Analysis and Frequency Response Tables.- A Dual Scaling Approach.- Review of One-way ANOVA Notation.- Scaling the Response Categories.- Some Alternative Approaches to Correspondence Analysis.- Bivariate Correlation.- Simultaneous Linear Regression.- Canonical Correlation.- 9.4.4 Other Sources of Information.- 9.4.5 Correspondence Analysis in Multidimensional Tables.- Multiple Correspondence Analysis and Burt Matrices.- 9.4.6 Other Sources of Information.- Cited Literature and References.- Exercises for Chapter 9.- Questions for Chapter 9.- 10 Cluster Analysis and Multidimensional Scaling.- 10.1 Proximity Matrices Derived from Data Matrices.- 10.1.1 The Measurement of Proximity Between Objects.- Similarity.- Dissimilarity.- Euclidean Distance.- Using Mean-Centered Variables.- Euclidean Distance in Matrix Form.- Standardized Euclidean Distance.- Mahalanobis Distance and Multivariate Distance.- Euclidean Distance and the Centroid.- Manhattan or City Block.- Metric.- Minkowski Metrics.- Distance Measures Averaged Over Variables.- Correlation Type Measures of Similarity.- Similarity Matrices.- Double Mean-Centered.- Profile Shape.- Scatter and Level.- Some Relationships Between Similarity and Euclidean Distance.- Proximity Measures for Categorical Data.- Matching Coefficients for Binary Variables.- Mixtures of Categorical and Interval Scaled Variables.- 10.1.2 The Measurement of Proximity Between Groups.- Single Linkage or Nearest Neighbor.- Complete Linkage of Furthest Neighbor.- Average Linkage.- An Algorithm for Updating the Proximity Measures.- Distance Between Centroids.- Incremental Sums of Squares.- Relationship to Analysis of Variance.- Algorithms for Determining Proximity.- Measures Based on Centroids and Sums of Squares.- Ultrametric Inequality.- Sums of Squares Derived from MANOVA Matrices.- A Multivariate Measure of Proximity.- 10.2 Cluster Analysis.- 10.2.1 Hierarchical Methods.- Agglomerative versus Divisive Processes.- Comparison of Group Proximity Measures.- Some Multivariate Approaches to Hierarchical Clustering.- An Example with Outliers.- 10.2.2 Assessing the Hierarchical Solution and Cluster Choice.- Dendograms and Derived Proximities.- Cophenetic Correlation and Cluster Validity.- Stress.- Alternative Derived Proximities Based on Centroids.- Choosing the Number of Clusters.- A Binary Data Example.- Test Statistics for Number of Clusters.- Some ANOVAType Statistics.- Pseudo-F.- Pseudo-t2and Beales' F-Ratio.- R2-Type Measures.- Correlation-Type Measures of Cluster Quality.- Point-Biserial Correlation.- Gamma and G(+).- 10.2.3 Combining Hierarchical Cluster Analysis With Other Multivariate Methods.- Interpretation of the Cluster Solution.- ANOVA.- MANOVA and Discriminant Analysis.- Principal Components and Factor Analysis.- Principal Components Analysis Prior to Cluster Analysis.- 10.2.4 Other Clustering Methods.- Partitioning Methods.- The k-Means Algorithm.- Selecting the Initial Partition.- Classification Typologies and Q-Sort Methods.- Density Methods.- Clumping Techniques or Fuzzy Clustering.- 10.2.5 Cluster Validity and Cluster Analysis Methodology.- Cluster Validity.- Monte Carlo Studies.- The Underlying Cluster Population.- Evaluation of Clustering Algorithms.- Evaluation of Internal Criterion Measures.- Cluster Choice.- Variable Standardization Procedures.- On the Measurement of Cluster Recovery and External Measurement Criteria.- 10.2.6 Other Sources of Information.- 10.3 Multidimensional Scaling.- 10.3.1 Metric Multidimensional Scaling.- Constructing a Positive Semidefinite Matrix Based on D.- The Fundamental Theorem of MDS.- The MDS Solution.- An Approximate Solution.- Metric Multidimensional Scaling Beginning with D.- Relation to Cluster Analysis.- Improving the Solution.- Using Similarities.- Metric MDS and Principal Coordinates Analysis.- Relation to Cluster Analysis.- An Alternative Derivation for A.- The Additive Constant Problem.- Application of Metric Scaling.- 10.3.2 Nonmetric Multidimensional Scaling.- Ordinal Scaling.- Shepard-Kruskal Algorithm.- The Nonmetric Phase and Monotone Regression.- The Pool Adjacent Violators Algorithm.- Ties and Types of Monotonicity.- Ties in the Original Dissimilarities.- The Metric Phase.- The Evaluation Phase.- Selection and Interpretation Phase.- Monte Carlo Studies of the Stress Function.- The ALSCAL Algorithm.- 10.3.3 Other Scaling Models.- Individual Difference Models.- Preference Models and Multidimensional Unfolding.- 10.3.4 Other Sources of Information.- Cited Literature and References.- Exercises for Chapter 10.- Questions for Chapter 10.- 1. Matrix Algebra.- 1.1 Matrices.- Matrix.- Transpose of a Matrix.- Row Vector and Column Vector.- Square Matrix.- Symmetric Matrix.- Diagonal Elements.- Trace of a Matrix.- Null or Zero Matrix.- Identity Matrix.- Diagonal Matrix.- Submatrix.- 1.2 Matrix Operations.- Equality of Matrices.- Addition of Matrices.- Additive Inverse.- Scalar Multiplication of a Matrix.- Product of Two Matrices.- Multiplicative Inverse.- Idempotent Matrix.- Kronecker Product.- 1.3 Determinants and Rank.- Determinant.- Nonsingular.- Relation Between Inverse.- and Determinant.- Rank of a Matrix.- 1.4 Quadratic Forms and Positive Definite Matrices.- Quadratic Form.- Congruent Matrix.- Positive Definite.- Positive Semidefinite.- Negative Definite.- Non-negative Definite.- 1.5 Partitioned Matrices.- Product of Partitioned Matrices.- Inverse of a Parti-tioned Matrix.- Determinant of a Partitioned Matrix.- 1.6 Expectations of Random Matrices.- 1.7 Derivatives of Matrix Expressions.- 2. Linear Algebra.- 2.1 Geometric Representation for Vectors.- n Dimensional Space.- Directed Line Segment.- Coordinates.- Addition of Vectors.- Scalar Multiplication.- Length of a Vector.- Angle Between Vectors.- Orthogonal Vectors.- Projection.- 2.2 Linear Dependence And Linear Transformations.- Linearly Dependent Vectors.- Linearly Independent Vectors.- Basis for an n-Dimensional Space.- Generation of a Vector Space and Rank of a Matrix.- Linear Transformation.- Orthogonal Transformation.- Rotation.- Orthogonal Matri.- 2.3 Systems of Equations.- Solution Vector for a System of Equations.- Homoge-neous Equations - Trivial and Nontrivial Solutions.- 2.4 Column Spaces.- Projection Operators and Least.- Squares.- Column Space.- Orthogonal Complement.- Projection.- Ordinary Least Squares Solution Vector.- Idempotent Matrix - Projection Operator.- 3. Eigenvalue Structure and Singular Value Decomposition.- 3.1 Eigenvalue Structure for Square Matrices.- Eigenvalues and Eigenvectors.- Characteristic Polynomial.- Characteristic Roots.- Latent Roots.- Eigen-values.- Eigenvalues and Eignevectors for Real Symmetric Matrices and Some Properties.- Spectral Decomposition.- Matrix Approximation.- Eigenvalues for Nonnegative Definite Matrices.- 3.2 Singular Value Decomposition.- Left and Right Singular Vectors.- Complete Singular Value Decomposition.- Generalized Singular Value Decomposition.- Relationship to Spectral Decomposition and Eigenvalues.- Data Appendix For Volume II.- Data Set V1.- Data Set V2.- Data Set V3.- Data Set V4.- Data Set V5.- Data Set V6.- Data Set V7.- Data Set V8.- Data Set V9.- Data Set V10.- Data Set Vll.- Data Set V12.- Data Set V13.- Data Set V14.- Data Set V15.- Data Set V16.- Data Set V17.- Data Set V18.- Data Set V19.- Data Set V20.- Data Set V21.- Data Set V22.- Table V1.- Table V2.- Table V3.- Table V4.- Table V5.- Table V6.- Table V7.- Table V8.- Table V9.- Table V10.- Table V11.- Table V12.- Table V13.- Table V14.- Table V15.- Table V16.- Table V17.- Table V18.- Table V19.- Table V20.- Table V21.- Table V22.- Author Index.