Applied Multivariate Data Analysis

6 Contingency Tables.- 6.1 Multivariate Data Analysis Data Matrices and Measurement Scales.- 6.2 Two-Dimensional Contingency Tables.- 6.3 Multidimensional Contingency Tables.- 6.4 The Weighted Least Squares Approach.- 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.- 7.2 The Multivariate Normal Distribution.- 7.3 Testing for Normality Outliers and Robust Estimation.- 7.4 Inference for the Multivariate Normal.- 7.5 Multivariate Regression and Canonical Correlation.- 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.- 8.2 Discriminant Analysis.- 8.3 Qualitative Response Regression Models and Logistic Regression.- 9 Principal Components Factors and Correspondence Analysis.- 9.1 Principal Components.- 9.2 The Exploratory Factor Analysis Model.- 9.3 Singular Value Decomposition and Matrix Approximation.- 9.4 Correspondence Analysis.- 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.- 10.2 Cluster Analysis.- 10.3 Multidimensional Scaling.- 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 SomeProperties.- 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.

"On the whole this volume on applied multivariate data analysis is a comprehensive treatise which will support students and teachers to a full extent in their coursework and researchers will find an easy ready-made material for the analysis of their multivariate data to arrive at correct conclusions. This is a masterpiece text." (Zentralblatt fuer Mathematik)