Applied Multivariate Data Analysis

A Second Course in Statistics The past decade has seen a tremendous increase in the use of statistical data analysis and in the availability of both computers and statistical software. Business and government professionals, as well as academic researchers, are now regularly employing techniques that go far beyond the standard two-semester, introductory course in statistics. Even though for this group of users shorl courses in various specialized topics are often available, there is a need to improve the statistics training of future users of statistics while they are still at colleges and universities. In addition, there is a need for a survey reference text for the many practitioners who cannot obtain specialized courses. With the exception of the statistics major, most university students do not have sufficient time in their programs to enroll in a variety of specialized one-semester courses, such as data analysis, linear models, experimental de sign, multivariate methods, contingency tables, logistic regression, and so on. There is a need for a second survey course that covers a wide variety of these techniques in an integrated fashion. It is also important that this sec ond course combine an overview of theory with an opportunity to practice, including the use of statistical software and the interpretation of results obtained from real däta.

Includes supplementary material: sn.pub/extras

Inhalt
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.