1. APPLIED MULTIVARIATE METHODS
  1.1 An Overview of Multivariate Methods
   Variable-and Individual-Directed Techniques
   Creating New Variables
   Principal Components Analysis
   Factor Analysis
   Discriminant Analysis
   Canonical Discriminant Analysis
   Logistic Regression
   Cluster Analysis
   Multivariate Analysis of Variance
   Canonical Variates Analysis
   Canonical Correlation Analysis
   Where to Find the Preceding Topics
  1.2 Two Examples
   Independence of Experimental Units
  1.3 Types of Variables
  1.4 Data Matrices and Vectors
   Variable Notation
   Data Matrix
   Data Vectors
   Data Subscripts
  1.5 The Multivariate Normal Distribution
   Some Definitions
   Summarizing Multivariate Distributions
   Mean Vectors and Variance-Covariance Matrices
   Correlations and Correlation Matrices
   The Multivariate Normal Probability Density Function
   Bivariate Normal Distributions
  1.6 Statistical Computing
   Cautions About Computer Usage
   Missing Values
   Replacing Missing Values by Zeros
   Replacing Missing Values by Averages
   Removing Rows of the Data Matrix
   Sampling Strategies
   Data Entry Errors and Data Verification
  1.7 Multivariate Outliers Locating Outliers Dealing with Outliers Outliers May Be Influential
  1.8 Multivariate Summary Statistics
  1.9 Standardized Data and/or Z Scores
   Exercises
 2. SAMPLE CORRELATIONS
  2.1 Statistical Tests and Confidence Intervals
   Are the Correlations Large Enough to Be Useful?
   Confidence Intervals by the Chart Method
   Confidence Intervals by Fisher's Approximation
   Confidence Intervals by Ruben's Approximation
   Variable Groupings Based on Correlations
   Relationship to Factor Analysis
  2.2 Summary
   Exercises
 3. MULTIVARIATE DATA PLOTS
  3.1 Three-Dimensional Data Plots
  3.2 Plots of Higher Dimensional Data
   Chernoff Faces
   Star Plots and Sun-Ray Plots
   Andrews' Plots
   Side-by-Side Scatter Plots
  3.3 Plotting to Check for Multivariate Normality
   Summary
   Exercises
 4. EIGENVALUES AND EIGENVECTORS
  4.1 Trace and Determinant
   Examples
  4.2 Eigenvalues
  4.3 Eigenvectors
   Positive Definite and Positive Semidefinite Matrices
  4.4 Geometric Descriptions (p = 2)
   Vectors
   Bivariate Normal Distributions
  4.5 Geometric Descriptions (p = 3)
   Vectors
   Trivariate Normal Distributions
  4.6 Geometric Descriptions (p > 3)
   Summary
   Exercises
 5. PRINCIPAL COMPONENTS ANALYSIS
  5.1 Reasons for Using Principal Components Analysis
   Data Screening
   Clustering
   Discriminant Analysis
   Regression
  5.2 Objectives of Principal Components Analysis
  5.3 Principal Components Analysis on the Variance-Covariance Matrix Σ
   Principal Component Scores
   Component Loading Vectors
  5.4 Estimation of Principal Components
   Estimation of Principal Component Scores
  5.5 Determining the Number of Principal Components
   Method 1
   Method 2
  5.6 Caveats
  5.7 PCA on the Correlation Matrix P
   Principal Component Scores
   Component Correlation Vectors
   Sample Correlation Matrix
   Determining the Number of Principal Components
  5.8 Testing for Independence of the Original Variables
  5.9 Structural Relationships
  5.10 Statistical Computing Packages
   SASR PRINCOMP Procedure
   Principal Components Analysis Using Factor Analysis
   Programs
   PCA with SPSS's FACTOR Procedure
   Summary
   Exercises
 6. FACTOR ANALYSIS
  6.1 Objectives of Factor Analysis
  6.2 Caveats
  6.3 Some History of Factor Analysis
  6.4 The Factor Analysis Model
   Assumptions
   Matrix Form of the Factor Analysis Model
   Definitions of Factor Analysis Terminology
  6.5 Factor Analysis Equations
   Nonuniqueness of the Factors
  6.6 Solving the Factor Analysis Equations
  6.7 Choosing the Appropriate Number of Factors
   Subjective Criteria
   Objective Criteria
  6.8 Computer Solutions of the Factor Analysis Equations
   Principal Factor Method on R
   Principal Factor Method with Iteration
  6.9 Rotating Factors
   Examples (m = 2)
   Rotation Methods
   The Varimax Rotation Method
  6.10 Oblique Rotation Methods
  6.11 Factor Scores
   Bartlett's Method or the Weighted Least-Squares Method
   Thompson's Method or the Regression Method
   Ad Hoc Methods
   Summary
   Exercises
 7. DISCRIMINANT ANALYSIS
  7.1 Discrimination for Two Multivariate Normal Populations
   A Likelihood Rule
   The Linear Discriminant Function Rule
   A Mahalanobis Distance Rule
   A Posterior Probability Rule
   Sample Discriminant Rules
   Estimating Probabilities of Misclassification
   Resubstitution Estimates
   Estimates from Holdout Data
   Cross-Validation Estimates
  7.2 Cost Functions and Prior Probabilities (Two Populations)
  7.3 A General Discriminant Rule (Two Populations)
   A Cost Function
   Prior Probabilities
   Average Cost of Misclassification
   A Bayes Rule
   Classification Functions
   Unequal Covariance Matrices
   Tricking Computing Packages
  7.4 Discriminant Rules (More than Two Populations)
   Basic Discrimination
  7.5 Variable Selection Procedures
   Forward Selection Procedure
   Backward Elimination Procedure
   Stepwise Selection Procedure
   Recommendations
   Caveats
  7.6 Canonical Discriminant Functions
   The First Canonical Function
   A Second Canonical Function
   Determining the Dimensionality of the Canonical Space
   Discriminant Analysis with Categorical Predictor Variables
  7.7 Nearest Neighbor Discriminant Analysis
  7.8 Classification Trees
   Summary
   Exercises
 8. LOGISTIC REGRESSION METHODS
  8.1 Logistic Regression Model
  8.2 The Logit Transformation
   Model Fitting
  8.3 Variable Selection Methods
  8.4 Logistic Discriminant Analysis (More Than Two Populations)
   Logistic Regression Models
   Model Fitting
   Another SAS LOGISTIC Analysis
   Exercises
 9. CLUSTER ANALYSIS
  9.1 Measures of Similarity and Dissimilarity
   Ruler Distance
   Standardized Ruler Distance
   A Mahalanobis Distance
   Dissimilarity Measures
  9.2 Graphical Aids in Clustering
   Scatter Plots
   Using Principal Components
   Andrews' Plots
   Other Methods
  9.3 Clustering Methods
   Nonhierarchical Clustering Methods
   Hierarchical Clustering
   Nearest Neighbor Method
   A Hierarchical Tree Diagram
   Other Hierarchical Clustering Methods
   Comparisons of Clustering Methods
   Verification of Clustering Methods
   How Many Clusters?
   Beale's F-Type Statistic
   A Pseudo Hotelling's T2 Test
   The Cubic Clustering Criterion
   Clustering Order
   Estimating the Number of Clusters
   Principal Components Plots
   Clustering with SPSS
   SAS's FASTCLUS Procedure
  9.4 Multidimensional Scaling
   Exercises
 10. MEAN VECTORS AND VARIANCE-COVARIANCE MATRICES
  10.1 Inference Procedures for Variance-Covariance Matrices
   A Test for a Specific Variance-Covariance Matrix
   A Test for SphericityA Test for Compound Symmetry
   A Test for the Huynh-Feldt Conditions
   A Test for Independence
   A Test for Independence of Subsets of Variables
   A Test for the Equality of Several Variance-Covariance
   Matrices
  10.2 Inference Procedures for a Mean Vector
   Hotelling's T2 Statistic
   Hypothesis Test for μ
   Confidence Region for μ
   A More General Result
   Special Case—A Test of Symmetry
   A Test for Linear Trend
   Fitting a Line to Repeated Measures
   Multivariate Quality Control
  10.3 Two Sample Procedures
   Repeated Measures Experiments
  10.4 Profile Analyses
  10.5 Additional Two-Group Analyses
   Paired Samples
   Unequal Variance-Covariance Matrices
   Large Sample Sizes
   Small Sample Sizes
   Summary
   Exercises
 11. MULTIVARIATE ANALYSIS OF VARIANCE
  11.1 MANOVA
   MANOVA Assumptions
   Test Statistics
   Test Comparisons
   Why Do We Use MANOVAs?
   A Conservative Approach to Multiple Comparisons
  11.2 Dimensionality of the Alternative Hypothesis
  11.3 Canonical Variates Analysis
   The First Canonical Variate
   The Second Canonical Variate
   Other Canonical Variates
  11.4 Confidence Regions for Canonical Variates
   Summary
   Exercises
 12. PREDICTION MODELS AND MULTIVARIATE REGRESSION
  12.1 Multiple Regression
  12.2 Canonical Correlation Analysis
   Two Sets of Variables
   The First Canonical Correlation
   The Second Canonical Correlation
   Number of Canonical Correlations
   Estimates
   Hypothesis Tests on the Canonical Correlations
   Interpreting Canonical Functions
   Canonical Correlation Analysis with SPSS
  12.3 Factor Analysis and Regression
   Summary
   Exercises
 APPENDIX A: MATRIX RESULTS
  A.1 Basic Definitions and Rules of Matrix Algebra
  A.2 Quadratic Forms
  A.3 Eigenvalues and Eigenvectors
  A.4 Distances and Angles
  A.5 Miscellaneous Results
 APPENDIX B: WORK ATTITUDES SURVEY
  B.1 Data File Structure
  B.2 SPSS Data Entry Commands
  B.3 SAS Data Entry Commands
 APPENDIX C: FAMILY CONTROL STUDY
 REFERENCES
 Index