| |
| |
| |
Getting Started | |
| |
| |
| |
Aspects of Multivariate Analysis | |
| |
| |
Applications of Multivariate Techniques | |
| |
| |
The Organization of Data | |
| |
| |
Data Displays and Pictorial Representations | |
| |
| |
Distance | |
| |
| |
Final Comments | |
| |
| |
| |
Matrix Algebra and Random Vectors | |
| |
| |
Some Basics of Matrix and Vector Algebra | |
| |
| |
Positive Definite Matrices | |
| |
| |
A Square-Root Matrix | |
| |
| |
Random Vectors and Matrices | |
| |
| |
Mean Vectors and Covariance Matrices | |
| |
| |
Matrix Inequalities and Maximization | |
| |
| |
| |
A Vectors and Matrices: Basic Concepts | |
| |
| |
| |
Sample Geometry and Random Sampling | |
| |
| |
The Geometry of the Sample | |
| |
| |
Random Samples and the Expected Values of the Sample Mean and Covariance Matrix | |
| |
| |
Generalized Variance | |
| |
| |
Sample Mean, Covariance, and Correlation as Matrix Operations | |
| |
| |
Sample Values of Linear Combinations of Variables | |
| |
| |
| |
The Multivariate Normal Distribution | |
| |
| |
The Multivariate Normal Density and Its Properties | |
| |
| |
Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation | |
| |
| |
The Sampling Distribution of 'X and S | |
| |
| |
Large-Sample Behavior of 'X and S | |
| |
| |
Assessing the Assumption of Normality | |
| |
| |
Detecting Outliners and Data Cleaning | |
| |
| |
Transformations to Near Normality | |
| |
| |
| |
Inferences About Multivariate Means And Linear Models | |
| |
| |
| |
Inferences About a Mean Vector | |
| |
| |
The Plausibility of ï¿½Ç m0 as a Value for a Normal Population Mean | |
| |
| |
Hotelling's T | |
| |
| |
| |
and Likelihood Ratio Tests | |
| |
| |
Confidence Regions and Simultaneous Comparisons of Component Means | |
| |
| |
Large Sample Inferences about a Population Mean Vector | |
| |
| |
Multivariate Quality Control Charts | |
| |
| |
Inferences about Mean Vectors When Some Observations Are Missing | |
| |
| |
Difficulties Due To Time Dependence in Multivariate Observations | |
| |
| |
| |
A Simultaneous Confidence Intervals and Ellipses as Shadows of the p-Dimensional Ellipsoids | |
| |
| |
| |
Comparisons of Several Multivariate Means | |
| |
| |
Paired Comparisons and a Repeated Measures Design | |
| |
| |
Comparing Mean Vectors from Two Populations | |
| |
| |
Comparison of Several Multivariate Population Means (One-Way MANOVA) | |
| |
| |
Simultaneous Confidence Intervals for Treatment Effects | |
| |
| |
Two-Way Multivariate Analysis of Variance | |
| |
| |
Profile Analysis | |
| |
| |
Repealed Measures, Designs, and Growth Curves | |
| |
| |
Perspectives and a Strategy for Analyzing Multivariate Models | |
| |
| |
| |
Multivariate Linear Regression Models | |
| |
| |
The Classical Linear Regression Model | |
| |
| |
Least Squares Estimation | |
| |
| |
Inferences About the Regression Model | |
| |
| |
Inferences from the Estimated Regression Function | |
| |
| |
Model Checking and Other Aspects of Regression | |
| |
| |
Multivariate Multiple Regression | |
| |
| |
The Concept of Linear Regression | |
| |
| |
Comparing the Two Formulations of the Regression Model | |
| |
| |
Multiple Regression Models with Time Dependant Errors | |
| |
| |
| |
A The Distribution of the Likelihood Ratio for the Multivariate Regression Model | |
| |
| |
| |
Analysis Of A Covariance Structure | |
| |
| |
| |
Principal Components | |
| |
| |
Population Principal Components | |
| |
| |
Summarizing Sample Variation by Principal Components | |
| |
| |
Graphing the Principal Components | |
| |
| |
Large-Sample Inferences | |
| |
| |
Monitoring Quality with Principal Components | |
| |
| |
| |
A The Geometry of the Sample Principal Component Approximation | |
| |
| |
| |
Factor Analysis and Inference for Structured Covariance Matrices | |
| |
| |
The Orthogonal Factor Model | |
| |
| |
Methods of Estimation | |
| |
| |
Factor Rotation | |
| |
| |
Factor Scores | |
| |
| |
Perspectives and a Strategy for Factor Analysis | |
| |
| |
Structural Equation Models | |
| |
| |
| |
A Some Computational Details for Maximum Likelihood Estimation | |
| |
| |
| |
Canonical Correlation Analysis | |
| |
| |
Canonical Variates and Canonical Correlations | |
| |
| |
Interpreting the Population Canonical Variables | |
| |
| |
The Sample Canonical Variates and Sample Canonical Correlations | |
| |
| |
Additional Sample Descriptive Measures | |
| |
| |
Large Sample Inferences | |
| |
| |
| |
Classification And Grouping Techniques | |
| |
| |
| |
Discrimination and Classification | |
| |
| |
Separation and Classification for Two Populations | |
| |
| |
Classifications with Two Multivariate Normal Populations | |
| |
| |
Evaluating Classification Functions | |
| |
| |
Fisher's Discriminant Functionï¿½Ç Ã±Separation of Populations | |
| |
| |
Classification with Several Populations | |
| |
| |
Fisher's Method for Discriminating among Several Populations | |
| |
| |
Final Comments | |
| |
| |
| |
Clustering, Distance Methods and Ordination | |
| |
| |
Similarity Measures | |
| |
| |
Hierarchical Clustering Methods | |
| |
| |
Nonhierarchical Clustering Methods | |
| |
| |
Multidimensional Scaling | |
| |
| |
Correspondence Analysis | |
| |
| |
Biplots for Viewing Sample Units and Variables | |
| |
| |
Procustes Analysis: A Method for Comparing Configurations | |
| |
| |
Appendix | |
| |
| |
Standard Normal Probabilities | |
| |
| |
Student's t-Distribution Percentage Points | |
| |
| |
ï¿½Ç c2 Distribution Percentage Points | |
| |
| |
F-Distribution Percentage Points | |
| |
| |
F-Distribution Percentage Points (ï¿½Ç a = .10) | |
| |
| |
F-Distribution Percentage Points (ï¿½Ç a = .05) | |
| |
| |
F-Distribution Percentage Points (ï¿½Ç a = .01) | |
| |
| |
Data Index | |
| |
| |
Subject Index | |