DRAFT

 

(NOTE: Each chapter begins with an Introduction, and concludes with Exercises and References.)

I. GETTING STARTED.

1. Aspects of Multivariate Analysis.

 

Applications of Multivariate Techniques. The Organization of Data. Data Displays and Pictorial Representations. Distance. Final Comments.

 

 

2. 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.

3. 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. Supplement 2A Vectors and Matrices: Basic Concepts.  

 

4. 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.

 

II. INFERENCES ABOUT MULTIVARIATE MEANS AND LINEAR MODELS.

5. Inferences About a Mean Vector.

 

The Plausibility of …m0 as a Value for a Normal Population Mean. Hotelling's T 2 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. Supplement 5A Simultaneous Confidence Intervals and Ellipses as Shadows of the p-Dimensional Ellipsoids.

 

6. 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 Repealed Measures, Designs, and Growth Curves.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.

 

7. 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. Supplement 7A The Distribution of the Likelihood Ratio for the Multivariate Regression Model.

 

III. ANALYSIS OF A COVARIANCE STRUCTURE.

8. Principal Components.

 

Population Principal Components. Summarizing Sample Variation by Principal Components. Graphing the Principal Components. Large-Sample Inferences. Monitoring Quality with Principal Components. Supplement 8A The Geometry of the Sample Principal Component Approximation.

 

9. 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. Supplement 9A Some Computational Details for Maximum Likelihood Estimation.

 

10. Canonical Correlation Analysis

 

Canonical Variates and Canonica

• Accessible level:– Presents the concepts and methods of multivariate analysis at a level that is readily understandable by readers who have taken two or more statistics courses. – Emphasizes the applications of multivariate methods and, consequently, they have made the mathematics as palatable as possible. The use of calculus is avoided. • Organization and approach:– Contains the methodological "tools" of multivariate analysis in chapters 5 through 12. – These chapters represent the heart of the book, but they cannot be assimilated without much of the material in the introductory chapters 1-4. – The approach in the methodological chapters (chapters 5-12) is to keep the discussion direct and uncluttered. Typically, the authors start with a formulation of the population models, delineate the corresponding sample results, and liberally illustrate everything with examples. • An abundance of examples and exercises based on real data – Includes, in some cases, snapshots of the corresponding SAS output. – Examples include: Two-way MANOVA for plastic film data (Example 6.11), Principal component analysis of turtle carapace data (Example 8.4), Factor analysis of consumer preference data (Example 9.9), Discriminant analysis of business school admission data (Example 11.11) and others. Highlights and boxes important results and formulas. • Targeted presentation of key concepts:– Directs students’ attention to essential material. – Examples include: Simultaneous confidence region and intervals in Section 6.2, Multivariate linear regression model in Section 7.7, Sample principal components and their properties in Section 8.3, Classification rules in Section 11.3 and others. • Emphasis on applications of multivariate methods. • A clear and insightful explanation of multivariate techniques. • Ample student assistance in navigating difficult topics – Examples include: – Simple numerical calculations to illustrate one-way MANOVA (Example 6.8) – K-means clustering (Example 12.13) and correspondence analysis (Example 12.18) – A clear distinction between population models and the corresponding sample results in all the methodological chapters – Many real data based examples with accompanying graphics and/or computer output (Example 1.8 Linked scatter plots and brushing with Paper Quality Data, Example 6.11) – Two-way MANOVA with Plastic Film Data, Example 10.5 – Canonical correlation analysis of Job Satisfaction Data, Example 12.15 – Multidimensional scaling of Public Utilities Data, and others) – Several “Strategy” and “Final Comments” sections to tie together chapter material (A Strategy for the Multivariate Comparison of Treatments, Perspectives and a Strategy for Factor Analysis, Final Comments-Nonhierarchical (clustering)). – Long and difficult proofs of important results have been relegated to a website.

• Twelve new real data sets (e.g. National track records for men andwomen, Psychological profile data, Car body assembly data, Concho water snake data, Stock price data, Census track data, Mali family farm data and others.)
• Thirty seven new exercises and twenty revised exercises (Most of new and revised exercises based on new data sets.)
• Four new examples and fifteen revised examples (New and revised examples based on new data sets or theoretical concepts new to this edition.)
• Six new or expanded sections (e.g. Section 6.6 Testing for Equalityof Covariance Matrices, Section 11.7 Logistic Regression and Classification, Section 12.5 Clustering Based on Statistical Models, Expanded Section 6.3 to include “An Approximation to the Distribution of T2 for Normal Populations When Sample Sizes are not Large,” Expanded Sections 7.6 and 7.7 to include Akaike’s Information Criterion, Expanded Section 12.8 to include material on new biplots.
• Consolidated old sections 11.3 and 11.5 on two group discriminant analysis into single section 11.3.
• To make the text more easily accessible to a wider audience who need to use the methods of applied multivariate analysis, we have removed several long proofs and placed them on the website.
• All data sets are available on the website for easy accessibility