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Like most academic authors, my views are a joint product of my teaching and my research. Needless to say, my views reflect the biases that I have acquired. One way to articulate the rationale (and limitations) of my biases is through the preface of a truly great text of a previous era, Cooley and Lohnes (1971, p. v). They draw a distinction between mathematical statisticians whose intel lect gave birth to the field of multivariate analysis, such as Hotelling, Bartlett, and Wilks, and those who chose to "concentrate much of their attention on methods of analyzing data in the sciences and of interpreting the results of statistical analysis . . . . (and) . . . who are more interested in the sciences than in mathematics, among other characteristics. " I find the distinction between individuals who are temperamentally "mathe maticians" (whom philosophy students might call "Platonists") and "scientists" ("Aristotelians") useful as long as it is not pushed to the point where one assumes "mathematicians" completely disdain data and "scientists" are never interested in contributing to the mathematical foundations of their discipline. I certainly feel more comfortable attempting to contribute in the "scientist" rather than the "mathematician" role. As a consequence, this book is primarily written for individuals concerned with data analysis. However, as noted in Chapter 1, true expertise demands familiarity with both traditions.
Contents
1 Introduction and Preview.- Overview.- Multivariate Analysis: A Broad Definition.- Multivariate Analysis: A Narrow Definition.- Some Important Themes.- The Role of Computers in Multivariate Analysis.- Choosing a Computer Package.- Problems in the Use of Computer Packages.- 2 Some Basic Statistical Concepts.- Overview.- Univariate Data Analysis.- Bivariate Data Analysis.- Statistical Control: A First Look at Multivariate Relations.- 3 Some Matrix Concepts.- Overview.- Basic Definitions.- Basic Matrix Operations.- An Application of Matrix Algebra.- More about Linear Combinations.- Eigenvalues and Eigenvectors.- 4 Multiple Regression and Correlation—Part 1. Basic concepts.- Overview.- Assumptions Underlying Multiple Regression.- Basic Goals of Regression Analysis.- The Case of Two Predictors.- The Case of More Than Two Predictors.- Inferential Tests.- Evaluating Alternative Equations.- Example 1—Perfect Prediction.- Example 2—Imperfect Prediction plus a Look at Residuals.- Example 3—Real Personality Assessment Data.- Alternative Approaches to Data Aggregation.- 5 Multiple Regression and Correlation—Part 2. Advanced Applications.- Overview.- Nonquantitative Variables.- The Simple Analysis of Variance (ANOVA).- Multiple Comparisons.- Evaluation of Quantitative Relations.- The Two-Way ANOVA.- The Analysis of Covariance (ANCOVA).- Repeated Measures, Blocked and Matched Designs.- Higher-Order Designs.- 6 Exploratory Factor Analysis.- Overview.- The Basic Factor Analytic Model.- Common Uses of Factor Analysis.- An Overview of the Exploratory Factoring Process.- Principal Components.- Factor Definition and Rotation.- The Common Factor Model.- An Example of the Common Factor Model.- Factor Scores.- Addendum: Constructing Correlation Matrices with a Desired FactorStructure.- 7 Confirmatory Factor Analysis.- Overview.- Comparing Factor Structures.- Oblique Multiple Groups Tests of Weak Structure.- LISREL Tests of Weak Substantive Models.- LISREL Tests of Strong Substantive Models.- Causal Models and Path Analysis.- Causal Models and LISREL.- Addendum: A Program to Obtain Oblique Multiple Groups Solutions.- 8 Classification Methods—Part 1. Forming Discriminant Axes.- Overview.- Discriminant Analysis with Two Groups and Two Predictors.- Discriminant Analysis with Two Predictors and Three Groups.- Discriminant Analysis—The General Case.- 9 Classification Methods—Part 2. Methods of Assignment.- Overview.- The Equal Variance Gaussian Model.- The Unequal Variance Gaussian Model.- Other Signal Detection Models.- Strategies for Individual Classification.- Alternative Strategies—An Overview.- A Numerical Example.- Classification Based on Salient Variables.- Discriminant Functions and Classification.- Classification Based on Distance Measures.- A Summary of Strategic Considerations in Classification.- 10 Classification Methods—Part 3. Inferential Considerations in the Manova.- Overview.- The Two-Group MANOVA and Hotelling's T2.- Tests of Vector Means with Multiple Groups.- The Simple MANOVA with Multiple Groups.- The Multivariate MANOVA.- The MANCOVA.- 11 Profile and Canonical Analysis.- Overview.- Profile Similarity.- Simple and Hierarchical Clustering.- Canonical Analysis.- 12 Analysis of Scales.- Overview.- Properties of Individual Items.- Test Reliability.- Numerical Example I: A Unifactor Scale.- Numerical Example II: A Two-Factor Scale.- Test Validity.- Appendix A—Tables of the Normal Curve.- Appendix D—Tables of Orthogonal Polynomial Coefficients.- Problems.- References.- Author Index.
