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| Preface | |
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| Introduction to Multivariate Statistics | |
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| Definition of Multivariate Statistics | |
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| Relationship of Multivariate Statistics to Univariate Statistics | |
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| Choice of Variables and Multivariate Method, and the Concept of Optimal Linear Combination | |
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| Data for Multivariate Analyses | |
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| Three Fundamental Matrices in Multivariate Statistics | |
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| Covariance Matrix | |
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| Correlation Matrix | |
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| Sums-of-Squares and Cross-Products Matrix | |
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| Illustration Using Statistical Software | |
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| Elements of Matrix Theory | |
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| Matrix Definition | |
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| Matrix Operations, Determinant, and Trace | |
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| Using SPSS and SAS for Matrix Operations | |
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| General Form of Matrix Multiplications With Vector, and Representation of the Covariance, Correlation, and Sum-of-Squares and Cross-Product Matrices | |
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| Linear Modeling and Matrix Multiplication | |
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| Three Fundamental Matrices of Multivariate Statistics in Compact Form | |
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| Raw Data Points in Higher Dimensions, and Distance Between Them | |
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| Data Screening and Preliminary Analyses | |
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| Initial Data Exploration | |
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| Outliers and the Search for Them | |
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| Univariate Outliers | |
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| Multivariate Outliers | |
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| Handling Outliers: A Revisit | |
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| Checking of Variable Distribution Assumptions | |
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| Variable Transformations | |
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| Multivariate Analysis of Group Differences | |
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| A Start-Up Example | |
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| A Definition of the Multivariate Normal Distribution | |
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| Testing Hypotheses About a Multivariate Mean | |
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| The Case of Known Covariance Matrix | |
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| The Case of Unknown Covariance Matrix | |
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| Testing Hypotheses About Multivariate Means of Two Groups | |
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| Two Related or Matched Samples (Change Over Time) | |
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| Two Unrelated (Independent) Samples | |
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| Testing Hypotheses About Multivariate Means in One-Way and Higher Order Designs (Multivariate Analysis of Variance, MANOVA) | |
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| Statistical Significance Versus Practical Importance | |
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| Higher Order MANOVA Designs | |
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| Other Test Criteria | |
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| MANOVA Follow-Up Analyses | |
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| Limitations and Assumptions of MANOVA | |
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| Repeated Measure Analysis of Variance | |
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| Between-Subject and Within-Subject Factors and Designs | |
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| Univariate Approach to Repeated Measure Analysis | |
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| Multivariate Approach to Repeated Measure Analysis | |
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| Comparison of Univariate and Multivariate Approaches to Repeated Measure Analysis | |
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| Analysis of Covariance | |
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| Logic of Analysis of Covariance | |
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| Multivariate Analysis of Covariance | |
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| Step-Down Analysis (Roy-Bargmann Analysis) | |
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| Assumptions of Analysis of Covariance | |
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| Principal Component Analysis | |
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| Introduction | |
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| Beginnings of Principal Component Analysis | |
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| How Does Principal Component Analysis Proceed? | |
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| Illustrations of Principal Component Analysis | |
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| Analysis of the Covariance Matrix [Sigma] (S) of the Original Variables | |
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| Analysis of the Correlation Matrix P (R) of the Original Variables | |
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| Using Principal Component Analysis in Empirical Research | |
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| Multicollinearity Detection | |
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| PCA With Nearly Uncorrelated Variables Is Meaningless | |
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| Can PCA Be Used as a Method for Observed Variable Elimination? | |
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| Which Matrix Should Be Analyzed? | |
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| PCA as a Helpful Aid in Assessing Multinormality | |
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| PCA as "Orthogonal" Regression | |
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| PCA Is Conducted via Factor Analysis Routines in Some Software | |
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| PCA as a Rotation of Original Coordinate Axes | |
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| PCA as a Data Exploratory Technique | |
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| Exploratory Factor Analysis | |
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| Introduction | |
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| Model of Factor Analysis | |
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| How Does Factor Analysis Proceed? | |
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| Factor Extraction | |
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| Principal Component Method | |
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| Maximum Likelihood Factor Analysis | |
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| Factor Rotation | |
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| Orthogonal Rotation | |
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| Oblique Rotation | |
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| Heywood Cases | |
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| Factor Score Estimation | |
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| Weighted Least Squares Method (Generalized Least Squares Method) | |
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| Regression Method | |
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| Comparison of Factor Analysis and Principal Component Analysis | |
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| Confirmatory Factor Analysis | |
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| Introduction | |
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| A Start-Up Example | |
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| Confirmatory Factor Analysis Model | |
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| Fitting Confirmatory Factor Analysis Models | |
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| A Brief Introduction to Mplus, and Fitting the Example Model | |
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| Testing Parameter Restrictions in Confirmatory Factor Analysis Models | |
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| Specification Search and Model Fit Improvement | |
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| Fitting Confirmatory Factor Analysis Models to the Mean and Covariance Structure | |
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| Examining Group Differences on Latent Variables | |
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| Discriminant Function Analysis | |
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| Introduction | |
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| What Is Discriminant Function Analysis? | |
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| Relationship of Discriminant Function Analysis to Other Multivariate Statistical Methods | |
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| Discriminant Function Analysis With Two Groups | |
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| Relationship Between Discriminant Function and Regression Analysis With Two Groups | |
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| Discriminant Function Analysis With More Than Two Groups | |
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| Tests in Discriminant Function Analysis | |
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| Limitations of Discriminant Function Analysis | |
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| Canonical Correlation Analysis | |
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| Introduction | |
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| How Does Canonical Correlation Analysis Proceed? | |
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| Tests and Interpretation of Canonical Variates | |
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| Canonical Correlation Approach to Discriminant Analysis | |
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| Generality of Canonical Correlation Analysis | |
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| An Introduction to the Analysis of Missing Data | |
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| Goals of Missing Data Analysis | |
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| Patterns of Missing Data | |
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| Mechanisms of Missing Data | |
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| Missing Completely at Random | |
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| Missing at Random | |
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| Ignorable Missingness and Nonignorable Missingness Mechanisms | |
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| Traditional Ways of Dealing With Missing Data | |
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| Listwise Deletion | |
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| Pairwise Deletion | |
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| Dummy Variable Adjustment | |
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| Simple Imputation Methods | |
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| Weighting Methods | |
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| Full Information Maximum Likelihood and Multiple Imputation | |
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| Examining Group Differences and Similarities in the Presence of Missing Data | |
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| Examining Group Mean Differences With Incomplete Data | |
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| Testing for Group Differences in the Covariance and Correlation Matrices With Missing Data | |
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| Multivariate Analysis of Change Processes | |
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| Introduction | |
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| Modeling Change Over Time With Time-Invariant and Time-Varying Covariates | |
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| Intercept-and-Slope Model | |
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| Inclusion of Time-Varying and Time-Invariant Covariates | |
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| An Example Application | |
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| Testing Parameter Restrictions | |
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| Modeling General Forms of Change Over Time | |
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| Level-and-Shape Model | |
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| Empirical Illustration | |
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| Testing Special Patterns of Growth or Decline | |
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| Possible Causes of Inadmissible Solutions | |
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| Modeling Change Over Time With Incomplete Data | |
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| Variable Naming and Order for Data Files | |
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| References | |
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| Author Index | |
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| Subject Index | |