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