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Preface | |
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Acknowledgments | |
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Introduction | |
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Why Multivariate Analysis? | |
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Prerequisites | |
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Objectives | |
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Basic Types of Data And Analysis | |
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Matrix Algebra | |
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Introduction | |
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Notation and Basic Definitions | |
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Operations | |
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Partitioned Matrices | |
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Rank | |
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Inverse | |
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Positive Definite Matrices | |
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Determinants | |
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Trace | |
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Orthogonal Vectors and Matrices | |
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Eigenvalues and Eigenvectors | |
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Kronecker and VEC Notation | |
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Problems | |
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Characterizing and Displaying Multivariate Data | |
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Mean and Variance of a Univariate Random Variable | |
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Covariance and Correlation Of Bivariate Random Variables | |
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Scatter Plots of Bivariate Samples | |
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Graphical Displays for Multivariate Samples | |
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Dynamic Graphics | |
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Mean Vectors | |
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Covariance Matrices | |
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Correlation Matrices | |
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Mean Vectors and Covariance Matrices for Subsets of Variables | |
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Two Subsets | |
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Three or More Subsets | |
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Linear Combinations of Variables | |
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Sample Properties | |
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Population Properties | |
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Measures of Overall Variability | |
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Estimation of Missing Values | |
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Distance Between Vectors | |
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Problems | |
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The Multivariate Normal Distribution | |
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Multivariate Normal Density Function | |
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Properties of Multivariate Normal Random Variables | |
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Estimation in the Multivariate Normal | |
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Assessing Multivariate Normality | |
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Transformations to Normality | |
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Outliers | |
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Problems | |
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Tests on One or Two Mean Vectors | |
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Multivariate Versus Univariate Tests | |
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Tests on � With ??Known | |
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Tests on � When ??is Unknown | |
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Comparing two Mean Vectors | |
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Tests on Individual Variables Conditional on Rejection of H0 by the T2-test | |
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Computation of T2 | |
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Paired Observations Test | |
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Test for Additional Information | |
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Profile Analysis | |
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Profile Analysis | |
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Problems | |
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Multivariate Analysis of Variance | |
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One-way Models | |
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Comparison of the Four Manova Test Statistics | |
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Contrasts | |
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Tests on Individual Variables Following Rejection of H0 by the Overall Manova Test | |
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Two-Way Classification | |
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Other Models | |
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Checking on the Assumptions | |
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Profile Analysis | |
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Repeated Measures Designs | |
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Growth Curves | |
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Tests on a Subvector | |
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Problems | |
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Tests on Covariance Matrices | |
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Introduction | |
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Testing a Specified Pattern for ∑ | |
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Tests Comparing Covariance Matrices | |
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Tests of Independence | |
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Problems | |
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Discriminant Analysis: Description of Group Separation | |
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Introduction | |
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The Discriminant Function for two Groups | |
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Relationship Between two-group Discriminant Analysis and Multiple Regression | |
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Discriminant Analysis for Several Groups | |
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Standardized Discriminant Functions | |
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Tests of Significance | |
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Interpretation of Discriminant Functions | |
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Scatter Plots | |
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Stepwise Selection of Variables | |
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Problems | |
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Classification Analysis: Allocation of Observations to Groups | |
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Introduction | |
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Classification into two Groups | |
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Classification into Several Groups | |
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Estimating Misclassification Rates | |
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Improved Estimates of Error Rates | |
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Subset Selection | |
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Nonparametric Procedures | |
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Problems | |
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Multivariate Regression | |
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Introduction | |
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Multiple Regression: Fixed X’s | |
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Multiple Regression: Random X’s | |
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Multivariate Multiple Regression: Estimation | |
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Multivariate Multiple Regression: Hypothesis Tests | |
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Multivariate Multiple Regression: Prediction | |
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Measures of Association Between the Y’s and the X’s | |
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Subset Selection | |
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Multivariate Regression: Random X’s | |
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Problems | |
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Canonical Correlation | |
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Introduction | |
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Canonical Correlations and Canonical Variates | |
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Properties of Canonical Correlations | |
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Tests of Significance | |
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Interpretation | |
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Relationships of Canonical Correlation Analysis to Other Multivariate Problems | |
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Principal Component Analysis | |
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Introduction | |
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Geometric and Algebraic Bases of Principal Components | |
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Principal Components and Perpendicular Regression | |
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Plotting of Principal Components | |
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Principal Components from the Correlation Matrix | |
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Deciding How Many Components to Retain | |
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Information in the Last Few Principal Components | |
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Interpretation of Principal Components | |
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Selection of Variables | |
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Problems | |
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Exploratory Factor Analysis | |
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Introduction | |
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Orthogonal Factor Model | |
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Estimation of Loadings and Communalities | |
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Choosing the Number of Factors, m | |
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Rotation | |
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Factor Scores | |
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Validity of the Factor Analysis Model | |
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Relationship of Factor Analysis to Principal Component Analysis | |
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Problems | |
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Confirmatory Factor Analysis | |
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Introduction | |
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Model Specification and Identification | |
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Parameter Estimation and Model Assessment | |
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Inference for Model Parameters | |
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Factor Scores | |
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Problems | |
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Cluster Analysis | |
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Introduction | |
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Measures of Similarity or Dissimilarity | |
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Hierarchical Clustering | |
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Nonhierarchical Methods | |
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Choosing the Number of Clusters | |
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Cluster Validity | |
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Clustering Variables | |
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Problems | |
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Graphical Procedures | |
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Multidimensional Scaling | |
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Correspondence Analysis | |
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Biplots | |
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Problems | |
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Tables | |
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Answers and Hints to Problems | |
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Data Sets and SAS Files | |
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References | |
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Index | |