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| Applied Multivariate Methods | |
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| An Overview of Multivariate Methods | |
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| Two Examples | |
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| Types of Variables | |
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| Data Matrices and Vectors | |
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| The Multivariate Normal Distribution | |
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| Statistical Computing | |
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| Multivariate Outliers | |
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| Multivariate Summary Statistics | |
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| Standardized Data and/or z-Scores | |
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| Exercises | |
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| Sample Correlations | |
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| Statistical Tests and Confidence Intervals | |
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| Summary | |
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| Exercises | |
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| Multivariate Data Plots | |
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| Three Dimensional Data Plots | |
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| Plots of Higher Dimensional Data | |
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| Plotting to Check for Multivariate Normality | |
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| Exercises | |
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| Eigenvalues and Eigenvectors | |
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| Trace and Determinant | |
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| Eigenvalues | |
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| Eigenvectors | |
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| Geometrical Descriptions (p=2) | |
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| Geometrical Descriptions (p=3) | |
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| Geometrical Descriptions (p>3) | |
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| Exercises | |
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| Principal Components Analysis | |
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| Reasons for Doing a PCA | |
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| Objectives of a PCA | |
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| PCA on the Variance-Covariance Matrix, Sigma | |
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| Estimation of Principal Components | |
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| Determining the Number of Principal Components | |
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| Caveats | |
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| PCA on the Correlation Matrix, P | |
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| Testing for Independence of the Original Variables | |
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| Structural Relationships | |
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| Statistical Computing Packages | |
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| Exercises | |
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| Factor Analysis | |
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| Objectives of an FA | |
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| Caveats | |
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| Some History on Factor Analysis | |
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| The Factor Analysis Model | |
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| Factor Analysis Equations | |
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| Solving the Factor Analysis Equations | |
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| Choosing the Appropriate Number of Factors | |
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| Computer Solutions of the Factor Analysis Equations | |
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| Rotating Factors | |
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| Oblique Rotation Methods | |
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| Factor Scores | |
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| Exercises | |
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| Discriminant Analysis | |
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| Discrimination for Two Multivariate Normal Populations | |
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| Cost Functions and Prior Probabilities (Two Populations) | |
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| A General Discriminant Rule (Two Populations) | |
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| Discriminant Rules (More than Two Populations) | |
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| Variable Selection Procedures | |
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| Canonical Discriminant Functions | |
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| Nearest Neighbor Discriminant Analysis | |
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| Classification Trees | |
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| Exercises | |
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| Logistic Regression Methods | |
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| Logic Regression Model | |
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| The Logit Transformation | |
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| Variable Selection Methods | |
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| Logistic Discriminant Analysis (More than Two Populations.) | |
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| Exercises | |
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| Cluster Analysis | |
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| Measures of Similarity and Dissimilarity | |
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| Graphical Aids in Clustering | |
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| Clustering Methods | |
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| Multidimensional Scaling | |
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| Exercises | |
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| Mean Vectors and Variance-Covariance Matrices | |
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| Inference Procedures for Variance-Covariance Matrices | |
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| Inference Procedures for a Mean Vector | |
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| Two Sample Procedures | |
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| Profile Analyses | |
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| Additional Two Groups Analyses | |
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| Exercises | |
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| Multivariate Analysis of Variance Manova | |
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| Dimensionality of the Alternative Hypothesis | |
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| Canonical Variates Analysis | |
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| Confidence Regions for Canonical Variates | |
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| Exercises | |
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| Prediction Models and Multivariate Regression | |
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| Multiple Regression | |
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| Canonical Correlation Analysis | |
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| Factor Analysis and Regression | |
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| Exercises | |
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| Matrix Results | |
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| Quadratic Forms | |
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| Eigenvalues and Eigenvectors | |
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| Distances and Angles | |
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| Miscellaneous Results | |
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| Work Attitudes Survey | |
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| Data File Structure | |
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| SPSS Data Entry Commands | |
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| SAS Data Entry Commands | |
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| Family Control Study | |
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| References | |