Applied Multivariate Methods for Data Analysts

1. Applied multivariate methods. An Overview of Multivariate Methods. Two Examples. Types of Variables. Data Matrices and Vectors. The Multivariate Normal Distribution. Statistical Computing. Multivariate Outliers. Multivariate Summary Statistics. Standardized Data and/or z-Scores. Exercises. 2. Sample correlations. Statistical Tests and Confidence Intervals. Summary. Exercises. 3. Multivariate data plots. Three-Dimensional Data Plots. Plots of Higher Dimensional Data. Plotting to Check for Multivariate Normality. Exercises. 4. Eigenvalues and eigenvectors. Trace and Determinant. Eigenvalues. Eigenvectors. Geometrical Descriptions (p=2). Geometrical Descriptions (p=3). Geometrical Descriptions (p>3). Exercises. 5. Principal components analysis. Reasons For Doing a PCA. Objectives of a PCA. PCA on the Variance-Covariance Matrix, Sigma. Estimation of Principal Components. Determining the Number of Principal Components. Caveats. PCA on the Correlation Matrix, P. Testing for Independence of the Original Variables. Structural Relationships. Statistical Computing Packages. Exercises. 6. Factor analysis. Objectives of an FA. Caveats. Some History on Factor Analysis. The Factor Analysis Model. Factor Analysis Equations. Solving the Factor Analysis Equations. Choosing the Appropriate Number of Factors. Computer Solutions of the Factor Analysis Equations. Rotating Factors. Oblique Rotation Methods. Factor Scores. Exercises. 7. Discriminant analysis. Discrimination for Two Multivariate Normal Populations. Cost Functions and Prior Probabilities (Two Populations). A General Discriminant Rule (Two Populations). Discriminant Rules (More Than Two Populations). Variable Selection Procedures. Canonical Discriminant Functions. Nearest Neighbour Discriminant Analysis. Classification Trees. Exercises. 8. Logistic regression methods. The Logit Transformation. Logistic Discriminant Analysis (More than Two Populations.) Exercises. 9. Cluster analysis. Measures of Similarity and/or Dissimilarity. Graphical Aids in Clustering. Clustering Methods. Multidimensional Scaling. Exercises. 10. Mean vectors and variance-covariance matrices. Inference Procedures for Variance-Covariance Matrices. Inference Procedures for a Mean Vector. Two Sample Procedures. Profile Analyses. Additional Two Groups Analyses. Exercises. 11. Multivariate analysis of variance. manova. Dimensionality of the Alternative Hypothesis. Canonical Variates Analysis. Confidence Regions for Canonical Variates. Exercises. 12. Prediction models and multivariate regression. Multiple Regression. Canonical Correlation Analysis. Factor Analysis and Regression. Exercises. Appendices: Matrix results, quadratic forms, eigenvalues and eigenvectors, distances and angles, miscellaneous results; work attitudes survey, data file structure, SPSS data entry commands, SAS data entry commands; family control study.