Unit 2963: Multivariate Analysis

1. Introduction to Multivariate Analysis

• Definition and scope of multivariate analysis
• Importance and rationale for multivariate approaches
• Applications in various fields:
  • Psychology
  • Biology
  • Marketing
  • Finance

2. Multivariate Data Types

• Types of multivariate data:
  • Continuous data
  • Categorical data
  • Mixed data
• Implications of data types for analysis techniques
• Data preprocessing considerations

3. Multivariate Data Visualization

• Importance of visualization in multivariate analysis
• Visualization techniques:
  • Scatter plots (including scatterplot matrices)
  • Heatmaps
  • Parallel coordinate plots
  • Multidimensional scaling (MDS)
• Interpreting visualizations for pattern detection

4. Multivariate Normal Distribution

• Introduction and definition
• Properties of the multivariate normal distribution
• Role in multivariate methods:
  • Factor analysis
  • Discriminant analysis
• Assumptions and diagnostics

5. Principal Component Analysis (PCA)

• Concept and objectives
• Dimensionality reduction and variance explanation
• Mathematical foundation: eigenvalues and eigenvectors
• Steps to perform PCA
• Interpretation of principal components
• Applications and limitations

6. Factor Analysis

• Purpose and conceptual overview
• Exploratory vs. confirmatory factor analysis
• Model assumptions and estimation methods
• Factor extraction, rotation, and interpretation
• Comparison with PCA

7. Cluster Analysis

• Objective of cluster analysis
• Types of clustering techniques:
  • Hierarchical clustering
  • K-means clustering
• Distance and similarity measures
• Steps in clustering analysis
• Evaluating cluster solutions

8. Discriminant Analysis

• Purpose and applications
• Linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA)
• Assumptions and model fitting
• Classification and prediction
• Evaluating classification performance

9. Multivariate Analysis of Variance (MANOVA)

• Concept and rationale
• Differences between ANOVA and MANOVA
• Assumptions and multivariate test statistics
• Interpreting MANOVA results
• Post hoc analyses and follow-up tests

10. Canonical Correlation Analysis

• Purpose and conceptual overview
• Relationship between two sets of variables
• Computing canonical variates and correlations
• Interpretation of canonical functions
• Applications and examples