UsefulLinks
Statistics
Multivariate Analysis
1. Introduction to Multivariate Analysis
2. Foundations in Matrix Algebra and Random Vectors
3. The Multivariate Normal Distribution
4. Data Preparation and Exploration
5. Principal Component Analysis
6. Factor Analysis
7. Multiple Linear Regression
8. Multivariate Analysis of Variance
9. Discriminant Analysis
10. Logistic Regression
11. Cluster Analysis
12. Canonical Correlation Analysis
13. Multidimensional Scaling
14. Advanced Multivariate Methods
13.
Multidimensional Scaling
13.1.
MDS Objectives
13.1.1.
Spatial Representation
13.1.2.
Similarity Visualization
13.1.3.
Perceptual Mapping
13.1.4.
Dimensionality Reduction
13.2.
Input Data Types
13.2.1.
Similarity Data
13.2.2.
Dissimilarity Data
13.2.3.
Distance Matrices
13.2.4.
Proximity Measures
13.3.
Types of MDS
13.3.1.
Classical MDS (Metric)
13.3.1.1.
Euclidean Distance Model
13.3.1.2.
Principal Coordinates Analysis
13.3.2.
Non-Metric MDS
13.3.2.1.
Ordinal Data Handling
13.3.2.2.
Monotonic Transformation
13.4.
Classical MDS Procedure
13.4.1.
Distance Matrix Analysis
13.4.2.
Double Centering
13.4.3.
Eigenvalue Decomposition
13.4.4.
Coordinate Extraction
13.5.
Non-Metric MDS Procedure
13.5.1.
Stress Function
13.5.2.
Iterative Optimization
13.5.3.
Kruskal's Algorithm
13.5.4.
Shepard Diagram
13.6.
Determining Dimensionality
13.6.1.
Stress Values
13.6.2.
Scree Plot
13.6.3.
Interpretability
13.6.4.
Elbow Criterion
13.7.
MDS Solution Interpretation
13.7.1.
Spatial Configuration
13.7.2.
Dimension Interpretation
13.7.3.
Cluster Identification
13.8.
Goodness-of-Fit Assessment
13.8.1.
Stress Measures
13.8.2.
R-Squared
13.8.3.
Shepard Diagram Analysis
13.9.
MDS Variants
13.9.1.
Individual Differences Scaling (INDSCAL)
13.9.2.
Weighted MDS
13.9.3.
Unfolding Models
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12. Canonical Correlation Analysis
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14. Advanced Multivariate Methods