Rotation in Correspondence Analysis from the Canonical Correlation Perspective.

Area of Science:

• Statistics
• Data Analysis
• Multivariate Analysis

Background:

• Correspondence Analysis (CA) is a statistical technique for visualizing relationships between categorical variables.
• Existing Canonical Correlation Analysis (CCA)-based CA formulations are limited to orthogonal rotations.
• There is a need for more flexible rotation methods in CCA-based CA to better capture variable relationships.

Purpose of the Study:

• To propose a novel CCA-based formulation for Correspondence Analysis that permits oblique rotation.
• To define a new CA loss function based on maximizing the generalized coefficient of determination.
• To demonstrate the advantages of the proposed oblique rotation method in CCA-based CA.

Main Methods:

• Developed a CCA-based formulation for Correspondence Analysis.
• Incorporated oblique rotation into the CCA-based CA framework.
• Defined the loss function as maximizing the generalized coefficient of determination.

Main Results:

• The proposed formulation successfully implements oblique rotation in CCA-based CA.
• The generalized coefficient of determination effectively measures proximity between variables in the reduced dimensional space.
• Simulation studies and real data examples validate the benefits of the new method.

Conclusions:

• The proposed CCA-based CA formulation offers a more flexible approach to analyzing categorical variable relationships.
• Oblique rotation enhances the interpretability and accuracy of CCA-based CA.
• This method provides a valuable alternative for researchers in various fields analyzing categorical data.