Simultaneous Two-Way Clustering of Multiple Correspondence Analysis.

Area of Science:

• Statistics
• Data Analysis
• Multivariate Statistics

Background:

• Multivariate categorical data analysis often faces challenges in accounting for heterogeneity.
• Existing methods may not fully capture joint relationships between respondent subgroups and variable category subsets.

Purpose of the Study:

• To propose a novel 2-way clustering approach for multiple correspondence analysis.
• To address cluster-level heterogeneity in both respondents and variable categories.
• To identify joint clusters linking specific respondent groups to distinct variable category subsets.

Main Methods:

• Combines multiple correspondence analysis (MCA) with k-means clustering in a unified framework.
• Applies k-means twice: first to respondent object scores, then to variable category weights.
• Generates a low-dimensional map displaying variable category points and joint cluster centroids.

Main Results:

• The proposed method successfully identifies joint clusters, revealing exclusive relationships between respondent subgroups and variable category subsets.
• Provides joint-cluster memberships for both respondents and variable categories.
• A Monte Carlo study demonstrated good parameter recovery capabilities.

Conclusions:

• The 2-way clustering approach enhances the analysis of multivariate categorical data by capturing complex heterogeneity.
• The method offers a valuable tool for understanding nuanced relationships, as shown in the Korean consumer preference example.
• Effectiveness is demonstrated through comparison with existing methods.