Multidimensional Scaling of Binary Dissimilarities: Direct and Derived Approaches

Area of Science:

• Quantitative Psychology
• Statistical Analysis
• Data Science

Background:

• Multidimensional scaling (MDS) is used to analyze dissimilarity matrices.
• Debate exists on whether to use original or derived matrices for MDS.
• Previous studies suggested derivative approaches for sorting data were less effective.

Purpose of the Study:

• To investigate the effectiveness of different approaches for multidimensional scaling of binary data.
• To compare direct scaling, derivative scaling using squared difference (δ), and Jaccard coefficient-based scaling.
• To evaluate the impact of row-centering on derivative approaches.

Main Methods:

• Monte Carlo simulation study using structured binary data.
• Data generated from known two-dimensional configurations.
• Analysis performed using ALSCAL (a multidimensional scaling algorithm).
• Comparison of scaling methods using Procrustes statistics.

Main Results:

• Direct scaling of binary data outperformed scaling of δ-derived data across various noise levels.
• Scaling Jaccard coefficient data yielded results consistently better or equal to δ data.
• Jaccard scaling sometimes improved upon direct scaling performance.
• Row-centering before applying the δ rule was generally ineffective.

Conclusions:

• Direct scaling or scaling using the Jaccard coefficient are recommended for analyzing binary dissimilarity data.
• The squared difference (δ) row-comparison rule has limitations.
• Findings are applicable to stimulus sorting and other coarse dissimilarity data analyses.