Measuring the Similarity of MDS Configurations.

Area of Science:

• Psychometrics
• Multivariate Statistics
• Data Analysis

Background:

• Assessing the similarity between multidimensional scaling (MDS) configurations is crucial for interpreting results.
• Existing methods often rely on correlating point coordinates or distances, each with limitations.

Purpose of the Study:

• To evaluate the suitability of different measures for assessing MDS configuration similarity.
• To address the inadmissibility of product-moment correlation for distance-based similarity.
• To introduce and provide norms for the congruence coefficient as a viable alternative.

Main Methods:

• Procrustean similarity transformations for coordinate-based comparison.
• Direct assessment of distance similarity.
• Derivation of statistical norms for the congruence coefficient across various parameters.

Main Results:

• Product-moment correlation is an inadmissible measure for assessing distance-based similarity.
• The congruence coefficient is an admissible measure for distance-based similarity.
• Norms for the congruence coefficient are established for diverse parameters.
• The two main measures of configurational similarity are not simply related and can yield different conclusions regarding statistical significance.

Conclusions:

• The congruence coefficient offers a statistically sound method for evaluating distance-based similarity in MDS configurations.
• Researchers should be aware that different similarity measures may lead to divergent conclusions about the significance of configuration similarity.
• Alternative approaches for assessing configurational similarity warrant further investigation.