Multidimensional Scaling Of Derived Dissimilarities.

Area of Science:

• Psychology
• Data Analysis
• Multidimensional Scaling

Background:

• Multidimensional scaling (MDS) is often applied to dissimilarity matrices (D).
• A delta transformation (δ) of squared profile distances is sometimes used instead of D.
• It is hypothesized that δ-derived MDS solutions have lower stress and better interpretability for sorted data.

Purpose of the Study:

• To investigate the consequences of applying the delta transformation (δ) in multidimensional scaling.
• To compare MDS solutions derived from δ matrices versus original dissimilarity matrices (D).

Main Methods:

• Simulated random numbers resembling sorted data.
• Generated simulated dissimilarity matrices from known stimulus configurations.
• Applied nonmetric multidimensional scaling to both δ and D matrices.

Main Results:

• MDS solutions from δ matrices consistently showed lower stress than those from D matrices.
• Under low error conditions, solutions based on D were more representative of the true configurations.
• Determining the correct dimensionality was more challenging with δ-derived solutions.

Conclusions:

• The delta transformation (δ) primarily reduces stress by altering distance relationships, not necessarily by improving interpretability.
• While δ can lower stress, it may obscure the true underlying stimulus configurations.
• Researchers should be cautious when using δ transformations, especially when accurate representation of original dissimilarities is crucial.