Metric vs. Non-Metric MDS: Key Differences and When to Use Each

Key Differences Between Metric and Non-Metric MDS

The fundamental difference between metric and non-metric MDS lies in how they treat input data. Metric MDS focuses on preserving actual distances in the data, while non-metric MDS maintains the rank order of similarities.

- Metric MDS works with quantitative data, preserving distances between points in a space as accurately as possible.

- Non-Metric MDS handles ordinal data, focusing on maintaining the ranking or order of relationships, even if the exact distances are not preserved.

Both techniques use a stress function to assess the quality of the resulting configuration, but they differ in how this stress is calculated. Metric MDS calculates stress based on distance discrepancies, while non-metric MDS calculates stress based on ranking errors.

When to Use Metric MDS

Metric MDS is preferred when working with quantitative distance measures. It is ideal when:

- Quantitative data, such as test scores, is available, and maintaining proportional relationships between the objects is essential.

- High accuracy in preserving true distances between points is necessary, making metric MDS well-suited for situations where even small deviations in spatial configurations can impact the analysis, such as in psychometrics or cognitive assessments.

When to Use Non-Metric MDS

Non-metric MDS is used when dealing with ordinal data, where the relative positioning of data points is more important than the exact distances. This method is suitable for:

- Situations where data provides only a ranking of relationships, such as surveys or preference rankings.

- Instances where maintaining the relative order of similarities or dissimilarities is more critical than preserving the actual distances, such as when respondents rank items or brands.

Trade-Offs Between Flexibility and Precision

Choosing between metric and non-metric MDS involves balancing precision and flexibility.

- Metric MDS offers higher precision but requires accurate distance measures, making it suitable for quantitative data where exact distances are meaningful.

- Non-Metric MDS is more flexible, as it works with ordinal data. However, it sacrifices some precision in preserving distances for the sake of maintaining rank order.

Practical Examples of Choosing Between Metric and Non-Metric MDS

Metric MDS Example

A study assessing cognitive abilities may use metric MDS if the data consists of numerical test scores. The differences between individual scores are meaningful, so preserving distances accurately is essential.

Non-Metric MDS Example

In a survey where participants rank their preferences for various brands, non-metric MDS is ideal. The exact distance between preferences isn't crucial—what matters is maintaining the relative order of brand rankings.