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

Multidimensional Scaling (MDS) helps visualize relationships between objects in a low-dimensional space. This article explores the differences between metric and non-metric MDS, detailing when each should be applied based on the data and analysis goals.

## 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 crucialâ€”what matters is maintaining the relative order of brand rankings.

## Conclusion

Metric MDS is used when data is quantitative and exact distance preservation is necessary. Non-metric MDS is preferred when working with ordinal data, where ranking is more important than precise distances. Each method is valuable depending on the data type and analytical goals.

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