Non Metric Scaling

TL;DR

Visualizes relationships among objects or variables in a multi-dimensional space without relying on measurement units or a fixed scale.
Common methods include multidimensional scaling (MDS) and correspondence analysis (CA); suitable for categorical and subjectively rated data.
Advantages: easier interpretation and reduced sensitivity to outliers; Limitations: no absolute distance measures and results depend on subjective judgments and data distribution.

Definition

Nonmetric scaling is a type of data analysis technique used to identify patterns and relationships within a dataset. It contrasts with metric scaling by not measuring distances with explicit units or a fixed scale; instead, it relies on the relationships among objects or variables to determine relative positions.

Explanation

Nonmetric scaling methods represent the relationships among objects or variables in a multi-dimensional space without using explicit measurement units. Rather than computing absolute distances, these techniques preserve the ordinal or relational structure implied by the data. This makes nonmetric approaches useful when direct measurement of distance is difficult or impossible, such as with categorical responses or subjectively rated items. Compared with metric scaling, nonmetric scaling focuses on the pattern of relationships rather than quantifying exact distances.

The approach is relatively straightforward to interpret because it produces visual representations of relationships. It is often less sensitive to outliers or extreme values than some other techniques and can accommodate a range of data types, including continuous and categorical data. However, nonmetric scaling does not yield absolute distance measures, depends on subjective judgments and assumptions about relationships, and can be affected by the number and distribution of the objects or variables being analyzed.

Examples

Multidimensional scaling (MDS)

MDS is a method used to visualize the relationships between a set of objects or variables in a multi-dimensional space. For instance, if a researcher wanted to understand the relationships between different types of fruit, they could use MDS to create a visual representation of these relationships. In this example, the different types of fruit would be the objects or variables being analyzed, and the relationships between them would be represented in the multi-dimensional space.

Correspondence analysis (CA)

CA is a method used to analyze categorical data, such as responses to a survey or the results of an experiment. For instance, if a researcher wanted to understand how different types of music are related to one another, they could use CA to analyze survey responses from a group of participants. In this example, the different types of music would be the categories being analyzed, and the relationships between them would be represented in the multi-dimensional space.

Use cases

Commonly used in the field of psychology to understand how different variables are related.
Analysis of categorical data or subjectively rated data where measuring distance directly is difficult.
Producing visual, interpretable representations of relationships for researchers and laypeople.

Notes or pitfalls

Nonmetric scaling does not provide an absolute measure of the distance between objects or variables, which complicates direct comparison with other analyses or precise prediction.
Results rely on subjective judgments and assumptions about relationships, which can introduce bias or error.
Sensitivity to the number and distribution of objects or variables can impact analysis outcomes.

Metric scaling
Multidimensional scaling (MDS)
Correspondence analysis (CA)