Page 269 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Quantitative Techniques-II

Notes 14.5 Multidimensional Scaling (MDS)

In addition to fulfilling the goals of detecting underlying structure and data reduction that is
shares with other methods, multidimensional scaling (MDS) provides the researcher with a
spatial representation of data that can facilitate interpretation and reveal relationships. Therefore,
we can define MDS as “a set of multivariate statistical methods for estimating the parameters in
and assessing the fit of various spatial distance models for proximity data.”
The spatial display of data provided by MDS is why it is also sometimes referred to as perceptual
mapping. MDS has much more flexibility about the types of data that can be used to generate the
solution. Almost any measures of similarity and dissimilarity can be used, depending on what
your statistical computer software will accept.

14.5.1 Types of MDS
In general, there are two types of MDS:
1. Metric
2. Non-metric
Metric MDS makes the assumption that the input data is either ratio or interval data, while the
non-metric model requires simply that the data be in the form of ranks. Therefore, the non-
metric model has more fewer restrictions than the metric model, but also less rigor. One technique
to use if you are unsure whether your data is ordinal or can be considered interval is to try both
metric and non-metric models. If the results are very close, the metric model may be used.
An advantage of the non-metric models is that they permit the researcher to categorize and
examine preference data, such as the kind obtained in marketing studies or other areas where
comparisons are useful.
Another technique, correspondence analysis, can work with categorical data, i.e., data at the
nominal level of measurement, however that technique will not be described here.

Similarities and Differences between Factor Analysis and MDS

We have already seen that MDS can accept more different measures of similarity and dissimilarity
than factor analysis techniques can. In addition, there are some differences in terminology.
These differences reflect the origin of MDS in the field of psychology. The measure corresponding
to factors are called alternatively dimensions or stimulus coordinates.
The output of MDS looks very similar to that of factor analysis and the determination of the
optimal number of dimensions is handled in much the same way.

Steps in using MDS

There are four basic steps in MDS:
1. Data collection and formation of the similarity/dissimilarity matrix
2. Extraction of stimulus coordinates
3. Decision about the number of stimulus coordinates that represent the data
4. Rotation and interpretation

Example: An example of MDS
Let us say that you have a matrix of distances between a number of major cities, such as you
might find on the back of a road map. These distances can be used as the input data to derive an

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