MDS and Permap

Multidimensional Scaling

Multidimensional (MDS) scaling is a set of techniques which help an analyst to find the key dimensions underlying respondents’ evaluation of a group of objects. It is often used in Marketing for identifying the key dimension underlying the consumer perception of services, products or other objects.

MDS had its origins in psychometrics where it helped to understand the people’s judgments of similarity of members in a set of objects. MDS pictures the structure of objects in a set from data about the distances between the pairs of objects. The data can be based on similarities, dissimilarities, proximity, or distance.

It can be divided into methods based on overall similarity and attribute base.

Overall Similarity – It is able to uncover latent needs in mind, which the respondents do not know of consciously. This method should be used only when the analyst has thorough knowledge of the objects and their environment.

Attribute Based – It is very easy for the respondent. For applying this method, the analyst should know everything in advance. This method may miss out on important attributes (latent needs).

MDS can be used for:

Principal components analysis – The aim of this method is to discover a new variable, called principal component, which is based on a linear combination of the original variables, so that the principal component accounts for most of the variation in the original variables.

Correspondence analysis – It aims to visualize the relations (like deviations from statistical independence) between the column and row categories. In this analysis the order of the distance between object-points reflects the preference ranking of the objects.

Cluster analysis – Applicable to proximity data.

PERMAP

The purpose of Permap is to uncover hidden data structure that might exist in a complex data set. The graphical model is easier to understand and its results can be easily interpreted. Permap is a map based on object to object relationships that are not visible from simple physical measurement.  Permap works on the principle of proximity between the objects based on either similarities or dissimilarities.

There are two types of input lists in Permap:

Similarity list – Has 1 in its diagonals. The closer the values are to 1, the higher the similarity between the objects.

Ex-

1

.23       1

.45       .81       1

.15       .43       .39       1

Dissimilarity list – Has 0 in its diagonals. Ex-

0

.23       0

.45       .81       0

.15       .43       .39       0

The data input syntax for Permap is like:

Title=Perception of Soft Drink           // The title of the Permap

nobjects=6                               // Number of objects in the list

similaritylist                             // Type of list. Similarity list in this case as all diagonals are 1.

Coke    1

Pepsi    0.85     1

Maaza  0.06     0.06     1

Slice    0.05     0.07     0.82     1

Sprite   0.43     0.37     0.17     0.15     1

MtDew            0.37     0.38     0.14     0.11     0.79     1

The following figure shows the Permap of objects in cola industry based on similarity rating from 0 to 9 by respondents.

Figure – Permap based on Similarity list between objects in Cola industry.

Through multiple iterations and rotation of axis, the factors like colour, taste, fizz and brand came to light. From the graphical analysis it can be shown that the respondents had these factors in their minds while assigning similarity values to the pairs of objects in the cola industry.

Permap can also be integrated Bubble Graph which shows data in 3 dimensions –

X axis

Y axis

Diameter of the bubble

In this case, the diameter of the bubble should be the object whose value has the highest variation.

Example –

Regards

Saurabh