Multidimensional Scaling: Marketing Tool For Testing The Preferences of Respondents

Multidimensional Scaling (MDS) For Testing the Preferences of Respondents

The multidimensional scaling is referred as a visual representation of dissimilarities or distance between two or set of objects. These objects can be faces, map pointers or even colors. The objects tend be closer which have the similarities or shorter distance among them. The object with long distance or dissimilarities are tend to be less similar. The term ‘scaling’ came from the psychometric which was a concept where numbers are assigned according to the rules.

Nowadays the use of Multidimensional scaling is used for different sectors and it is not limited to specific type of matrix or data set. It is used for a type of matrix that use of the relational data like multiple ratings, distances, scales and similarities. Sometimes it is difficult to understand if the basic knowledge is not understood on the multidimensional scaling.

Data is a scale down in different dimension for keeping similar properties for instance it can be said that two data points are closed together in high dimensional space will be getting close together in low dimensional space. The multidimensional part is mainly due to the fat that the calculation is not limited to two dimensions it can be done in multiple dimensions as well.

What is the Difference Between Metric and Non-Metric Multidimensional Scaling

The main difference between Metric and Non-metric multidimensional scaling is that the metric MDS has the long distances as the input value for creating a map for the physical locations by calculating the distance between the long-distance objects.  Whereas the non-metric MDS shows the distances as physical representations of ranking like high as in 6 and low as in 1. For the non-metric MDS the representation does not have any specific meaning.

A map is mainly created by using the Euclidean geometry and the it is used for showing the distances between the coordinates in a map. Another key difference is that the metric dimension is mainly used for interval scale data only and the non-metric multinational data is used for scaling the original data ad show the results. The nonmetric multi-dimensional data is used as the ingredient approach that is an ordination on the distance or dissimilarity matrix.

The metric multinationals scaling is used for perceptual mapping which is creation of map using the different than usual measure of distance and it is also used for product development. Whereas the non-metric multidimensional scaling is also used for applied marketing and psychology where the data is presented in pairs on the measurement scale of 1-7.

Assumption and Limitations of Multidimensional Scaling (MDS)

The main purpose of multidimensional scaling is to provide a visual representation of information rather than showing the numbers directly. The multidimensional scale chart will be used for showing the relationship between the different variables the variable that have the similarity will be appearing closely and the different ones will be appearing from far away. There are different types of MDS which has benefits and limitation differently.

For instance, the advantage of the relationship modeling is that it helps in assessing how closely the values are related or how different the values are form each other. But the main limitation of this model is that it cannot deal with real numbers. There is another modelling method which is simplifying tables, which provides the facility to work with a large number of data but the limitation of this modeling method is that is uses complex formulas for converting the raw figures into the multidimensional scale.

Another benefit of using MDS is that is used in psychology, graphic subject response and the main key limitation of this method is that it does it adds a separate subjectivity layer on the psychological data.

Important Steps to Consider While Conducting Multidimensional Scaling Research

There are few basic steps which is followed to conduct multidimensional scaling like- Assigning a number of points to the coordinates in N dimensional space- the n dimensional space can be a 3- dimensional or 2- dimensional space or even higher spaces. Usually most of the researchers choose the orientation of co-ordinate Axis as arbitrary.

Calculating the Euclidean distances for all the pair of points- the Euclidean distance is referred as the straight line distance between two points X and y which is also referred as 'as the crow flies' line in Euclidean space. It is mainly calculated as the Pythagorean formula and it is becoming more complicated for the N-dimensional space.

Comparing the original input matrix with similarity matrix- after evaluating the stress function which is a goodness of feet measurement is done based on differences between the predicted and actual distances.

In the original paper of MDS it was mention by Kruskal that "fits close to zero are excellent while anything over". And the last step of conducting multi-dimensional scaling in a proper way is adjusting the coordinates and if it is necessary minimizing it.

Relationship among Multidimensional Scaling, Factor Analysis and Discriminant Analysis

The multidimensional scaling is mainly based on subjects that are direct assessment of similarities between stimuli whereas the factor analysis requires subject to rate the stimuli based on some list of attributes and this factor is referred as the main factor or relationship between multidimensional scaling and factor analysis. In simple term it can be said that factor analysis is a referred as the way to take a massive amount of data shrinking to a smaller size of data for better storage management.

The major factor about discriminant function analysis is that it is done to determine which variables can discriminate between two or more naturally occurring group.

The major relation between multi-dimensional scaling and discriminant function analysis is that multi-dimensional scaling involves the creation for cluster by checking the correlation among data from two dimension array or three dimensional arrays and similarly multi-dimensional scaling does not provide the similar thing but instead it helps in finding the correlation between MDS and two dimensional arrays.

Whereas the discriminant function analysis is used to predict group membership in short list of continuous variable.