### MDS

What is Multidimensional Scaling ?

• It enables graphically leveling the similarity of individual cases of a dataset.
• It is also known as perceptual mapping.
• It enables to determine the perceived relative image of set of objects (firms, products and other item associated with commonly help perceptions.

Why Multidimensional scaling ?

• The purpose of MDS is to transform consumer judgements of overall similarity of preference ( e.g. : Preference of store or bands) into distance represented in multidimensional space.
• Dimension Reduction technique

Creating Perceptual Map

MDS to other interdependence techniques:

• The goal of MDS is to take a set of similarity measure. One can ask people to rate how similar a group of things are pair by pair. Then using MDS we can figure out which attributes of the things people are using to rate the similarity.
• Cluster Analysis: The goal of the cluster analysis is to take a bunch of subjects and see how to cluster them so they are near each other on some set of variables.
• Factorial Analysis: Defines structures by grouping variables into variates that represent underlying dimensions in the original set of variables. Variables that are highly correlated are grouped together.

MDS differ to cluster and Factor Analysis in two

• A solution can be obtained from each individual.
• It does not use variate.

Conceptual Approach !!!

• A way to "rearrange" objects in an efficient manner, so as to arrive at a configuration that best approximates the observed distances.
• It actually moves objects around in the space defined by the requested number of dimensions, and checks how well the distances between objects can be reproduced by the new configuration.
• It uses a function minimization algorithm that evaluates different configurations with the goal of maximizing the goodness-of-fit (or minimizing "lack of fit".

Similarities Vs Preference Data

• Similarities Based Perceptual maps represent attribute similarities and perceptual dimensions of comparison but do not reflect any direct insight into the determinants of choice.
• Preference based Perceptual maps do reflect proffered choices but may not correspond in any way to the similarity based positions, because the respondents may base their choices on entirely different dimensions or criteria from those on which they base comparison.

** Hence based on the research question in mind the decision of similarities or preference data must be made.

### Changed Axes

Aggregate and Disaggregate Analysis:

• Disaggregate: Here the researcher generates the perceptual maps on a subject to subject basis. The advantage is the representation of the unique elements of each respondents perceptions. The disadvantage is that the respondents must identify the common dimensions of the perceptual maps across multiple respondents.
• Aggregate: MDS technique can also combine respondents and create a single perceptual map through an aggregate analysis.
• - Aggregate using cluster analysis.

De-compositional And Compositional !!

• The de-compositional or (attribute free) method measures only over impression or evaluation of an object and then attempts to derive spatial position in multidimensional space that reflect this perception.
• The compositional or (attribute based) method that adopts several of multivariate techniques already discussed that are used in forming an impression or evaluation based on combination of specific attributes.

Metric or Non Metric data

• Nonmetric method : Generated by rank-ordering pairs of objects, are more flexible in that they do not assume any specific any specific type of relationship between the calculated distance and similarity measure. Because non metric methods contain less information for creating perceptual map. Wide variations occurs between respondents or the perceptions between objects.
• Metric : Discrete or continuous. The input as well as the output is metric. This assumptions strengthen the relationship between the final output dimensionality and the input data