Attribute Based PERMAP_Group G_Nishtha Verma

PERMAP is a program that uses multidimensional scaling (MDS) to reduce multiple pair wise relationships to 2-D pictures called perceptual maps.

Perpetual Mapping can be done using two techniques:

1.      Overall similarity where we present the respondents with different pairs of objects and ask how similar or dissimilar are the objects

2.       Attribute based where we ask people to rank attributes and map them. This is a very easy but subjective technique and the person may miss mapping an important attribute.

An attribute is some aspect of an object. The attributes should be presented in a form where each is normalized  (standardized) to some kind of range or standard deviation, but Permap can do the normalizing internally if so desired.

The MDS algorithm uses object-to-object proximity information to construct the map. Proximity is some measure of likeness or nearness, or difference or distance, between objects.  It can be either a similarity or dissimilarity. Proximity values are based on some mathematical measure of association (correlation, distance, interaction, relatedness, dependence, confusability, joint or conditional probability and so forth) operating on a set of attributes.

In today’s class, we mapped the variable ‘store satisfaction’ for 4 stores based on 6 attributes: Price satisfaction, quality satisfaction, overall satisfaction, etc. The proximity matrix looks like this:

Title=Store Satisfaction nObjects=4 nAttributes=6 AttributeList Store1  3.007   3.082   3.253   3.178   3.171   2.986 Store2  3.206   3.096   2.941   2.875   3.309   3.000 Store3  3.159   3.094   3.232   3.297   3.080   3.312 Store4  2.969   3.037   3.315   3.006   3.080   3.068

The PERMAP is as shown:

A major advantage of MDS and perceptual maps is that they deal with problems associated with substantiating and communicating results based on data involving more than two dimensions.

Another important aspect of perceptual maps is that they are forgiving of missing or imprecise data points. Whereas some analytical techniques cannot tolerate missing elements in the input matrix, MDS results are often unaffected. This is because it is not uncommon for there to be much redundancy in the information given by a complete matrix of dissimilarities.