Group D - Sep 12 (MDS Maps)

Ankur Goel - Group D

MDS Maps:

Perceptual maps are sometimes called product maps, sociograms, sociometric maps, psychometric maps, stimulus-response diagrams, relationship maps, concept maps, etc.  A perceptual map is a piece of paper, or any plane, with symbols on it that convey information about perceived relationships between the objects represented by the symbols. What is the difference between a perceptual map and any ordinary map?  Not much, although some people make a big deal about it.  Usually, a perceptual map is taken to be a map that involves object-to-object relationships that are not amenable to simple, physical measurement. What is an object?  Objects can be anything.  They can be stimuli, constructs, artifacts, characteristics, traits, people, companies, bones, arrowheads, words, discussion topics, and so forth.  Anything that you want to study can be an object.  If you are interested in how certain objects relate to each other, and if you would like to present these relationships in the form of a map, then MDS is the technique you need.

The MDS algorithm uses object-to-object proximity information to construct the map.  What is a proximity?  A proximity is some measure of likeness or nearness, or difference or distance, between objects.  It can be either a similarity (called a resemblance in some disciplines) or a dissimilarity.  If the proximity value gets larger when objects become more alike or closer in some sense, then the proximity is a similarity.  If the opposite is the case, the proximity is a dissimilarity. Proximity values can be calculated, measured, or just assigned based on someone's best judgment.  If calculated, they typically are based on some mathematical measure of association (correlation, distance, interaction, relatedness, dependence, confusability, joint or conditional probability, pilesort counts, and so forth) operating on a set of attributes.

What is an attribute?  An attribute is some aspect of an object.  It may be called a factor, characteristic, trait, property, component, quantity, variable, dimension (not a good choice in MDS work, but occasionally seen), parameter, and so forth.  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.  An attribute in one study may be an object in another study.  It is all a matter of perspective and interest.In this manual we present all formulas in terms of dissimilarities and refer to dissimilarities rather than proximities or similarities, but the choice is arbitrary.  Typeset documents usually represent dissimilarities by the Greek del, Dij, where the indices i and j indicate that it is the proximity between object i and object j.  However, the Greek symbols do not translate correctly in some MS Word versions configured for languages other than English, so here we use Dij to represent a dissimilarity.