EXAMPLE D

Title=Department Store Perception Factors (Churchill's Data)
SubTitle=Multiple stores were evaluated based on 10 factors and then MDS was used to see if the factors clustered.
NObjects=10

DissimilarityList
Handy,  0
Speed,  .21, 0
Clean,  .59, .68, 0
Organ,  .74, .79, .2, 0
Junky,  .88, .8, .24, .25, 0
Times,  .11, .1, .66, .7, .89, 0
Close,  .13, .17, .6, .72, .77, .22, 0
Atmos,  .63, .69, .18, .22, .26, .7,  .71, 0
Decor,  .68, .65, .22, .19, .23, .61, .74, .18, 0
Large,  .82, .77, .28, .2, .17, .84, .83, .22, .23, 0 

Teaching: Churchill used this data to find the relationships between 
various characteristics of department stores.  The research question 
was posed in an unusual way.  Usually one would look for 
groupings of stores (i.e. object=store) and use the customer's
perceived characteristics as attributes.  Then one would 
calculate proximities between stores and make an MDS analysis.
However, Churchill chose to focus on the characteristics instead.  
So, he defined Handy, Speed, ... as objects and calculated the 
correlation between them using a set of department store data.  
Either approach is acceptable, although the issue of causality 
usually provides some guidance. 

Teaching: Using factor analysis, Churchill concluded that there are 
two groups.  After analyzing the components of these groups
he identified them as Convenience and Atmosphere.  You will 
find the same groupings using MDS with the added advantage
that the relationships between the ten factors will be clearly 
shown when displayed as overlay vectors on the map.

Teaching: This data set provides an excellent example of how to 
deal with local minima.  It can be tedious to find
the global minima (answer: Stress1 = 0.0793 for
ratio MDS, two dimensions, Euclidean distances, centering indifferent)
because the problem has so many nearly identical local minima.  
This shows that the use of 'rational starting locations' can be very 
dangerous.

Note: Previous editions of this example showed 0.00625 for the 
optimal normalized stress, instead of showing 0.0793 for the optimal 
Stress1 value.  Because this has caused some user confusion 
both objective function values are now shown.  Of course, the 
MDS map is identical for both cases.  The only difference lies 
in the choice of normalizing constant.  

Teaching: In passing, it should be noted that the early MDS 
literature did not use consistent formulas for several of the various
named stress values.  Even Kruskal changed the formula for Stress1
during his stream of MDS publications.  So, if you are trying to 
compare current stress values to older values it is important to 
check the underlying formulas that were used.  In some cases 
you will find that the paper's stress formula is never specified!

Program Note: If you don't see names on the objects use the View 
menu to turn on the 'names feature.'


