EXAMPLE G

TITLE=Persistent Circles Despite Extreme Dij Degradation - MDS Is Robust!
SUBTITLE=Case 1: Using ratio level dissimilarity data. 
NOBJECTS=12

DISSIMILARITYLIST
 0.000, 
 0.183 0.000, 
 0.354 0.183 0.000, 
 0.500 0.354 0.183 0.000, 
 0.612 0.500 0.354 0.183 0.000, 
 0.683 0.612 0.500 0.354 0.183 0.000, 
 0.707 0.683 0.612 0.500 0.354 0.183 0.000, 
 0.683 0.707 0.683 0.612 0.500 0.354 0.183 0.000, 
 0.612 0.683 0.707 0.683 0.612 0.500 0.354 0.183 0.000, 
 0.500 0.612 0.683 0.707 0.683 0.612 0.500 0.354 0.183 0.000, 
 0.354 0.500 0.612 0.683 0.707 0.683 0.612 0.500 0.354 0.183 0.000, 
 0.183 0.354 0.500 0.612 0.683 0.707 0.683 0.612 0.500 0.354 0.183 0.000, 

This data file has three separate cases designed to illustrate 
an extreme case of Dij degradation that leaves the MDS map 
unchanged.  This stability in the face of severe data degradation is 
one of the extremely useful aspects of MDS.  MDS is robust!

The data cases are: (1) The original ratio-level data.  (2) The original
data reduced to rank order data.  (3) The original data reduced all
the way to binary nearest neighbor data.

Use ratio MDS, Euclidean distances, Stress1, and two dimensions.  
In all three cases you will get a circle.

To run the other cases, use the Edit menu and "Edit Data Input File"
(or just press F4) to access the data.  Then, "uncover" the four keywords 
of the desired case by removing the x's in front of its keywords, 
while leaving x's on the other two cases.  Use the SaveExitRead
menu item to quickly save the file, exit this screen, reload 
the example, and restart the analysis.

Teaching: These examples show that MDS is very robust.  This
is an important concept that every student should understand.  It
is why you can sometimes get good results from bad data.

Advanced: One can use the Precision control button to instantly 
make a similar data degradation analysis for any problem.  If the 
Precision control is not showing on the main screen then use the 
View menu to activate it.  



xTITLE=Persistent Circles Despite Extreme Dij Degradation
xSUBTITLE=Case 2: Using ordinal level dissimilarity data (ranks). 
xNOBJECTS=12
xDISSIMILARITYLIST
 0
 1 0
 2 1 0
 3 2 1 0
 4 3 2 1 0
 5 4 3 2 1 0
 6 5 4 3 2 1 0
 5 6 5 4 3 2 1 0
 4 5 6 5 4 3 2 1 0
 3 4 5 6 5 4 3 2 1 0
 2 3 4 5 6 5 4 3 2 1 0
 1 2 3 4 5 6 5 4 3 2 1 0


xTITLE=Persistent Circles Despite Extreme Dij Degradation
xSUBTITLE=Case 3: Using binary level (nearest neighbor) dissimilarity data. 
xNOBJECTS=12
xDISSIMILARITYLIST
 0
 0 0
 1 0 0
 1 1 0 0
 1 1 1 0 0
 1 1 1 1 0 0
 1 1 1 1 1 0 0
 1 1 1 1 1 1 0 0
 1 1 1 1 1 1 1 0 0
 1 1 1 1 1 1 1 1 0 0
 1 1 1 1 1 1 1 1 1 0 0
 0 1 1 1 1 1 1 1 1 1 0 0






