Date:         Mon, 7 Jul 2008 17:20:12 -0700
Reply-To:     jenmoocat <sollje2002@YAHOO.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         jenmoocat <sollje2002@YAHOO.COM>
Organization: http://groups.google.com
Subject:      PROC MDS using preference rankings
Comments: To: sas-l@uga.edu
Content-Type: text/plain; charset=ISO-8859-1

Ever have one of those days where you feel like you are just missing
something?
Hopefully someone can help -- because I am beginning to feel like an
idiot.

I have preference rankings for 6 brands for two time periods (t=0 and
t=1).
I would like to overlay the preference map from time t=0 with the map
from time t=1, so we can easily see how preferences have changed over
time.

My data looks like the following (for one time period and 5000
respondents):

respondent       brand1        brand2       brand3     brand4
brand5      brand 6
1                        5                2                1
2                3             5
2                        4                3                3
3                3             3
3                        2                2                5
1                1             1
4                        1                2                4
4                4             4
...
...
...
5000                   2                5                5
3               2              1


And I have another dataset for the next time period --- with changed
rankings (hopefully).

I've spent the past couple of days reading the PROC MDS documentation
pages and the MDS chapter in "Multivariate Data Analysis" by Hair, et
al.,  and searching around the web --- and I am stymied.

Although the textbook talks about being about to use preference
rankings, all examples that I've seen (in the book and on the web)
have been based on starting with a similarity matrix.  And I just
don't quite grok the best way to go from my preference ranking data to
a similarity matrix.  Or whether PROC MDS can be used with raw ranking
data, instead of the matrices.

Should the similarity matrix just simply be constructed using the
following steps:

for each respondent, calculate a matrix that contains the simple
numerical difference between the rankings:
so for respondent 1, it would look something like:

               brand1        brand2       brand3        brand4
brand5     brand6
brand1     0                 3              4
3                  2             0
brand2    -3                 0              1
0                 -1            -3
brand3    -4                -1              0
-1                 -2            -4
brand4    -3                 0              1
0                 -1            -3
brand5    -2                 1              2
1                  0            -2
brand6     0                 3              4
3                  2             0


then either 1) create one "similarity matrix" by taking the averages
over all responders or
2)  stack these matrices, one responder over another (and use the
CONDITION=ROWS option)

Am I on the right track?  I feel like I am just missing something
obvious and am at the point where I feel like banging my head against
the wall.

Can anyone shed a little light on this for me?

Thanks muchly in advance,

-jennifer