multidimensional scaling

[elke]

dear statisticians,

I have a question concerning an MDS-analysis.
Suppose we want to examine the interrelations in an organisation.
we ask the collegeas (n=15) the two following questions:
- number your collegeas from 'I like to work with the most' till 'I
like to work with the least'. The one you like the most you give
number one, than two, and so on.
- number your collegeas from 'has the most skills and knowledge about
the problems concerning the organisation' till 'has the least skills
and knowledge'. The one with the most skills and knowledge receives
the score of one, the second best the score of two, and so on.

To examine the interrelations in the organisation we can use MDS. Now,
the following problem occured:
I can put each question in a 15x15 matrix (collegeas with respect to
other collegeas), with row conditionality and than do the MDS-
analysis. But I'm extremely interested in how those two configurations
coincide. How can I do this? Do I use three-way MDS (because all the
information I have concerning three-way MDS involves situations where
matrices stand for individuals. I want to examine two different
constructs in two different matrices)? Or can I use procrustes
procedures? Or are their other possibilities? Is all this also
possible with SAS?


Thank you in advance,
E.

[Tony Coxon]

Hi "E"
A few preliminary points:
-- your data are rankings rather than ratings (This affects the rescaling transformation you use -- ordinal in this case)
-- the data are asymmetric and row-conditional, which you recognise; in the normal case this would mean a 2W2M solution with both row-point and column-point solution (unfolding solution -- PREFSCAL in SPSS or MINI-RSA in NewMDSX) or row-point and column-vector solution (MDPREF or CORRESP model in NewMDSX), though there are row-conditional models which give a single point solution (ASYMSCAL in SPSS; MINI-CPA in Roskam-Lingoes).
Which choice have you made? (your answer affects the comments below).  I assume for simplicity that you have chosen unfolding and therefore have p row points and p column points in your solution.

Your main interest is how the 2 configurations compare. With only two criteria I would not even think of using the third way. It is much simpler to rotate them to maximum conformity using simple Procrustes analysis (PROCRUSTES or PINDIS in NewMDSX).

I am afraid I have no intimate knowledge of SAS, so cannot answer that one; to my knowledge it does not have any 2-way 2-mode models.

A final point: Have you thought of using a network representation rather than (or in addition to) a scaling solution? UCINET (http://tech.groups.yahoo.com/group/ucinet/ ) is a companion group with NewMDSX , and uses the basic MDS model [MINISSA from NewMDSX] to position points from which the network is drawn. Their Netdraw program (freeware) is very flexible.

I hope this is helpful; if you want further help, let me have a copy of the data.

Tony

Professor A.P.M. Coxon; NewMDSX Manager

--
Professor A.P.Macmillan Coxon
Honorary Professorial Research Fellow, University of Edinburgh.
Tigh Cargaman
Port Ellen
Isle of Islay
Argyll PA42 7BX, Scotland
Phone: 01496 302345
URLs:
www.tonycoxon.com, www.newmdsx.com, www.methodofsorting.com, www.sigmadiaries.com

--
Professor A.P.Macmillan Coxon
Honorary Professorial Research Fellow, University of Edinburgh.
Tigh Cargaman
Port Ellen
Isle of Islay
Argyll PA42 7BX, Scotland
Phone: 01496 302345
URLs:
www.tonycoxon.com, www.newmdsx.com, www.methodofsorting.com, www.sigmadiaries.com