Hi Don,
Thank you for drawing my attention to the email exchanges on graphical
display
of correspondence analysis. I will try to answer the original question.
Correspondence analysis for contingency tables (C) and multiple
correspondence
analysis for multiple-choice data (MC) were born in France (see
publications by
such people as Benzecri, Escofier, Escoufier, Lebart, Saporta and many
others)
and popularized among English-speaking countries by Greenacre's 1984 book.
Dual scaling (DS) (see books by myself published in 1980 and 1994) are
mathematically
the same as correspondence analysis (C) for contingency-frequency tables
(CF)
and multiple correspondence analysis (M)for multiple-choice data (MC).
For data
types CF and MC, there exist exact geometric representations. DS, C and
MC
look at the data in terms of principal hyper-sphere (i.e., in terms of
principal axes).
DS, however, has extended its applications to also what I call 'dominance
data' as
opposed to 'incidence data' for which C and MC were developed. Dominance
data
contain information of greater than, samller than, equal, the example of
which are
ranking data and paired comparisons. Since the information of 'greater
than,' for
example, does not say 'how much greater than', dominance data do not have
simple
geometric representations. In DS, therefore, we want to obtain a joint
geometric
representation of rows (e.g., judges) and columns (e.g., applicants) of
the data matrix
in such a way that each judge ranks applicants according to the distances
(the applicant
closest to a particular judge is ranked first by that judge). When we
have such a joint
representation of judges and applicants, from which the original rank
orders can be
reproduced by ranks of distances, that is the DS solution. This is a
solution to
Coombs' multidimensional unfolding problem.
As is clear from the above, DS is a more comprehensive framework than C or
MC and
the latter two are special cases of DS, contrary to what many peoploe
believe.
For a joint graph, the problem is that rows and columns do not span the
same space
unless the row-column association is perfect. So, the exact geometric
representations
of the results are obtained by, for example, projecting rows onto the
space of columns
or vice versa. But the most common practice is to plot both projected
quantities in
a joint graph, with a caution that the two sets of variables do not span
the same space,
this being popular because they have the same norm. In this latter
approach, it is
advisable to plot them only when the singular values are 'reasonably
large,' say solution
(component) 1 versus solution 2.
The above are probably too technical to be useful. As for joint graphs,
one can get
them by the program in SPSS and also the DUAL3 ( a package for both
incidence data
and dominance data, available from MicroStats in Toronto). For the
latter, see my
website
http://fcis.oise.utoronto.ca/~snishisato
I have conducted annual workshop on DS, and the next one (22nd annual)
will be held
on November 2 (the deadline is noon, Oct.30), Canadian $65 for students and
Canadian $175 for others, which include the DUAL3 for Windows, the handout
and a copy of "Dual scaling in a nutshell" by S. Nishisato and I.
Nishisato. For
detailed information, see the above website.
As for graphical display, see Greenacre (1984, Academic Press), Gifi
(1991,
Wiley), and Nishisato (1994, Lawrence Erlbaum; 1996, Psychometrika).
See also the above website for some tips on dual scaling.
[EMAIL PROTECTED] writes:
>On Wed, 24 Oct 2001, Rich Ulrich wrote in part:
>
>> It has been my impression (from google) that CA is more popular
>> in European journals than in the US, so there might be better
>> sites out there in a language I don't read.
>
>("CA" = correspondence analysis,
> ou en francais analyse des correspondances)
>
>In Canada, and to a lesser extent in the U.S., correspondence analysis is
>also known under the name "dual scaling". For references consult
>Professor Emeritus Shizuhiko Nishisato of the University of Toronto:
>Shizuhiko Nishisato <[EMAIL PROTECTED]>.
> -- Don.
> ------------------------------------------------------------------------
> Donald F. Burrill [EMAIL PROTECTED]
> 184 Nashua Road, Bedford, NH 03110 603-471-7128
>
_______________________________________________________________
Shizuhiko Nishisato, Professor Emeritus, Measurement and Evaluation
Program,
CTL, OISE/UT, 252 Bloor Street West, Toronto, Ontario, Canada M5S 1V6
[EMAIL PROTECTED]
(Tel): 416-923-6641, X2696
http://fcis.oise.utoronto.ca/~snishisato
http://fcis.oise.utoronto.ca/~icmma
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
