R help - Mar 2001 - [OT] correspondence analysis w/ non-mutually-exclusive categories

Greetings, again. This is not strictly an R question, so please feel free
to ignore it if you like. 

My question is about the substance of correspondence
analysis. Specifically, is it appropriate to use ca on a matrix of values
such that the columns and/or rows are not mutually exclusive?  To be more
detailed:

- The standard use of ca is illustrated in the example of corresp() (from
MASS):

data(caith)
library(mva)
corresp(caith)
biplot(corresp(caith, nf=2))
> caith
       fair red medium dark black
blue    326  38    241  110     3
light   688 116    584  188     4
medium  343  84    909  412    26
dark     98  48    403  681    85

in this table, presumably, an observation can fall in only one
cell: red/light, say, or dark/fair.  

- However, my data are different, in that a single observation can
(theoretically) fall in two or more cells. Consider:

	voted98	voted00	donated	protested no_partic
male
female

a given observation might fall, for example, in male/voted98 and
male/voted00.  What are the implications of this?

- I am aware of the multiple correspondence technique, which I believe
answers (some of) this issue. However I have a different problem with
it: I have so many observations (ca. 5700) that the plot becomes
unreadable. That's because each *observation* is plotted in mca, whereas
each unique profile is what's plotted in ca.

Any advice will be met with tremendous gratitude :)

Andy Perrin

----------------------------------------------------------------------
Andrew J Perrin - Ph.D. Candidate, UC Berkeley, Dept. of Sociology  
Chapel Hill, North Carolina, USA - http://demog.berkeley.edu/~aperrin
        aperrin at socrates.berkeley.edu - aperrin at igc.apc.org

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> My question is about the substance of correspondence
> analysis. Specifically, is it appropriate to use ca on a matrix of values
> such that the columns and/or rows are not mutually exclusive?
Correspondence analysis is applied extremely frequently to data with rows
and columns that are not mutually exclusive.  In market research, for
example, brand-attribute matrices are created of the form:

		Reliable	Fast	Sexy
Ford		25		35	40
Honda		50		28	100
Toyota	21		25	21

and correspondence analysis is then applied to create positioning maps.
There may be some theoretical reason why this is not sound, but practical
experience suggests it is very useful.  Of course, traditional approaches to
statistical inference on such maps - such as confidence intervals - become
inappropriate.
> - I am aware of the multiple correspondence technique, which I believe
> answers (some of) this issue. However I have a different problem with
> it: I have so many observations (ca. 5700) that the plot becomes
> unreadable. That's because each *observation* is plotted in mca,
whereas
> each unique profile is what's plotted in ca.
I'm not sure how you're doing MCA, but it can certainly be done without
plotting each observation.  From memory, there is a good description of how
to do it in

Greenacre, Michael and Blasius, Jorg 1994 (eds.) Correspondence Analysis in
the Social Sciences. Recent Developments and Applications. London: Academic
Press.

Tim
>
> Any advice will be met with tremendous gratitude :)
>
> Andy Perrin
>
> ----------------------------------------------------------------------
> Andrew J Perrin - Ph.D. Candidate, UC Berkeley, Dept. of Sociology
> Chapel Hill, North Carolina, USA - http://demog.berkeley.edu/~aperrin
>         aperrin at socrates.berkeley.edu - aperrin at igc.apc.org
>
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> -.-.-.-.-.-.-
> r-help mailing list -- Read
> http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
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> _._._._._._._
>
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