
Correspondence analysis


Following the longterm
championing of
this technique by Benzecri (eg Benzecri, 1992) and others who termed
the process
Correspondence Analysis, this term has become the generally accepted
name
for a group of techniques used various to create a spatial
representation of the rows and columns of a contingency table. It is
related very closely to singularvaluedecomposition
and is similar to principal component analysis
in that the technique seeks to find linear weights for the categories
of two variables such that the correlation between them is maximized.
Like eigendecomposition, a
second set of weights can be found to provide a maximal correlation
that accounts for the residual data after the first, and then a third,
and so on. Although it was devised for categorical data, it can be
applied to other kinds of data such as ranked or rated variables, and
consequently has been introduced as a technique for the representation
of repertory grid data in the computer programme of Feixas and Cornejo
(2002). The eigendecomposition procedure is identical with that for singularvaluedecomposition and the grid may
be similarly reconstructed and the fit to the original grid data
evaluated. It is similar to singularvaluedecomposition
in that it can scale rows and columns that have no variation (making it
a suitable representation for dependency
grids
where such an occurrence is common), however it differs from that
procedure in that it involves a specified prescaling of the grid (by a
function of row and column totals). Because of this requirement it
cannot be used to provide representations of grids that use negative
ratings.


References


 Benzecri,
J.P. (1992) Correspondence Analysis Handbook. New York: Marcel
Dekker.
 Feixas,
G., and Cornejo, J.M. (2002) GRIDCOR: Correspondence analysis for
grid data v.4.0. [Computer software] Barcelona: Authors.


Richard C. Bell


