Predictive Mapping
One application of multiple
correspondence analysis is to perform the equivalent of a Multiple
Regression for categorical variables, by adding supplementary columns
to a design matrix (see also Burt
tables). For example, suppose you had a design matrix containing various
categorical indicators of health related behaviors (e.g., whether or not
the individual smoked, exercised, etc.). You could add two columns to
indicate whether or not the respective subject had or had not been ill
over the past year (i.e., you could add one column
Ill and another column Not ill,
and enter 0's and 1's to indicate each subject's health status). If in
a simple correspondence analysis
of the design matrix, you added those columns as supplementary columns
to the analysis, then (1) the summary statistics for the quality
of representation (see the Correspondence
Analysis Introductory Overview) for those columns would give
you an indication of how well you can "explain" illness as a
function of the other variables in the design matrix, and (2) the display
of the column points in the final coordinate system would provide an indication
of the nature (e.g., direction) of the relationships between the columns
in the design matrix and the column points indicating illness. This technique
(adding supplementary points to a multiple correspondence analysis) is
also called predictive mapping.
For more information, see Correspondence
Analysis.