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Comparison of the PRINQUAL and CORRESP Procedures

Both PROC PRINQUAL and PROC CORRESP can be used to summarize associations among variables measured on a nominal scale. PROC
PRINQUAL searches for a single nonlinear transformation of the original scoring of each nominal variable that optimizes some
aspect of the covariance matrix of the transformed variables. For example, PROC PRINQUAL could be used to find scorings that
maximize the fit of a principal component model with one component. PROC CORRESP uses the crosstabulations of nominal variables,
not covariances, and produces multiple scores for each category of each nominal variable. The main conceptual difference between
PROC PRINQUAL and PROC CORRESP is that PROC PRINQUAL assumes that the categories of a nominal variable correspond to values
of a single underlying interval variable, whereas PROC CORRESP assumes that there are multiple underlying interval variables
and therefore uses different category scores for each dimension of the correspondence analysis. Scores from PROC CORRESP on
the first dimension match the single set of PROC PRINQUAL scores (with appropriate standardizations for both analyses).