Categorical Principal Components Analysis

Categorical principal components analysis can be thought of as a method of dimension reduction. A set of variables is analyzed to reveal major dimensions of variation. The original data set can then be replaced by a new, smaller data set with minimal loss of information. The method reveals relationships among variables, among cases, and among variables and cases.

The criterion used by categorical principal components analysis for quantifying the observed data is that the object scores (component scores) should have large correlations with each of the quantified variables. A solution is good to the extent that this criterion is satisfied.

Two examples of categorical principal components analysis will be presented. The first employs a rather small data set useful for illustrating the basic concepts and interpretations associated with the procedure. The second example examines a practical application.

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