Principal Component Analysis (PCA) changes ,any X variables into a few new variables.
Tne new variable is called "principal component".
The new variables tell us the main information of the data set.
New variables have orthogonal relationship. So, if we use the variables as the X of multi-regression analysis , the analysis is easier.
For Category Data, Broadly defined Quantification theory 3 is available as PCA.
New variable is made to maximize the variance of it. Maximization is done using Lagrange's method of undetermined multipliers.
The analysist have to consider the meanings of each new variable.
Example of R is in the page, Principal component analysis by R .
Principal Component Regression Analysis
Analysis Using Intermediate Layer
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Canonical Correlation Analysis
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