Principal Component and Regression Analysis for Categorical Data.Application to Arterial Hypertension.

The present work is about the statistical processing of categorical data. The mathematical details of the Categorical Principal Components and the Categorical Regression Analysis are explained. The combination of both techniques can be used to solve classification problems. Because these techniques are relatively new, we decided to use another technique (classification trees following the chi squared criteria) to make a comparison of their results, with the help of the theory of ROC curves. In the application, supposedly healthy patients of Santa Clara, Cuba, were diagnosed as hypertensive, pre hypertensive and no hypertensive by a Committee of Medical Experts. Categorical Component Analysis and Categorical Regression Analysis were applied in order to successfully solve the classification problem.