Principal Component Analysis with external information: some qualitative cases

Regression analysis is a useful tool to decompose data according to known structures. In this sense, it is a powerful method when meaningful structures are known in advance and it cannot be applied when such structures are unknown. Principal Component Analysis (PCA), on the other hand, can be viewed as an explorative technique for describing and interpreting a large data collection without making any assumption about an underlying probabilistic model or an a priori data structure, providing the researcher with a graphical representation and interpretation of the results. The interpretation of the representation can be improved when additional information on the structure of the variables and/or on the statistical units are available. According to the Takane and Shibayama’s factorial model, the au- thors highlight how other qualitative approaches could be considered as particular cases using suitable constraint tables or proper data decomposition.