Multidimensional Joint Graphical Display of Symmetric Analysis: Back to the Fundamentals

Abstract

The basic premise of dual scaling/correspondence analysis lies in the simultaneous or symmetric analysis of rows and columns of the data matrix, a task that resembles the analysis of principal component analysis of both the person-to-person correlation matrix and the item-by-item correlation matrix together. Our main quest: whether or not we can represent both analyses in the same Euclidean space. The traditional graphical methods are very problematic: symmetric display or French plot suffers from the discrepancy between the row space and the column space; non-symmetric display involves the projection of data onto standardized space, which does not contain coordinate information in the data; a variety of biplots, of which criticisms we rarely see, involve operations that do not typically maintain row and column measurements on the equal metrics, or if they do they are not the coordinates of the data. Thus, none of these provides a precise description of complex information in data, hence failing in the basic objective of symmetric data analysis. This paper will identify logical problems of the current practice and offers a justifiable alternative to joint graphical display. “Graphing is believing” may in reality remain to be a wishful thinking.