Correspondence analysis for symbolic contingency tables based on interval algebra

In this paper, we propose interval algebraic correspondence analysis (IACA), a new correspondence analysis method for interval contingency tables based on interval algebra. The interval contingency table, which is made by counting up the observations measured by two multi-valued variables, is an extension of the classical contingency table. Correspondence analysis for the interval contingency table has been proposed by Rodŕiguez[8], (SymCA); this analysis is based on the centers method in principal component analysis for the interval variables (Cazes, et al.,[2]). However, his method has the disadvantage that when computing statistical indices, the internal variation of intervals is lost. To overcome this problem, we propose a new correspondence analysis through which the internal variation of the interval is retained. A numerical example using IACA is discussed and the usefulness is shown.