Correspondence analysis for symbolic contingency tables based on interval algebra

摘要

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 Rodriguez (SymCA); this analysis is based on the centers method in principal component analysis for the interval variables (Cazes, et al.). 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.