On the applicability of truncated component analysis based on correlation coefficients for nominal scales

Abstract

The possibility of using component analysis for nominal data is discussed. Particularly, two nominal scale correlation coefficients are applicable, namely, Tschuprow’s coefficient and the J index. The reason is that they are E-correlation coefficients; that is, they satisfy the requirements of a scalar product between normalized vectors in a Euclidean space. Some characteristics of these coefficients are described. The contingency coefficient and Cramer’s V are shown not to be applicable in a component analysis. An example of a truncated component analysis on artificial nominal data is included with both the J index and Tschuprow’s coefficient.