Correspondence analysis of multivariate categorical data by weighted least-squares

Abstract

A generalization of correspondence analysis to multivariate categorical data is proposed, where all two-way contingency tables of a set of categorical variables are simultaneously fitted by weighted least-squares. An alternating least-squares algorithm is developed to perform the fitting. This technique has a number of advantages over the usual generalization known as multiple correspondence analysis. It is also an analogue of least-squares factor analysis for categorical data.