Simple and multiple correspondence analysis for ordinal-scale variables using orthogonal polynomials

TLDR

Correspondence analysis typically relies on singular value decomposition to explore associations among categorical variables, but can also be performed with bivariate moment decomposition using orthogonal polynomials, and a hybrid decomposition combines both approaches. The paper demonstrates the applicability of the hybrid decomposition for simple and multiple correspondence analysis. Keywords: multiple correspondence analysis, ordinal‑scale variables, singular value decomposition, bivariate moment decomposition, orthogonal polynomials, hybrid decomposition.

Abstract

Abstract Correspondence analysis (CA) has gained a reputation for being a very useful statistical technique for determining the nature of association between two or more categorical variables. For simple and multiple CA, the singular value decomposition (SVD) is the primary tool used and allows the user to construct a low-dimensional space to visualize this association. As an alternative to SVD, one may consider the bivariate moment decomposition (BMD), a method of decomposition that involves using orthogonal polynomials to reflect the structure of ordered categorical responses. When the features of BMD are combined with SVD, a hybrid decomposition (HD) is formed. The aim of this paper is to show the applicability of HD when performing simple and multiple CA. Keywords: multiple correspondence analysisordinal-scale variablessingular value decompositionbivariate moment decompositionorthogonal polynomialshybrid decomposition