Three-Way Correspondence Analysis in R

Abstract

Three-way correspondence analysis is a suitable multivariate method for visualising the association in three-way categorical data, modelling the global dependence, or reducing dimensionality. This paper provides a description of an R package for performing three-way correspondence analysis: CA3variants. The functions in this package allow the analyst to perform several variations of this analysis, depending on the research question being posed and/or the properties underlying the data. Users can opt for the classical (symmetrical) approach or the non-symmetric variant - the latter is particularly useful if one of the three categorical variables is treated as a response variable. In addition, to perform the necessary three-way decompositions, a Tucker3 and a trivariate moment decomposition (using orthogonal polynomials) can be utilized. The Tucker3 method of decomposition can be used when one or more of the categorical variables is nominal while for ordinal variables the trivariate moment decomposition can be used. The package also provides a function that can be used to choose the model dimensionality.