Orthogonal rotation in PCAMIX

TL;DR

This paper introduces a new, efficient method for orthogonal rotation in PCAMIX, a technique combining PCA and MCA, with direct computation of loadings and an application demonstrating its practical benefits.

Contribution

It presents a novel SVD-based approach for PCAMIX, including a computationally efficient varimax rotation and a direct solution for the optimal rotation angle.

Findings

The proposed algorithm shows good computational performance in simulations.

Rotation improves interpretability in MCA applications.

Source code is available in the R package 'PCAmixdata'.

Abstract

Kiers (1991) considered the orthogonal rotation in PCAMIX, a principal component method for a mixture of qualitative and quantitative variables. PCAMIX includes the ordinary principal component analysis (PCA) and multiple correspondence analysis (MCA) as special cases. In this paper, we give a new presentation of PCAMIX where the principal components and the squared loadings are obtained from a Singular Value Decomposition. The loadings of the quantitative variables and the principal coordinates of the categories of the qualitative variables are also obtained directly. In this context, we propose a computationaly efficient procedure for varimax rotation in PCAMIX and a direct solution for the optimal angle of rotation. A simulation study shows the good computational behavior of the proposed algorithm. An application on a real data set illustrates the interest of using rotation in MCA. All source codes are available in the R package "PCAmixdata".