Oblique rotation in correspondence analysis: a step forward in the simplest interpretation

Correspondence analysis (CA) is a popular method that can be used to analyze relationships between categorical variables. It is closely related to several popular multivariate analysis methods such as canonical correlation analysis and principal component analysis. Like principal component analysis, CA solutions can be rotated orthogonally as well as obliquely to simple structure, without affecting the total amount of explained inertia. However, some specific aspects of CA prevent standard rotation procedures from being applied in a straightforward fashion. In particular, the role played by weights assigned to points and dimensions, and the duality of CA solutions, are unique to CA. For orthogonal simple structure rotation, recently procedures have been proposed. In this paper, we construct oblique rotation methods for CA that takes into account these specific difficulties. We illustrate the benefits of our oblique rotation procedure by means of two illustrative examples.