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Oblique rotation in correspondence analysis: A step forward in the search for the simplest interpretation
Author(s) -
LorenzoSeva Urbano,
Velden Michel,
Kiers Henk A. L.
Publication year - 2009
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711008x368295
Subject(s) - oblique case , principal component analysis , rotation (mathematics) , categorical variable , interpretation (philosophy) , mathematics , simple (philosophy) , correspondence analysis , canonical correlation , multiple correspondence analysis , duality (order theory) , algorithm , computer science , geometry , statistics , pure mathematics , philosophy , linguistics , epistemology , programming language
Correspondence analysis (CA) is a popular method that can be used to analyse 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 into a 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, procedures recently have been proposed. In this paper, we construct oblique rotation methods for CA that take into account these specific difficulties. We illustrate the benefits of our oblique rotation procedure by means of two illustrative examples.