Multivariate co-inertia analysis for qualitative data by partial least squares

Abstract

In this paper we propose a new strategy to study a dependence problem among qualitative variables, based upon 1) a generalization of the covariance criterion (Tucker, 1958), 2) a monotone regression in order to preserve the original ordering of categories on the axis of maximal covariance, and 3) the Partial Least Squares (PLS) approach (Wold, 1966) to compute the remaining axes. From a practical point of view, the use of a complete ordering of predictors can be considered as a way to extract more interpretable information Under the completer order constraint of the scores, different techniques have been proposed in literature, specifically within the context of optimal scaling (Nishisato, 1980; Nishisato and Arri, 1975).