A new scaling proposal for handling ordinal categorical variables in Co-Inertia (-PLS) Analysis

In order to investigate the symmetrical relationships between several sets of variables, or regress one or more quantitative response variables on a set of variables of different nature, it is well known that it is necessary to transform non-quantitative variables in such a way that they can be analyzed together with the others measured on an interval scale.This paper suggests a proposal to cope with the problem of the treatment of ordinal qualitative variables in Co-Inertia(-PLS) Analysis. In the literature there are different proposals based on the application of known statistical techniques to quantify ordinal variables. The approach consists in quantifying each non-quantitative variable according to the empirical distributions of the variables involved in the analysis assuming the presence of a continuous underlying variable for each ordinal indicator.