A Proposal for Handling Categorical Predictors in PLS Regression Framework

Abstract

To regress one or more quantitative response variables on a set of predictor variables of different nature, it is necessary to transform non-quantitative predictors in such a way that they can be analyzed together with the other variables measured on an interval scale. Here, a new proposal to cope with this issue in Partial Least Squares (PLS) regression framework is presented. The approach consists in quantifying each non-quantitative predictor according to Hayashi’s first quantification method, using the dependent variable (or, in the multivariate case, a linear combination of the response variables) as an external criterion. The PLS weight of each variable which is quantified according to the proposed approach is coherent with the statistical relationship between its original non-quantitative variable and the response variable(s) as expressed in terms of Pearson’s correlation ratio. Firstly, the case where one variable depends on a set of both categorical and quantitative variables is discussed; then, a modified PLS algorithm, called PLS-CAP, is proposed to obtain the quantifications of the categorical predictors in the multi-response case. An application on real data is presented in order to enhance the properties of the quantification approach based on the PLS-CAP with respect to the classical approach based on the dummy code of the categorical variables.