PLS Path modelling and multiple table analysis. Application to the cosmetic habits of women in Ile-de-France

Abstract

Many statistical methods can be used to study data presented in the form of J blocks of variables observed on the same subjects. The most well-known methods are the following: Horst's generalised canonical correlation analysis, Carroll's generalised canonical correlation analysis, Escofier and Pagès' multiple factor analysis and second order confirmatory factor analysis. The aim of all these methods is to identify a common structure among the J data tables. The partial least squares (PLS) Path modelling approach of Herman Wold can also be used on this type of data. Generalised canonical correlation analyses of Horst and Carroll and multiple factor analysis are special cases of PLS Path modelling, but this approach also leads to new useful methods. In the first part of this paper, we briefly review PLS Path modelling, then we look in greater detail at the specific case of tables without structural relations. In the second part, we have applied PLS Path modelling to a study of the cosmetic habits of women in the Ile-de-France region. Lohmöller's LVPLS software release 1.8 allowed us to carry out the application without too many difficulties.