Multiblock Analysis of Distributional Data
Résumé
The classic data representation model becomes too restrictive when the data to be analysed are not real numbers but include variability. This is the case when the units analysed are not isolated elements, but groups formed on the basis of certain common properties, and the variability observed within each group must be taken into account. We are interested in distributional numerical data, where, for each variable, the units are described by empirical distributions. In our model, each distribution is represented by a location measure and interquantile ranges, for a chosen set of quantiles. This leads naturally to blocks of variables associated with each of the initial descriptive variables. We propose to take into account this structure into homogeneous blocks using multiblock methods. In this work, we address regression between distribution valued variables within the proposed framework. As the variables in each block may, by nature, be strongly related, we use PLS multiblock regression to manage multicollinearity. Applications to real data put in evidence the interest of the proposed approach.