Mod\'elisation factorielle des interactions entre deux ensembles d'observations : la m\'ethode PLS-FILM (Partial Least Squares Factor Interaction Linear Modelling)

TL;DR

This paper introduces PLS-FILM, a new geometrically grounded method for modeling interactions between two observation sets using hierarchical factors derived from their descriptions, bridging existing analytical approaches.

Contribution

The paper presents PLS-FILM, a novel factorization technique that models interactions between two data sets based on their descriptive variables, offering a new perspective beyond RLQ and L-PLS methods.

Findings

Provides a new geometric exploratory technique for interaction analysis.

Models interactions with hierarchical subject- and object-factors.

Bridges gap between RLQ analysis and L-PLS, with unique rank 1 components.

Abstract

In this work, we consider a data array encoding interactions between two sets of observations respectively referred to as "subjects" and "objects". Besides, descriptions of subjects and objects are available through two variable sets. We propose a geometrically grounded exploratory technique to analyze the interactions using descriptions of subjects and objects: interactions are modelled using a hierarchy of subject-factors and object-factors built up from these descriptions. Our method bridges the gap between those of Chessel (RLQ analysis) and Martens (L-PLS), although it only has rank 1 components in common with them.