Modélisation factorielle des interactions entre deux ensembles d'observations : la méthode PLS-FILM (Partial Least Squares Factor Interaction Linear Modelling)

Xavier Bry (1, 2) , Thomas Verron (3)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 IMAG - Institut Montpelliérain Alexander Grothendieck
3 CEFE - Centre d’Ecologie Fonctionnelle et Evolutive

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.

Mots clés: PLS; PLS-FILM; RLQ; Structural Equation Modelling; Interactions; Latent Variables; L-PLS

Domaines: Méthodologie [stat.ME]; Statistiques [math.ST]; Théorie [stat.TH]

Xavier Bry, Thomas Verron. Modélisation factorielle des interactions entre deux ensembles d'observations : la méthode PLS-FILM (Partial Least Squares Factor Interaction Linear Modelling). 2006. ⟨hal-00239493⟩