A multiple covariance approach to PLS regression with several predictor groups: Structural Equation Exploratory Regression

Xavier Bry (1, 2) , Thomas Verron (3) , Pierre Cazes (4)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 IMAG - Institut Montpelliérain Alexander Grothendieck
3 CEFE - Centre d’Ecologie Fonctionnelle et Evolutive
4 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

A variable group Y is assumed to depend upon R thematic variable groups X 1, ..., X R . We assume that components in Y depend linearly upon components in the Xr's. In this work, we propose a multiple covariance criterion which extends that of PLS regression to this multiple predictor groups situation. On this criterion, we build a PLS-type exploratory method - Structural Equation Exploratory Regression (SEER) - that allows to simultaneously perform dimension reduction in groups and investigate the linear model of the components. SEER uses the multidimensional structure of each group. An application example is given.

Mots clés: Linear Regression; Latent Variables; PLS Path Modelling; PLS Regression; Structural Equation Models; SEER

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

Xavier Bry, Thomas Verron, Pierre Cazes. A multiple covariance approach to PLS regression with several predictor groups: Structural Equation Exploratory Regression. 2008. ⟨hal-00239491v2⟩