A multiple covariance approach to PLS regression with several predictor   groups: Structural Equation Exploratory Regression
  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. 
Xavier Bry (I3M), Thomas Verron (CEFE), Pierre Cazes (CEREMADE)