Partitioning predictors in multivariate regression models

A Multivariate Regression Model Based on the Optimal Partition of Predictors (MRBOP) useful in applications in the presence of strongly correlated predictors is presented. Such classes of predictors are synthesized by latent factors, which are obtained through an appropriate linear combination of the original variables and are forced to be weakly correlated. Specifically, the proposed model assumes that the latent factors are determined by subsets of predictors characterizing only one latent factor. MRBOP is formalized in a least squares framework optimizing a penalized quadratic objective function through an alternating least-squares (ALS) algorithm. The performance of the methodology is evaluated on simulated and real data sets.