Multivariate regression model based on an optimal partition of predictors.

A multivariate regression model based on an optimal partition of predictors (MRBOP) is presented. The proposed model attempts to identify latent predictors, defined as linear combinations of groups of explanatory variables which similarly predict the responses. In MRBOP the explanatory variables are partitioned into groups and the important groups with high prediction power are identified. The model is formalized in a least squares framework optimizing a quadratic objective function subject to a set of constraints due to the required clustering structure for the explanatory variables. An alternating least-squares (ALS) algorithm for fitting the MRBOP model is developed, and the performance of the new methodology is evaluated on simulation studies and on a real data set.