Regression modeling via latent predictors

A proposal for multivariate regression modeling based on latent predictors (LPs) is presented. The idea of the proposed model is to predict the responses on LPs which, in turn, are built as linear combinations of disjoint groups of observed covariates. The formulation naturally allows to identify LPs that best predict the responses by jointly clustering the covariates and estimating the regression coefficients of the LPs. Clearly, in this way the LP interpretation is greatly simplified since LPs are exactly represented by a subset of covariates only. The model is formalized in a maximum likelihood framework which is intuitively appealing for comparisons with other methodologies, for allowing inference on the model parameters and for choosing the number of subsets leading to LPs. An Expectation Conditional Maximization (ECM) algorithm is proposed for parameter estimation and experiments on simulated and real data show the performance of our proposal.