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. © 2013 Springer Science+Business Media New York

Clusterwise analysis for multiblock component methods

International audienceMultiblock component methods are applied to data sets for which several blocks of variables are measured on a same set of observations with the goal to analyze the relationships between these blocks of variables. In this article, we focus on multi-block component methods that integrate the information found in several blocks of explanatory variables in order to describe and explain one set of dependent variables. In the following, multiblock PLS and multiblock redundancy analysis are chosen, as particular cases of multiblock component methods when one set of variables is explained by a set of predictor variables that is organized into blocks. Because these multiblock techniques assume that the observations come from a homogeneous population they will provide suboptimal results when the observations actually come from different populations. A strategy to palliate this problem-presented in this article-is to use a technique such as clusterwise regression in order to identify homogeneous clusters of observations. This approach creates two new methods that provide clusters that have their own sets of regression coefficients. This combination of clustering and regres-B Stéphanie Bougeard 123 S. Bougeard et al. sion improves the overall quality of the prediction and facilitates the interpretation. In addition, the minimization of a well-defined criterion-by means of a sequential algorithm-ensures that the algorithm converges monotonously. Finally, the proposed method is distribution-free and can be used when the explanatory variables outnumber the observations within clusters. The proposed clusterwise multiblock methods are illustrated with of a simulation study and a (simulated) example from marketing