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**Prediction for regularized clusterwise multiblock regression.**
*(English)*
Zbl 1414.62230

Summary: In a large variety of fields such as epidemiology, process monitoring, chemometrics, marketing, and social sciences among others, many research questions pertain to regression analysis from large data sets. Although in some cases standard regression will suffice, modeling is sometimes more challenging for various reasons (i) explain several variables; (ii) with a large number of explanatory variables organized into meaningful, usually ill-conditioned, multidimensional matrices; (iii) where observations come from different subpopulations; and (iv) with the opportunity to predict new observations. Although some developed methods partially meet these challenges, none of them covers all these aspects. To fill this gap, a new method, called regularized clusterwise multiblock regression (CW.rMBREG), is proposed. The method CW.rMBREG combines clustering and a component-based (multiblock) model associated with a well-defined criterion to optimize. It provides simultaneously a partition of the observations into clusters along with the regression coefficients associated with each cluster. To go further, we propose to investigate a key feature generally neglected in clusterwise regression, ie, the prediction of new observations. The usefulness of CW.rMBREG is illustrated on the basis of both a simulation study and a real example in the field of indoor air quality. It results that CW.rMBREG improves the quality of the prediction and facilitates the interpretation of complex ill-conditioned data. The proposed method is available for users through the R package mbclusterwise.

### MSC:

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

62M20 | Inference from stochastic processes and prediction |

62J07 | Ridge regression; shrinkage estimators (Lasso) |

62P12 | Applications of statistics to environmental and related topics |