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Multivariate linear regression for heterogeneous data

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  • Donatella Vicari
  • Maurizio Vichi

Abstract

The problem of multivariate regression modelling in the presence of heterogeneous data is dealt to address the relevant issue of the influence of such heterogeneity in assessing the linear relations between responses and explanatory variables. In spite of its popularity, clusterwise regression is not designed to identify the linear relationships within ‘homogeneous’ clusters exhibiting internal cohesion and external separation. A within-clusterwise regression is introduced to achieve this aim and, since the possible presence of a linear relation ‘between’ clusters should be also taken into account, a general regression model is introduced to account for both the between-cluster and the within-cluster regression variation. Some decompositions of the variance of the responses accounted for are also given, the least-squares estimation of the parameters is derived, together with an appropriate coordinate descent algorithms and the performance of the proposed methodology is evaluated in different datasets.

Suggested Citation

  • Donatella Vicari & Maurizio Vichi, 2013. "Multivariate linear regression for heterogeneous data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(6), pages 1209-1230, June.
    • Handle: RePEc:taf:japsta:v:40:y:2013:i:6:p:1209-1230
    DOI: 10.1080/02664763.2013.784896
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    Cited by:

    1. Stéphanie Bougeard & Hervé Abdi & Gilbert Saporta & Ndèye Niang, 2018. "Clusterwise analysis for multiblock component methods," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(2), pages 285-313, June.
    2. Lessmann, Stefan & Voß, Stefan, 2017. "Car resale price forecasting: The impact of regression method, private information, and heterogeneity on forecast accuracy," International Journal of Forecasting, Elsevier, vol. 33(4), pages 864-877.

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