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Parameter Choice, Stability and Validity for Robust Cluster Weighted Modeling

Author

Listed:
  • Andrea Cappozzo

    (MOX-Department of Mathematics, Politecnico di Milano, 20133 Milan, Italy
    These authors contributed equally to this work.)

  • Luis Angel García Escudero

    (Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Valladolid, 47002 Villadolid, Spain)

  • Francesca Greselin

    (Department of Statistics and Quantitative Methods, University of Milano-Bicocca, 20126 Milan, Italy
    These authors contributed equally to this work.)

  • Agustín Mayo-Iscar

    (Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Valladolid, 47002 Villadolid, Spain)

Abstract

Statistical inference based on the cluster weighted model often requires some subjective judgment from the modeler. Many features influence the final solution, such as the number of mixture components, the shape of the clusters in the explanatory variables, and the degree of heteroscedasticity of the errors around the regression lines. Moreover, to deal with outliers and contamination that may appear in the data, hyper-parameter values ensuring robust estimation are also needed. In principle, this freedom gives rise to a variety of “legitimate” solutions, each derived by a specific set of choices and their implications in modeling. Here we introduce a method for identifying a “set of good models” to cluster a dataset, considering the whole panorama of choices. In this way, we enable the practitioner, or the scientist who needs to cluster the data, to make an educated choice. They will be able to identify the most appropriate solutions for the purposes of their own analysis, in light of their stability and validity.

Suggested Citation

  • Andrea Cappozzo & Luis Angel García Escudero & Francesca Greselin & Agustín Mayo-Iscar, 2021. "Parameter Choice, Stability and Validity for Robust Cluster Weighted Modeling," Stats, MDPI, vol. 4(3), pages 1-14, July.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:3:p:36-615:d:589298
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    References listed on IDEAS

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