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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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    1. Francesca Torti & Marco Riani & Gianluca Morelli, 2021. "Semiautomatic robust regression clustering of international trade data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 863-894, September.
    2. Salvatore Ingrassia & Antonio Punzo, 2020. "Cluster Validation for Mixtures of Regressions via the Total Sum of Squares Decomposition," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 526-547, July.
    3. Andrea Cerioli & Marco Riani & Anthony C. Atkinson & Aldo Corbellini, 2018. "The power of monitoring: how to make the most of a contaminated multivariate sample," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 559-587, December.
    4. Glenn Milligan & Martha Cooper, 1985. "An examination of procedures for determining the number of clusters in a data set," Psychometrika, Springer;The Psychometric Society, vol. 50(2), pages 159-179, June.
    5. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    6. Francesca Torti & Domenico Perrotta & Marco Riani & Andrea Cerioli, 2019. "Assessing trimming methodologies for clustering linear regression data," 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. 13(1), pages 227-257, March.
    7. Neykov, N. & Filzmoser, P. & Dimova, R. & Neytchev, P., 2007. "Robust fitting of mixtures using the trimmed likelihood estimator," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 299-308, September.
    8. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, August.
    9. Andrea Cerioli & Marco Riani & Anthony C. Atkinson & Aldo Corbellini, 2018. "Rejoinder to the discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 661-666, December.
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    Cited by:

    1. Gabriele Perrone & Gabriele Soffritti, 2024. "Parsimonious Seemingly Unrelated Contaminated Normal Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 41(3), pages 533-567, November.

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