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Robust regression with compositional covariates including cellwise outliers

Author

Listed:
  • Nikola Štefelová

    (Palacký University)

  • Andreas Alfons

    (Erasmus Universiteit Rotterdam)

  • Javier Palarea-Albaladejo

    (Biomathematics and Statistics Scotland, JCMB)

  • Peter Filzmoser

    (Vienna University of Technology)

  • Karel Hron

    (Palacký University)

Abstract

We propose a robust procedure to estimate a linear regression model with compositional and real-valued explanatory variables. The proposed procedure is designed to be robust against individual outlying cells in the data matrix (cellwise outliers), as well as entire outlying observations (rowwise outliers). Cellwise outliers are first filtered and then imputed by robust estimates. Afterwards, rowwise robust compositional regression is performed to obtain model coefficient estimates. Simulations show that the procedure generally outperforms a traditional rowwise-only robust regression method (MM-estimator). Moreover, our procedure yields better or comparable results to recently proposed cellwise robust regression methods (shooting S-estimator, 3-step regression) while it is preferable for interpretation through the use of appropriate coordinate systems for compositional data. An application to bio-environmental data reveals that the proposed procedure—compared to other regression methods—leads to conclusions that are best aligned with established scientific knowledge.

Suggested Citation

  • Nikola Štefelová & Andreas Alfons & Javier Palarea-Albaladejo & Peter Filzmoser & Karel Hron, 2021. "Robust regression with compositional covariates including cellwise outliers," 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. 15(4), pages 869-909, December.
    • Handle: RePEc:spr:advdac:v:15:y:2021:i:4:d:10.1007_s11634-021-00436-9
    DOI: 10.1007/s11634-021-00436-9
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    References listed on IDEAS

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    1. Mike Danilov & Víctor J. Yohai & Ruben H. Zamar, 2012. "Robust Estimation of Multivariate Location and Scatter in the Presence of Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1178-1186, September.
    2. Claudio Agostinelli & Andy Leung & Victor Yohai & Ruben Zamar, 2015. "Rejoinder on: Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 484-488, September.
    3. K. Hron & P. Filzmoser & K. Thompson, 2012. "Linear regression with compositional explanatory variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1115-1128, November.
    4. Hron, K. & Templ, M. & Filzmoser, P., 2010. "Imputation of missing values for compositional data using classical and robust methods," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3095-3107, December.
    5. Filzmoser, P. & Höppner, S. & Ortner, I. & Serneels, S. & Verdonck, T., 2020. "Cellwise robust M regression," Computational Statistics & Data Analysis, Elsevier, vol. 147(C).
    6. Leung, Andy & Zhang, Hongyang & Zamar, Ruben, 2016. "Robust regression estimation and inference in the presence of cellwise and casewise contamination," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 1-11.
    7. Leung, Andy & Yohai, Victor & Zamar, Ruben, 2017. "Multivariate location and scatter matrix estimation under cellwise and casewise contamination," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 59-76.
    8. Claudio Agostinelli & Andy Leung & Victor Yohai & Ruben Zamar, 2015. "Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 441-461, September.
    9. Templ, Matthias & Kowarik, Alexander & Filzmoser, Peter, 2011. "Iterative stepwise regression imputation using standard and robust methods," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2793-2806, October.
    10. Khan, Jafar A. & Van Aelst, Stefan & Zamar, Ruben H., 2007. "Robust Linear Model Selection Based on Least Angle Regression," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1289-1299, December.
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