Robust regression with compositional covariates including cellwise outliers

Nikola Štefelová (), Andreas Alfons (), Javier Palarea-Albaladejo (), Peter Filzmoser () and Karel Hron ()
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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

Advances in Data Analysis and Classification, 2021, vol. 15, issue 4, No 3, 869-909

Abstract: 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.

Keywords: Cellwise outliers; Compositional data; Logratio coordinates; Regression analysis; Robust statistics; 62J05; 62H99 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11634-021-00436-9

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