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Model-based replacement of rounded zeros in compositional data: Classical and robust approaches

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  • Martín-Fernández, J.A.
  • Hron, K.
  • Templ, M.
  • Filzmoser, P.
  • Palarea-Albaladejo, J.

Abstract

The log-ratio methodology represents a powerful set of methods and techniques for statistical analysis of compositional data. These techniques may be used for the estimation of rounded zeros or values below the detection limit in cases when the underlying data are compositional in nature. An algorithm based on iterative log-ratio regressions is developed by combining a particular family of isometric log-ratio transformations with censored regression. In the context of classical regression methods, the equivalence of the method based on additive and isometric log-ratio transformations is proved. This equivalence does not hold for robust regression. Based on Monte Carlo methods, simulations are performed to assess the performance of classical and robust methods. To illustrate the method, a case study involving geochemical data is conducted.

Suggested Citation

  • Martín-Fernández, J.A. & Hron, K. & Templ, M. & Filzmoser, P. & Palarea-Albaladejo, J., 2012. "Model-based replacement of rounded zeros in compositional data: Classical and robust approaches," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2688-2704.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:9:p:2688-2704
    DOI: 10.1016/j.csda.2012.02.012
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    References listed on IDEAS

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    1. 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.
    2. Amemiya, Takeshi, 1984. "Tobit models: A survey," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 3-61.
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    Cited by:

    1. Tsagris, Michail, 2014. "The k-NN algorithm for compositional data: a revised approach with and without zero values present," MPRA Paper 65866, University Library of Munich, Germany.
    2. Germ`a Coenders & N'uria Arimany Serrat, 2023. "Accounting statement analysis at industry level. A gentle introduction to the compositional approach," Papers 2305.16842, arXiv.org, revised Feb 2024.
    3. Theophilus K. Agbenyezi & Gordon Foli & Simon K. Y. Gawu, 2020. "Geochemical Characteristics Of Gold-Bearing Granitoids At Ayanfuri In The Kumasi Basin, Southwestern Ghana: Implications For The Orogenic Related Gold Systems," Earth Sciences Malaysia (ESMY), Zibeline International Publishing, vol. 4(2), pages 127-134, June.
    4. Tsagris, Michail, 2015. "Regression analysis with compositional data containing zero values," MPRA Paper 67868, University Library of Munich, Germany.
    5. Juan José Egozcue & Vera Pawlowsky-Glahn, 2019. "Compositional data: the sample space and its structure," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 599-638, September.
    6. M. Templ & K. Hron & P. Filzmoser, 2017. "Exploratory tools for outlier detection in compositional data with structural zeros," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(4), pages 734-752, March.

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