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

  • Authors:

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

  • Affiliations:

  • Department of Computer Science and Applied Mathematics, University of Girona, Campus Montilivi, P4, E-17071 Girona, Spain;Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic;Department of Statistics and Probability Theory, Vienna University of Technology, Wiedner Hauptstraíe 8-10, 1040 Vienna, Austria and Department of Methodology, Statistics Austria, Guglgasse 1 ...;Department of Statistics and Probability Theory, Vienna University of Technology, Wiedner Hauptstraíe 8-10, 1040 Vienna, Austria;Biomathematics & Statistics Scotland, JCMB, The King's Buildings, Edinburgh, EH9 3JZ, UK

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2012

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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.