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

• Published in: Computational statistics & data analysis Vol. 56; no. 9; pp. 2688 - 2704
• Main Authors: Martín-Fernández, J.A., Hron, K., Templ, M., Filzmoser, P., Palarea-Albaladejo, J.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2012; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Algorithms; Balances; Balances EM algorithm Log-ratio transformations Robust regression Values below detection limit; Computer simulation; Data processing; EM algorithm; Geochemistry; Log-ratio transformations; Monte Carlo methods; Robust regression; Statistical analysis; Statistics; Transformations; Values below detection limit; Balances; Log-ratio transformations; Robust regression; EM algorithm; Values below detection limit
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2012.02.012

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.