Values below detection limit in compositional chemical data

作     者：Palarea-Albaladejo, J. Martin-Fernandez, J. A. 

作者机构：JCMB Biomath & Stat Scotland Edinburgh EH9 3JZ Midlothian Scotland Univ Girona Dept Comp Sci & Appl Math E-17071 Girona Spain 

出 版 物：《ANALYTICA CHIMICA ACTA》 (分析化学学报)

年 卷 期：2013年第764卷

页      面：32-43页

核心收录：

学科分类：081704[工学-应用化学] 07[理学] 08[工学] 0817[工学-化学工程与技术] 070302[理学-分析化学] 0703[理学-化学] 

基　　金：Agència de Gestió d’Ajuts Universitaris i de Recerca of the Generalitat de Catalunya, (2009SGR424) Spanish Ministerio de Ciencia e Innovación, (MTM2009-13272) Rural and Environment Science and Analytical Services Division, RESAS 

主　　题：Compositional data Detection limits Expectation-Maximisation algorithm Log-normal distribution Log-ratio approach Imputation methods 

摘      要：Samples representing part of a whole, usually called compositional data in statistics, are commonplace in analytical chemistry say chemical data in percentage, ppm, or mu g g(-1). Their distinctive feature is that there is an inherent relationship between all the analytes constituting a chemical sample as they only convey relative information. Some compositional data analysis principles and the log-ratio based methodology are outlined here in practical terms. Besides, one often finds that some analytes are not present in sufficient concentration in a sample to allow the measuring instruments to effectively detect them. These non-detects are usually labelled as DL (less-thans) in the data set, indicating that the values are below known detection limits. Many data analysis techniques require complete data sets. Thus, there is a need of sensible replacement strategies for less-thans. The peculiar nature of compositional data determines any data analysis and demands for a specialised treatment of less-thans that, unfortunately, is not usually covered in chemometrics. Some well-founded statistical methods are revisited in this paper aiming to prevent practitioners from relying on popular but untrustworthy approaches. A new proposal to estimate less-thans combining a log-normal probability model and a multiplicative modification of the samples is also introduced. Their performance is illustrated and compared on a real data set, and guidelines are provided for practitioners. Matlab and R code implementing the methods are made available for the reader. (C) 2012 Elsevier B.V. All rights reserved.