Rounded zeros: some practical aspects for compositional data

Abstract It is very important to realize that the well-known ‘zeros problem’ in compositional data is inherent in the nature of the data rather than in the log-ratio methodology. In a strict sense, any null value is informative itself and needs specific treatment before a multivariate method is applied. In the rounded zero case specific techniques of missing data should be applied as a previous step, taking into account that any of these techniques must respect the compositional nature of the data. In practice, when an imputation method is applied, then it is necessary to make a sensitivity analysis of the results from multivariate analysis. These methodological aspects are applied and illustrated using compositional data from geological samples.

[1]  V. Pawlowsky-Glahn,et al.  Zero Replacement in Compositional Data Sets , 2000 .

[2]  J. A. Martín-Fernández,et al.  MARKOV CHAIN MONTE CARLO METHOD APPLIED TO ROUNDING ZEROS OF COMPOSITIONAL DATA: FIRST APPROACH , 2003 .

[3]  H. Redkey,et al.  A new approach. , 1967, Rehabilitation record.

[4]  John Bacon-Shone.  Modelling Structural Zeros in Compositional data , 2003 .

[5]  V. Pawlowsky-Glahn,et al.  Dealing with Zeros and Missing Values in Compositional Data Sets Using Nonparametric Imputation , 2003 .

[6]  J. Aitchison,et al.  Possible solution of some essential zero problems in compositional data analysis , 2003 .

[7]  V. Pawlowsky-Glahn,et al.  Compositional data and their analysis: an introduction , 2006, Geological Society, London, Special Publications.

[8]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[9]  Spurious Clusters in Granulometric Data Caused by Logratio Transformation , 1999 .

[10]  Vidal.  A MEASURE OF DIFFERENCE FOR COMPOSITIONAL DATA BASED ON MEASURES OF DIVERGENCE , 2007 .

[11]  V. Pawlowsky-Glahn,et al.  Simplicial geometry for compositional data , 2006, Geological Society, London, Special Publications.

[12]  Jane M. Fry,et al.  Compositional data analysis and zeros in micro data , 2000 .

[13]  R. A. Crovelli,et al.  An objective replacement method for censored geochemical data , 1993 .

[14]  J. Aitchison,et al.  Biplots of Compositional Data , 2002 .

[15]  John Aitchison,et al.  The Statistical Analysis of Compositional Data , 1986 .

[16]  Nicole A. Lazar,et al.  Statistical Analysis With Missing Data , 2003, Technometrics.