Exploratory tools for outlier detection in compositional data with structural zeros
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2017
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01A - Journal article
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Journal of Applied Statistics
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44
Issue / Number
4
Pages / Duration
734-752
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Taylor & Francis
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Abstract
The analysis of compositional data using the log-ratio approach is based on ratios between the compositional parts. Zeros in the parts thus cause serious difficulties for the analysis. This is a particular prob- lem in case of structural zeros, which cannot be simply replaced by a non-zero value as it is done, e.g. for values below detection limit or missing values. Instead, zeros to be incorporated into further sta- tistical processing. The focus is on exploratory tools for identifying outliers in compositional data sets with structural zeros. For this pur- pose, Mahalanobis distances are estimated, computed either directly for subcompositions determined by their zero patterns, or by using imputation to improve the efficiency of the estimates, and then pro- ceed to the subcompositional and subgroup level. For this approach, new theory is formulated that allows to estimate covariances for imputed compositional data and to apply estimations on subgroups using parts of this covariance matrix. Moreover, the zero pattern structure is analyzed using principal component analysis for binary data to achieve a comprehensive view of the overall multivariate data structure. The proposed tools are applied to larger compositional data sets from official statistics, where the need for an appropriate treatment of zeros is obvious.
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1360-0532
0266-4763
0266-4763
Language
English
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No
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Published
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Citation
Templ, M., Hron, K., & Filzmoser, P. (2017). Exploratory tools for outlier detection in compositional data with structural zeros. Journal of Applied Statistics, 44(4), 734–752. https://doi.org/10.1080/02664763.2016.1182135