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Imputation of missing values for compositional data using classical and robust methods

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  • Hron, K.
  • Templ, M.
  • Filzmoser, P.

Abstract

New imputation algorithms for estimating missing values in compositional data are introduced. A first proposal uses the k-nearest neighbor procedure based on the Aitchison distance, a distance measure especially designed for compositional data. It is important to adjust the estimated missing values to the overall size of the compositional parts of the neighbors. As a second proposal an iterative model-based imputation technique is introduced which initially starts from the result of the proposed k-nearest neighbor procedure. The method is based on iterative regressions, thereby accounting for the whole multivariate data information. The regressions have to be performed in a transformed space, and depending on the data quality classical or robust regression techniques can be employed. The proposed methods are tested on a real and on simulated data sets. The results show that the proposed methods outperform standard imputation methods. In the presence of outliers, the model-based method with robust regressions is preferable.

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  • Hron, K. & Templ, M. & Filzmoser, P., 2010. "Imputation of missing values for compositional data using classical and robust methods," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3095-3107, December.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3095-3107
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    References listed on IDEAS

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    1. Yucel, Recai M. & Demirtas, Hakan, 2010. "Impact of non-normal random effects on inference by multiple imputation: A simulation assessment," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 790-801, March.
    2. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
    3. Serneels, Sven & Verdonck, Tim, 2008. "Principal component analysis for data containing outliers and missing elements," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1712-1727, January.
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    Cited by:

    1. Nikola Štefelová & Andreas Alfons & Javier Palarea-Albaladejo & Peter Filzmoser & Karel Hron, 2021. "Robust regression with compositional covariates including cellwise outliers," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(4), pages 869-909, December.
    2. Maria Anna Di Palma & Michele Gallo, 2019. "External Information Model in a Compositional Perspective: Evaluation of Campania Adolescents’ Preferences in the Allocation of Leisure-Time," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(1), pages 117-133, November.
    3. Templ, Matthias & Kowarik, Alexander & Filzmoser, Peter, 2011. "Iterative stepwise regression imputation using standard and robust methods," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2793-2806, October.
    4. M. A. Di Palma & M. Gallo, 2016. "A co-median approach to detect compositional outliers," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(13), pages 2348-2362, October.
    5. repec:jss:jstsof:37:i03 is not listed on IDEAS
    6. Garrido-Vega, Pedro & Ortega Jimenez, Cesar H. & de los Ríos, José Luis Díez Pérez & Morita, Michiya, 2015. "Implementation of technology and production strategy practices: Relationship levels in different industries," International Journal of Production Economics, Elsevier, vol. 161(C), pages 201-216.
    7. Martín-Fernández, J.A. & Hron, K. & Templ, M. & Filzmoser, P. & Palarea-Albaladejo, J., 2012. "Model-based replacement of rounded zeros in compositional data: Classical and robust approaches," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2688-2704.
    8. Tutz, Gerhard & Ramzan, Shahla, 2015. "Improved methods for the imputation of missing data by nearest neighbor methods," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 84-99.
    9. Frahm, Gabriel & Nordhausen, Klaus & Oja, Hannu, 2020. "M-estimation with incomplete and dependent multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    10. M. Templ & K. Hron & P. Filzmoser, 2017. "Exploratory tools for outlier detection in compositional data with structural zeros," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(4), pages 734-752, March.
    11. Matthias Templ & Andreas Alfons & Peter Filzmoser, 2012. "Exploring incomplete data using visualization techniques," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 6(1), pages 29-47, April.
    12. K. Hron & P. Filzmoser & K. Thompson, 2012. "Linear regression with compositional explanatory variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1115-1128, November.
    13. Peter Filzmoser & Karel Hron & Matthias Templ, 2012. "Discriminant analysis for compositional data and robust parameter estimation," Computational Statistics, Springer, vol. 27(4), pages 585-604, December.
    14. Takahiro Yoshida & Morito Tsutsumi, 2018. "On the effects of spatial relationships in spatial compositional multivariate models," Letters in Spatial and Resource Sciences, Springer, vol. 11(1), pages 57-70, March.
    15. Mark A. Engle & Charles W. Nye & Ghanashyam Neupane & Scott A. Quillinan & Jonathan Fred McLaughlin & Travis McLing & Josep A. Martín-Fernández, 2022. "Predicting Rare Earth Element Potential in Produced and Geothermal Waters of the United States via Emergent Self-Organizing Maps," Energies, MDPI, vol. 15(13), pages 1-21, June.
    16. Hazen, Benjamin T. & Overstreet, Robert E. & Jones-Farmer, L. Allison & Field, Hubert S., 2012. "The role of ambiguity tolerance in consumer perception of remanufactured products," International Journal of Production Economics, Elsevier, vol. 135(2), pages 781-790.
    17. Elena Catanese, 2016. "Data Editing for Complex Surveys in Presence Of Administrative Data: An Application to Fss 2013 Livestock Survey Data Based on The Joint Sequential Use Of Different R Packages," Romanian Statistical Review, Romanian Statistical Review, vol. 64(2), pages 101-117, June.

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