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

• Published in: Computational statistics & data analysis Vol. 54; no. 12; pp. 3095 - 3107
• Main Authors: Hron, K., Templ, M., Filzmoser, P.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-12-2010; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Accounting; Data processing; Iterative methods; Mathematical models; Proposals; Statistics
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2009.11.023

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.